Online Test

Question # 1

O (0,0)is called:

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Position vector

Free vector

Unite vector

Null vector

If Z₁= 1 + i, Z₂= 2+3i, then |Z₂- Z₁| = ?

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π

π/6

-π/2

2π

If 2x +y + λ =0 is normal to parabola y² =-8x,λ= _____

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12

8

24

-24

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-1

0

1

undefined

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5 / 12

3 / 8

5 / 8

7 / 4

The roots of px² - (p-q)x-q=0 are

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equal

Irrational

Rational

Imaginary

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0

1

Fundamental law is

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Roots of the equation 9x²- 12x + 4 = 0 are

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Real and equal

Real and distinct

Complex

None of these

If x²- 7x + a has remainder 1 when divided by x + 1, then a = ______

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-7

7

0

None of these

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a²b²c²

4a²b²c²

4abc

None

Given X.Y are any two sets such that number of elements in X = 18, number of elements in set Y = 24,and number of elements in set X ∪ Y =40,then number of elements in set x ∩ Y =

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3

1

2

4

The value of p for which both the roots of the equation 4x²- 20 ox + (25p²+ 15 p - 66) = 0 are less than 2, lies in

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∀a,b, c ε R ac = bc ⇒ a = b, c ≠ 0 is a

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Symmetric property

Cancellation property w.r.t multiplication

Reflexive property

Transitive property

The set of positive integers, 0 and negative integers is known as the set of

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Natural numbers

Rational numbers

All integers

Irrational numbers

The condition for polynomial equation ax² + bx + c = 0 to be quadratic is

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a > 0

a < 0

a ≠ 0

a ≠ 0,b ≠ 0

{1, 2, 3, 4,.....} us set if ______

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Natural numbers

Whole numbers

Integers

Rational numbers

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none of these

For all points (x,y) in second quadrant

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x > 0 , y < 0

x > 0 , y > 0

x < 0 , y < 0

x < 0 , y > 0

Range of cosecθis

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W - {y | -1 < y < 1}

R - {y | -1 < y < 1}

O - {y | -1 < y < 1}

R

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0

-1

1

The line 2x +√6y =2 is a tangent to the curve x² -2y² =4 The point of contact is

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(√6,1)

(2,3)

(7,-2√6)

(4,-√6)

The general term in the expansion of (a+x)ⁿ is

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(r-1)th term

(r+1)th term

rth term

none

Additive inverse of - a - b is

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a

-a + b

a - b

a + b

Roots of the equation 2x²- 7x + 3 = 0 are

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Rational

Irrational

Complex

None of these

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sin 2x + c

-sin 2x + c

Let S_ndenote the sum of the first n terms of an A.P. If S_2n= 3 S_n: S_nis equal to

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4

6

8

10

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Set of whole number

Rational Numbers

Complex numbers

Whole numbers

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The longer side of a parallelogram is 10 cm and the shorter is 6 cm. If the longer diagonal makes an angles 30° with the longer side, the length of the longer diagonal is

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If a set S contains n elements then P (S) has ........ number of elements

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2ⁿ

2ⁿ²

2.n

n²

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2x

3x²

1

0

The graph of a quadratic function is

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Circle

Ellipse

Parabola

Hexagon

1/3 is ______

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A prime number

An integer

A rational number

An irrational number

If x² + px + 1 is a factor of ax³+ bx +c, then

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a²+ c²= -ab

a²- c²= -ab

a²- c²= ab

None of these

The positive real number which is the measure of the length of a vector is called the

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Unit vector

Modulus

Inverse

None of these

For each real number, there is a number which is its

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Negative

Possitive

Opposite

Similar

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(-1, 2)

(-1, 1)

(1, 2)

{-1}

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In natural logarithm the base is

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1

0

10

e

There are ______ basic techniques for solving a quadratic equation

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Two

Three

Four

None of these

The set (Z,+) forms a group

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Forms a group w.r.t addition

Non commutative group w.r.t multiplication

Forms a group w.r.t multiplication

Doesn't form a group

If the circle x²+ y²+ 2gx +2fy + c = 0 passes through the origin then

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c = 0

c = -1

c = -2

c = 1

√11 is

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an irrational number

Rational number

odd number

Negative number

Only one of the root of ax² + bx + c =0, a ≠ 0 is zero if

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c = 0

c = 0,b ≠ 0

b = 0,c = 0

b = 0,c ≠ 0

If a > 0,b > 0, c > 0 then the roots of the equation ax² + bx + c =0 are

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Real and negative

Non-real with negative real parts

Real and positive

Nothing can be said

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none of these

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In a class of 100 students, 60 drink tea, 50 drink coffee and 30 drink both. A student from his class is selected at takes at last one of 2 drinks is

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2 / 5

3 / 5

4 / 5

None of these

In a school, there are 150 students. Out of these 80 students enrolled for mathematics class, 50 enrolled for English class, and 60 enrolled for Physics class. The students enrolled for English cannot any other class, but the students of mathematics and Physics can take two courses at a time. Find the number of students who have taken both physics and mathematics

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40

30

50

20

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2 and 9

3 and 2

2/3 and 9

3/2 and 6

The domain of the function x/x² -4 is given by

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R

R + 2

[R - (+2)

R-4

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If C={p/p < 18, p is a prime number}, then C =

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{2,3,4,.........17}

{2,4,6,8................16}

{1,3,5,7,9,11,13,15,17}

{3,6,9,12,15}

The matrix A = [a_ij]_1xn is a

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Vector

Rectangular matrix

Column vector

Square matrix

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perpendicular vectors

concurrent vectors

parallel vectors

none of these

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Which of the following does not represent absolute value of a vector

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magnitude

length

norm

number

If f(x) = x³- 2x²+ 4x -1 then f(0) is

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0

1

-1

none of these

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The point P (5,8) and the origin lie on the side of the line 3x+ 7y+ 15 =0

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Same side

P above and origin below

Opposite side

P below and origin above

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1 x 1

3 x 3

3 x 1

1 x 3

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R/[0,4]

R/(0,4)

(0,4)

[0,4]

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The set {1,-1,i,-i}

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Form a group w.r.t addition

Form a group w.r.t multiplication

Does not form a group w.r.t multiplication

Not closed under multiplication

∫x/Sin² x dx is equal to:

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x cot x + ln|sin⁡x |

-x cot x - ln|sin⁡x |

x cot x - ln|sin⁡x |

x. tan x- ln|sec⁡x |

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If f:A→B is an injective function and second elements of no two of its ordered pairs are equal, then f is called

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1-1 and onto

Bijective

1-1 and into

None of these

If a,b = 0 then

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a | b

a||b

a = b

None

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3/4

r

v

None of these

The equation x²+ y²= 0 represents

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A circle

A degenerate circle

An empty set

A st. line

The radius of the circle (x - 1)²+ (y + 3)²= 61 is

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8

4

64

None of these

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11

61

1

Trival solution of homogeneous linear equation is

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(1, 1, 1)

(1, 2, 3)

(1, 3, 5)

a, b and c

A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then CP²+ CQ²+ CR²+ CS²=

Choose an answer

r²

2 r²

3 r²

4 r²

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Range of secθis

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Z - {x | -1 < x < 1}

W - {x | -1 < x < 1}

R - {x | -1 < x < 1}

R

Both the roots of the equation (x - b) (x - c) + (x - c)(x - a) + (x - a)(x - b) = 0 are always

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Positive

Negative

Real

None of these

The angle between he vectors 3i + j - k and 2i - j + k is

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One-one but not onto

One-one and onto

Onto but not one-one

Neither one-one nor onto

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If | x | < 1, then the first two terms of (1 - x)^1/2are

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1

0

3

-1

Choose an answer

6x - 2 + c

x³- x²+ x + c

6x - x²+ c

6x³- x²+ c

An A.P., a G.P. and a H.P. have the same first and last terms and the same odd numbers of terms, the middle terms of the three series are in

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A.P.

G.P.

H.P.

None of these

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28 / 81

28 / 243

81 / 28

243 / 82

A vector of magnitude zero is called

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Position vector

Null vector

Free vector

None of these

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If all members of a sequence are real numbers then it is called a

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Series

Function

Real sequence

Range

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The eccentricity of the conic 9x²- 16y²= 144 is

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4/5

5/4

4/3

3/4

Range of y = exc x is

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-1 ≤ y ≤ 1

y ≥ 1 or y ≤ -1

y ≤ 1or y ≥ -1

-∞ < y < +∞

The roots of (x-a)(x-b) = ab x²are always

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Real

Depends upon a

Depends upon b

Depends upon a and b

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30°

45°

60°

90°

The distance of the point (2.3) from x-axis is

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2

3

5

If the intersection of two sets is non-empty, but either is a subset of other are called

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Disjoint sets

Over lapping

Equal sets

None of these

The set of even prime numbers is

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(2,4,6,8,10}

{2,4,6,8,10,12}

{1,3,5,7,9}

{2}

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If y=f(x) is a function then x is called

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dependent variable

independent variable

constant

none of these

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l²+ m²+ n²= 0

l²- m²+ n²= 1

l²+ m²+ n²= 1

l²+ m²- n²= 0

The length of perpendicular from (3,1) to 4x +3y +20 =0 is

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6

7

3

8

An event having more than one sample point is called

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Certain event

Compound event

Simple event

None

The number of subsets of a set having three elements is

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4

6

8

none of these

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The smallest positive root of the equation tan x - x = 0 lies on

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If c is a constant number and if f is the function defined by the equation f(x) =c for all values of x, then f is differentiable at every x and f is defined by the equation f(x)

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f

1

C

0

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pth term of an H.P. is qr and qth term is pr then the rth term of the H.P. is

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pqr

1

pq

pqr²

The solution set of the equation |3x + 2| = 5 is

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(x-1) is a factor of

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2x³-3x²+9

2x³-5x-8

48x^2-46x-9

x⁹-1

Range if y = cos x is

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-1 ≤ y ≤ 1

-1 < y < 1

-∞ < x < + ∞

None of these

If the roots of ax²+ bx + c = 0 (a > 0) be greater than unity, then

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a + b + c = 0

a + b + c > 0

a + b + c < 0

None of these

The tangents drawn from the point P to a circle are real and distinct if

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P is on the circle

P is inside the circle

P is outside the circle

none of these

If C is the mid point of AB and P is any point outside AB, then

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ax² +2hxy +by² +2gx +2fy +c =0 may represent a circle if

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h² -ab <0

h² -ab ≠ 0

h² -ab =0

h² -ab >0

The distance of the point (a, b) from x-axis is

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a

b

a + b

Which element is the additive inverse of (a,b) in Complex numbers

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(a,0)

(0,b)

(a,b)

(-a,-b)

Choose an answer

(-6,4)

(-3,2)

(6,-4)

(3, -2)

The distance of the point (-2, -3) from the origin is

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2

-5

-3

A point where two of its boundary lines intersect is called

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Corner point

Feasible point

Vertex

Feasible solution

Number of conics is

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1

3

2

4

x = _________ is in the solution of 2x + 3 < 0

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0

2

-1

-2

√x = ______ if is a prime number

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Rational no

Natural no

Irrational no

Complex no

Choose an answer

-1

0

1

None of these

The domain of an infinite sequence is a

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Set of natural numbers

R

Subset of N

None of the above

Intersection of two parabolas

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parabola

Two points

Four points

Hyperobla

Equation of normal to the circle x² + y² =25 at (5cosθ,5sinθ)

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xcosθ+ysinθ =5

xcosθ -ysinθ =0

xsinθ -ycosθ =0

None of these

A right angle is the angle of measure

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90'

60°

60"

90°

Choose an answer

none of these

Choose an answer

The exact degree value of the function sin-1( -√3/2) is

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70^ο

50^ο

90^ο

60^ο

For all points (x,y) in fourth quadrant

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x > 0 , y < 0

x > 0 , y > 0

x < 0 , y < 0

x < 0 , y > 0

The set {{a,b}} is

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Infinite set

Singleton set

Two points set

None

If the domain of sequence is finite set then the sequence is called

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geometric sequence

infinite sequence

finite sequence

arithmetic sequence

A rule that assigns to each elements x in X a unique element y in Y is called a ____________

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domain

range

function

none of these

The lotus of intersection of perpendicular tangents to the parabola y² = 4ax is:

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Axis of the parabola

Focal chord of the parabos

The tangent at vertex of the parabola

a directrix of the parabola

If (2,0) is the vertex and y-axis is directrix of parabola then focus is

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(2,0)

(-2,0)

(4,0)

(-4,0)

Choose an answer

The line joining the center of a circle to the midpoint of the chord is

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Perpendicular to the tnagent

Perpendicular to the normal

Perpendicular to the chord

Choose an answer

A^t

-A

A

A^-1

The equation of the line perpendicular to x- axis and passing through (-5,3) is

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y -3 =0

x+ 3 =0

y- 3 =∞

x +5 =0

Which of the following is the subset of all sets

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Φ

{1,2,3}

{Φ}

{0}

The greatest term in the expansion of (3+2x)⁹, when x=1 is

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4th

4th and 5th

5th

6th

Water seeps out of a conical filter at eh constant rate of 5 c.c/sec. the height of the cone of water in the filter is 15 cm. the height of the filter is 20 cm and radius of the base is 10 cm. the rate at which the height of the water decreases is

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The statement that a group can have more than one identity elements is

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True

False

Fallacious

Some times true

A Series which does not coverage to a Unique sum is called

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Harmonic Series

Oscillatroy Series

Arithmetic Series

None of these

Choose an answer

1

2

-1

0

The set {{a,b}} is

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Infinite set

Singleton set

Two points set

None

The quadratic equation 8 sec²θ- 6 secθ+1 = 0 has

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Infinitely many roots

Exactly two roots

Exactly four roots

No roots

In polar form of complex number r =

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Equation of the chord of contact to the tangents drawn from (-3,4) to the circle x² + y² = 21

Choose an answer

-3x + 4y =21

4x - 3x = 0

-3x + 4y = 25

None of these

Choose an answer

1

-i

i

0

Cos-1 (-x) =

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-x

1/x

tan^-1x

π-cos^-1 x

Choose an answer

1

2

3

The different of tan x is

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sec² x

ln |sec x|

sec² xdx

-cos ec² x

If n is add the expansion (a + x)ⁿhas middle terms

Choose an answer

2

3

4

5

The coefficient of xⁿ in the expansion of (1-2x)^-1 is

Choose an answer

(-1)ⁿ2ⁿ

2ⁿ

(-1)(n+1)x^r

(n+1)2ⁿ

For f(x) = x² = x, what is the value of f(a) +f (-a) in terms of a?

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3a²

2a²

2a

-7a

If x - 2 is a factor of ax²- 12x + a, then a = ______

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-5

5

0

1

Choose an answer

both a & c

Period of cos x is _____

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A triangle which is not right angle is called ______ triangle

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acute

Obtuse

Right

Oblique

Choose an answer

Power set of X i.e P(X)..........under the binary operation of union U

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Forms a group

Does not form a group

Has no identity element

Infinite set although X is infinite

If f(x) = tan x then f(0) is

Choose an answer

0

1

1/2

Choose an answer

The solution of the equation cos²θ+ sinθ+ 1 = 0 lies in the interval

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The equation of the parabola with directirx x = 2 and the axis y = 0 is

Choose an answer

y²= 8x

y²= -8x

y²= 4x

y²= -4x

(A∪B)∪C= --------------------------

Choose an answer

A∩B(B∪C)

A∪(B∪C)

A∪(B∩C)

None of these

Choose an answer

0

1

The perimeter of a sector of a central angle of measure 1 radian out off an are of length 35cm is

Choose an answer

35 cm

70 cm

140 cm

105 cm

Identity w.r.t intersection in a power set of any set is

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∅

Set itself

Singleton set

{0}

There are ______ types of rational fraction

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Three

Four

Five

Two

The coordinates of the point that divides the join of A(-6,3) and B(5, -2) in the ratio 2:3 externally are

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2x - 3x + c

x²- 3x + c

If (2, 3) and (2, 5) are end points of a diameter of a circle, then the centre of the circle is

Choose an answer

(2, 4)

(4, 8)

(0, 2)

(0, -2)

What is the value of cos (cos-1 2) ?

Choose an answer

√2

1/2

undefine

0

Choose an answer

0

1

-1

undefined

Name the property used in 4.1 + (-4.1) = 0

Choose an answer

Additive inverse

Multiplication inverse

Additive identity

Multiplication identity

Choose an answer

R

2R

r

2r

Choose an answer

2

0

Multiplicative inverse of "1" is

Choose an answer

0

±1

1

{0,1}

Choose an answer

3/4 is ______

Choose an answer

An odd number

An even number

A natural number

A rational number

√2 is a number

Choose an answer

Rational

Irrational

Even

Odd

The logic in which every statement is regarded as true or false and no other possibility is called

Choose an answer

Aristotelian login

Inductive logic

Non-Aristotelian logic

None of these

Period of cot x is ______

Choose an answer

1

0

If f (x) = |x|, then (0,0) is the

Choose an answer

Critical point

Inflection point

Stationary point

None of these

The axis of the parabola y²= 4ax is

Choose an answer

X = 0

Y = 0

X = y

X = -y

Choose an answer

x³- x²+ x + c

6x - 2 + c

x³- 2x + c

Choose an answer

Evert element of A is in B

Every element of B is in A

Every element of A is in B'

Every element of A is in A

3j . k x i

Choose an answer

0

1

3

9

Find the next two terms of 7, 9, 12, 16,...

Choose an answer

18, 20

19, 22

20, 25

21, 27

Te order of the differential equation of all conics whose axes coincide with the axes of co-ordinates is

Choose an answer

2

3

4

1

The straight lines represented by the equation ax²+ 2hxy +by² =0 intersects at

Choose an answer

(1,1)

(0,1)

(1,0)

(0,0)

The sets {1, 2, 4} and {4, 6, 8, 10} are

Choose an answer

Equal sets

Equivalent sets

Disjoint sets

Over lapping sets

The proposition S(k+1) is true when ______ is true ∀K∈N

Choose an answer

S(n)

S(k)

S(1)

S(k-1)

tan (-135°) = ______θ

Choose an answer

0

1

2

3

Choose an answer

The set of complex numbers forms

Choose an answer

Commutative group w.r.t addition

Commutative group w.r.t multiplication

Commutative group w.r.t division

Non commutative group w.r.t addition

If circumference of circle is divided into 360 congruent parts the angle subtended by one part at the centre of circle is

Choose an answer

1 degree

1 second

1 minute

1 radian

Choose an answer

-1

0

1

None of these

Choose an answer

45°

30°

75°

60°

Choose an answer

The equation x² + y² +2g +2fy + c =0 represents a circle whose centre is :

Choose an answer

(g,f)

(-g,-f)

(2g ,2f)

(-2f ,-2g)

The factorial of a positive integers is a (an)

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Rational number

Positive integer

Real number

None

A triangle hs six

Choose an answer

side

elements

angle

tangents

Choose an answer

Sin^-1 x=

Choose an answer

sin(π/2-x

Sin-1 (π/2-x)

π/2-cos^-1x

π/2 + cos^-1x

A circle drawn inside a triangle and touching its sides is called ______;

Choose an answer

Circumcirle

Incircle

Escribed circle

unit circle

Choose an answer

12

13

14

15

Choose an answer

0

1

2

4

Multiplicative inverse of 0 is

Choose an answer

0

1

+-1

Does not exist

Given X,Y are any two sets such that number of elements in set X = 28, number of elements in set Y = 28, and number of elements in set X∪Y = 54, then number of elements in set X ∩ Y =

Choose an answer

4

3

2

1

Choose an answer

A finite set

An infinite set

An empty set

None of these

Choose an answer

In (x +iy) y is called as

Choose an answer

Imaginary part

Complex number

Real part

None of above

How many types of an equation

Choose an answer

1

3

2

None

A point (x,y) which satisfy a linear inequality in two variables form its

Choose an answer

Solution

Domain

Range

None

A relation in which the equality is true only for some values of the known is called ______

Choose an answer

An identity

An equation

A polynomial

None of these

For any two sets A and, A ⊆ B if

Choose an answer

x ∈ A ⇒ x ∈ B

x ∉ A ⇒ x ∉ B

x ∈ A ⇒ x ∉ B

None of these

Choose an answer

If 3x⁴+ 4x³+ x - 5 is divided by x + 1, then the reminder is

Choose an answer

0

7

-7

5

The sum of the even coefficients in the expansion (1 + x)ⁿis

Choose an answer

n²

2^n-2

2^n-1

2ⁿ

The sample space for tossing a coin twice is

Choose an answer

{H, T}

{HH, HT, TH, TT}

{H, T, HH}

{HH, HT, TT}

Choose an answer

A^-

A^t

-A

A

Choose an answer

a tan(ax + b) + c

- a tan(ax + b) + c

Choose an answer

202.04 is an example of

Choose an answer

Recurring decimals

Non-recurring decimals

Terminating decimals

None of these

Rank of matrix [1 3 5 0] is

Choose an answer

1

3

2

4

Choose an answer

Rule of quotient of fraction

Golden rule of fraction

Rule for product of fraction

Principle for equality of fraction

A relation in which the equality is true for all values of the unknown is called ______

Choose an answer

An identity

An equation

A polynomial

None of these

Choose an answer

Additive inverse of -a -b is

Choose an answer

a

-a + b

a - b

a + b

Choose an answer

0

1

If b₁, b₂, b₃, ... are in G.P. with first term unity and common ratio r, then the minimum value of b₁- b₃+ b₅is equal to

Choose an answer

3/4

1/4

1

None of these

Choose an answer

none of these

A coin is tossed. If head comes up, a die is thrown but if tail comes up, the coin is tossed again. The probability of obtaining a head and an even number is

Choose an answer

1/8

2/8

3/8

None of these

The set {-1,1} is

Choose an answer

Group under the multiplication

Group under addition

Does not form a group

Contains no identity element

The product of the four fourth roots of unity is

Choose an answer

0

1

-1

None of these

A number A is called the arithmetic mean between a and b if a, A, b is ______

Choose an answer

Arithmetic sequence

Geometric sequence

Harmonic sequence

Arithmetic sequence

If S is a sample space and event set E = S then P(E) is

Choose an answer

>0

1

<1

0

If k²x² +2hxy- 4y² =0 represents two perpendicular lines then

Choose an answer

k = 2

k = ±2

k = -2

k ≠0

If the angle between two vectors with magnitude 2 and 15 is 30°then their scalar product is

Choose an answer

15

30

Choose an answer

0

20

90

80

20. 19. 18. 17= _______

Choose an answer

The transport of a square matrix is a

Choose an answer

Row matrix

Column matrix

Square matrix

Null matrix

If in a set of real no a is multiplicative identity then

Choose an answer

a,a = a²

a,a = 1

a,a = 0

None of these

Choose an answer

f(x) = log x + 3 is a

Choose an answer

trigonometric function

algebraic function

exponential function

logarithmic function

Choose an answer

n! > 2ⁿ-1 is true when

Choose an answer

n≤ 3

n≤ 6

n≥ 4

n≤ 6

For two events A and B if P(A) = P (A/B) = 1/4 and P(B/A) = 1/2, then

Choose an answer

A is sub-event of B

A and B are mutually exclusive

A and B are independent and P(A/B) = 3/4

None of these

If A ⊆ B then A ∪ B is

Choose an answer

A

B

A'

A ∩ B

Choose an answer

3/4

-3/4

4/3

-4/3

The total cost of 2 apples and 3 oranges is $1.70, which of the following is true

Choose an answer

The cost of one apple

The cost of one orange

Both have equal cost per item

Cost of each single item can not be determined

Equation of parabola with focus F(-3,1) directrix x=3 is

Choose an answer

(y -1)² =-12x

(y-1)² =4x

(x+3)² =4a(y-1)

y² =-12(x-1)

Choose an answer

Diagonal matrix

Scalar matrix

Triangular matrix

Identity matrix

Choose an answer

6, -12, -18

-6, 4, 9

-6, -4, -9

-6, 12, 18

Which of the following is an identity matrix?

Choose an answer

none of these

The point of concurrency of the medians of a triangle is called

Choose an answer

incentre

circumcentre

e-centre

centroid

Which of the following is skew symmetric matrix

Choose an answer

If A is an event then which of the following is true

Choose an answer

P(A)<0

0≥P(A)≤1

P(A)>0

None

If z₁ =√-36 ,z₂ =√-25,z3 =√-16 then

Choose an answer

15

15i

-15i

-15

If a, b, c are in A.P., then 3^a, 3^b, 3^care in

Choose an answer

A.P.

G.P.

H.P.

None of these

Choose an answer

The set of complex numbers forms a group under the binary operation of

Choose an answer

Addition

Multiplication

Division

Subtraction

The cube roots of 8 are

Choose an answer

The third term of a G.P. is the square of first term. If the second term is 8, then the 6th term is

Choose an answer

120

124

128

132

The solution of differential equation:

Choose an answer

dy/dx+y/x = x²is :

4xy = x⁴+ c

4x = x⁴= c

4 y = x⁴+ c

4x=4x³ + c

There are 25 tickets bearing number from 1 to 25. One ticket is drawn at random. The probability that the number on it is a multiple of 5 or 6 is

Choose an answer

7 / 25

9 / 25

11 / 25

None of these

If ax²+ bx + x = 0 is satisfied by every value of x, then

Choose an answer

b = 0, c = 0

c = 0

b = 0

a = b = c = 0

The equation of motion of a stone thrown vertically up wards is s = ut - 4.9t²the maximum height attained by it =

Choose an answer

If (a, b) is the mid-point of a chord passing thro' the vertex of the parabola y²= 4x, then

Choose an answer

a = 2b

2a = b

a²= 2b

2a = b²

Let A,B and C be any sets such that A∪B = A ∪C and A ∩ B = A ∩ C then

Choose an answer

A = B

B = C

A ≠ C

A ≠ B

Choose an answer

If a I-I correspondence can be established b/w two sets A and B, then they are called

Choose an answer

Equal sets

Equivalent sets

Over lapping sets

None of these

Choose an answer

From an empty set

1

2

>2

The obtuse angle between lines = -2 and y = x +2 is

Choose an answer

120°

135°

150°

140°

Choose an answer

If the line 2x -y +k =0 is a diameter of the circle x2 +y2 +6x -6y +5 =0 then k is equal to

Choose an answer

12

9

6

3

The distance of the point (-2 , -3) from y-axis is

Choose an answer

2

-2

3

-3

Decimal part of irrational number is

Choose an answer

Terminating

Repeating only

Neither repeating nor terminating

Repeating and terminating

Choose an answer

The maximum value of the quadratic function f(x) = x2+6x +2, is

Choose an answer

11

6

-11

13

The condition for polynomial equation ax²+ bx + c = 0 to be quadratic is

Choose an answer

1/x

-x

2x

0.5 x

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 meters away from the tree the angle of elevation becomes 30°. The breadth of the river is

Choose an answer

40 m

30 m

20 m

60 m

Choose an answer

The distance of the point (a,b) from y-axis is

Choose an answer

a

b

a + b

The sum of n terms of a series is denoted by

Choose an answer

d

n

S_n

a_n

Choose an answer

System of linear equations is inconsistent if

Choose an answer

System has no solution

System has one solution

System has two solution

None of above

The function f{(x,y)|y = ax² +bx +c} is

Choose an answer

One-one function

Constant function

Onto function

Quadratic function

Product of any n consecutive positive integers is divisible by

Choose an answer

n

√n

n!

None

Choose an answer

Scalar matrix

Identity matrix

Null matrix

Symmetric matrix

An even function is symmetric about the line

Choose an answer

y = x

x = 0

y = -x

y = 0

Choose an answer

4(x³- 3x²)³+ c

3x²- 6x + c

If A is a non-singular matrix then adj A is

Choose an answer

Non-singular

Symmetric

Singular

Non defined

Choose an answer

15/23

7/15

7/8

15/7

The maximum value of sin x + cos x is

Choose an answer

In R the left cancellation property w.r.t addition is

Choose an answer

0

1

(-28,12) divides the join of A(-6,3) and B(5,-2) in ratio

Choose an answer

1:2

3:2

2:3

2:1

If the expansion of (1 + x)²⁰, then co-efficient of rth ad (r + 4)th term are equal, then r is

Choose an answer

7

8

9

10

The middle term in the expansion of (a +x)¹²is

Choose an answer

7th

8th

9th

6th

The vertex of the graph of the quadratic function f(x) = x2 =10, is

Choose an answer

(0-10)

(-10,0)

(10,0)

(0,10)

Write the first four terms of the sequence if a_n= (-1)ⁿn²

Choose an answer

-1, 4, -9, 16

1, -4, 9, 16

1, 4, 9, 16

None of these

The unit vector along x-axis is

Choose an answer

none of these

Empty set is

Choose an answer

Not the member of real numbers

Infinite set

Finite set

Not subset of every set

Choose an answer

2

7

8

12

The roots of the equation ax²+ bx + x = 0 are real and distinct if

Choose an answer

b²- 4ac <0

b²- 4ac = 0

b²- 4ac > 0

None of these

x = sin^-13, then the value of sin x is

Choose an answer

√(3/2)

3

Not possible

-1

if a_{9 =19,a9=31 are the 6th and 9th term of an A.P. and d=4 is the common difference, then 18th term of the sequence is}

Choose an answer

65

67

71

75

If the exponent in the binomial expansion is 6, then the middle term is

Choose an answer

2nd

3rd

4th

5th

sin (2π-θ)

Choose an answer

cosθ

sinθ

tanθ

-sinθ

The set {1, -1, i, -i}

Choose an answer

Form a group w.r.t addition

Form a group w.r.t multiplication

Does not form a group w.r.t multiplication

Not closed under multiplication

Choose an answer

-a -b -c

1

0

-1

The set of natural numbers is a subset of

Choose an answer

{1, 2, 3, .... 100}

The set of whole numbers

{2, 4, 6, 8, .....}

None of these

Area bounded between the curve xy=2 and the lines x=1 and x=2

Choose an answer

ln2 square units

ln√2 square units

ln4 square units

Square units

Choose an answer

[0, 0, 0]

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Sin 45° = ______

Choose an answer

The differential equation representing the family of curves y = A cos (x + B), where A, B are parameters, is

Choose an answer

The intercepts of the plane 2x - 3y + 4z = 12 on the co-ordinate axes are given by

Choose an answer

2, -3, 4

6, -4, -3

6, -4, 3

3, -2, 1.5

If E = { } , then P(E)

Choose an answer

∅

{ }

{(2),(4),(6)....}

(∅)

Choose an answer

ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

Choose an answer

2^x

2^xIn x

2^xIn 2

The middle term of the expansion (1 + 2x)⁶is ______

Choose an answer

1st term

4th term

2nd term

5th term

Choose an answer

Closure law of addition

Associative law of addition

Commutative law of multiplication

Associative law of multiplication

(A∩B^c)^c= -------------------------

Choose an answer

A^c∪B^c

A^c∪B

A^c∩B

None of these

The solution set of the equation tan^-1x - cot^-1x = cos^-1(2 - x) is

Choose an answer

[0, 1]

[-1, 1]

[1, 3]

None of these

The√ is used for the

Choose an answer

Positive square root

Negative square root

+ve and -ve square root

Whole number

Choose an answer

0

1

2

none of these

A circle passing through the vertices of any triangle is called ______

Choose an answer

In circle

Circum circle

Escribed circle

None of these

n different objects can be arranged taken all at a time in ______

Choose an answer

(n + 1)! ways

(n - 1)! ways

n! ways

n ways

Express the perimeter P of square as a function of its area A?

Choose an answer

P = 4√A

P =√A

P = 2A

P =π√A

Inequalities have ______ symbol

Choose an answer

2

3

4

1

If the roots of ax² + b =0 are real and distinct then

Choose an answer

ab > 0

a = 0

ab < 0

a > 0,b > 0

Cycle tyres are supplied in lots of 10 and there is a chance if 1 in 500 tyres to be defective. Using Poisson distribution, the approximate number of lots containing no defective tyre in a consignment of 10, 0000 lots is

Choose an answer

9028

9208

9802

9820

Choose an answer

Square matrix

Row matrix

Symmetric matrix

Null matrix

cos(a-β) = ______;

Choose an answer

sin a cos β + cos a sin β

sin a cos β - cos a sin β

cos a cos β + sin a sin β

cos a cos β - sin a sin β

The set { {a,b} } is

Choose an answer

Infinite set

Singleton set

Two points set

Empty set

The integral of 3x⁵dx is:

Choose an answer

15 x⁴

x⁶/2

1/6x⁵

x⁵/ln3

The radius of the circle x²+ y² - 6 x + 4 y +13 = 0 , is

Choose an answer

1

2

0

None of these

The number of points of intersection of two curves y = 2 sin x and y = 5x²+ 2x + 3 is

Choose an answer

0

1

2

None of these

The term involving x4 the expansion (3-2x)⁷is

Choose an answer

217 x⁴

15120x⁴

313x⁴

-25x⁴

Choose an answer

Root of the equation 3^x-1+ 3^1-x= is

Choose an answer

2

1

0

-1

A triangle has ____ elements

Choose an answer

3

4

5

6

The roots of the equation 4^x - 3.2^x+2 + 32 = 0 would include

Choose an answer

1 and 3

1 and 4

1 and 2

2 and 3

A sequence having no last term is called

Choose an answer

arithmetic sequence

Geometric sequence

Finite sequence

Infinite sequence

The locus of the centre of a circle which touches two given circles externally is:

Choose an answer

a hyperbola

an ellipse

a circle

a parabola

One second is denoted by

Choose an answer

1⁰

1'

1"

1 rad

The set {Z\{0}} is group w.r.t

Choose an answer

Addition

Multiplication

Division

Subtraction

If all members of a sequence are real numbers then it is called

Choose an answer

A.P

Real Sequence

G.P

None of these

The probability that a person A will be alive 15 years hence is 5/7 and the probability that another person B will be alive 15 years hence is 7/9. Find the probability that both will be alive 15 years hence

Choose an answer

4/63

5/9

45/49

None of these

Choose an answer

Domain of cosecθis

Choose an answer

Domain of cos x is ______

Choose an answer

The inclination of a line parallel to x-axis is

Choose an answer

If f(√x)=sin x , then f^′(x) =______;

Choose an answer

2xcosx²

cosx²

cos√x

None of these

The multiplicative inverse of x such that x = 0 is

Choose an answer

-x

does not exist

1/x

0

Domain of 2 cos x is ______

Choose an answer

[-2, 2]

R

Negative real numbers

None of these

If Sin A = sin B, cos A = cos B, then the value of A in terms of B is

Choose an answer

QUQ =

Choose an answer

N

R

W

Z

The standard parabolic form of the equation f(x) = x² +4 x +1 is

Choose an answer

x(x+4)+1

(x+2)²-3

(x+4)³ + 9

x(x-2)²+1

The expansion of (1 + 2x)^-2is valed if

Choose an answer

| x | < 1/2

| x | < 1

| x | < 2

| x | < 3

Choose an answer

2x cos x²

-2x Sin x²

2x Sin x²

-Sin x²

3x + 4 > 0 is

Choose an answer

equation

identity

inequality

none of these

If A is skew Hermitian Matrix then which of the following is not skew Hermitian matrix

Choose an answer

A²

A5

A³

A⁷

Find a if 1 is a root of the equation x²+ ax + 2 = 0

Choose an answer

3

-3

2

0

The set of real numbers is a subset of

Choose an answer

The set of natural numbers

The set of rational numbers

The set of integers

The set of complex numbers

Choose an answer

110

220

1320

None of these

Choose an answer

-1

0

1

undefined

Choose an answer

a = 2, b = 3

a = 3, b = 2

a = 2, b = 2

a = 3, b = 3

Choose an answer

0

-1

1

not defined

If A = [a_ij] is (m x n) matrix, then transpose of A is of the order

Choose an answer

m x m

m x n

n x n

n x m

Choose an answer

In R, the multiplicative inverse of a is

Choose an answer

0

1

-a

1/a

Choose an answer

1

0

5

2

Choose an answer

The number of significant numbers which can be formed by using any number of the digits 0, 1, 2, 3, 4 but using each not more than once in each number is

Choose an answer

260

356

410

96

The ortho center of triangle whose vertices are (0,0)(3,0)(0,4) is

Choose an answer

(0,0)

(1,1)

(2,2)

(3,3)

An infinite arithmetic series is always

Choose an answer

Convergent

Oscillatory

Divergent

None of these

The domain of the principal tan function is

Choose an answer

If a plane passes through the vertex of a cone then the intersection is

Choose an answer

an ellipse

a hyperbola

a point circle

a parabola

The multiplicative inverse of 1 is

Choose an answer

1

-1

0

Does not exist

Choose an answer

The magnitude of a vector can never be

Choose an answer

Zero

Negative

Positive

None of these

Choose an answer

none of these

The complement of set A relative to universal set U is the set

Choose an answer

{x / x ∈ A∧ x ∈ U}

{x / x ∉ A ∧ x ∈ U}

{x / x ∈ A and x ∉ U}

A-U

The interval in which f(x)=x³-6x²+9x is increasing

Choose an answer

1<x<3

x<1 and x>3

X ≥ 1 and x ≤ 3

-∞ < x < ∞

sec (-360°) = ______

Choose an answer

0

1

2

3

The graph of y < 2 is the

Choose an answer

Left half plane

upper half plane

Right half plane

Lower half plane

Choose an answer

An empty set

Universal set

A singleton set

None of these

Let A be a square matrix. Then, 1/2 (A-A') is

Choose an answer

Skew-symmetric

Symmetric

Null

None of the above

Let P(x₁, y₁) and Q(x₂, y₂) be two points in the co-ordinate plane. Let d = distance between P and Q

Choose an answer

quadratic function

constant function

trigonometric function

linear function

The square roots of negative numbers is called

Choose an answer

Real no

Complex no

Positive no

Negative no

The eccentricity of parabola is:

Choose an answer

1

0

Greater than 1

Less than 1

4^1+x+ 4^1-x= 10 is called

Choose an answer

Reciprocal equation

Exponential equation

Radical equation

None of these

Choose an answer

3 x 1

1 x 3

3 x 3

1 x 1

Which is an explicit function

Choose an answer

y = x²+ 2x - 1

x²+ xy + y²= 2

x²+ y²= xy + 2

All are

Choose an answer

How many signals can be given by 5 flags of different colours, using 3 flags at a time

Choose an answer

120

60

24

15

Choose an answer

The points of intersection of the line y = 2x -3 and the circle x²+ y² - 3x =2y -3 = 0 are:

Choose an answer

two

three

less thean two

not intersect

f(x) = 2^x+ 3 . 2^2x+ 5 is

Choose an answer

trigonometric function

algebraic function

exponential function

logarithmic function

Choose an answer

0

1

8

∞

The solution set of the inequality ax + by < c is

Choose an answer

straight line

half plane

parabola

none of these

IfΔABC is right, law of cosine reduce to

Choose an answer

Law of sine

Law of tangent

Phthogorous theorem

Hero's formula

If 4 ⁶P_r= ⁶P_r+1, then r is equal to

Choose an answer

4

3

2

1

What is the probability of being born on Wednesday?

Choose an answer

1/7

1/2

1/3

1/8

For any positive integer n

Choose an answer

ABⁿ = Bⁿ A ⇔ AB = BA

ABⁿ = Bⁿ A ⇔ A,B are square matrices and AB = BA

ABⁿ = BⁿA ⇔ A + B

ABⁿ = BⁿA ⇔ A and B are square matries

A bag contains 7 whit, 5 black and 4 rd balls. If two balls are drawn at random from the bag, the probability that they are not of the same color is

Choose an answer

73 / 120

83 / 120

67 / 120

43 / 120

Choose an answer

30°

60°

45°

None of these

The domain of the function y = sin x , is

Choose an answer

-π/2≤ x≤ π/2

π/ ≤ x≤ π

-2π ≤ x≤ 2π

-1 ≤ x≤ 1

Choose an answer

π / 4

π / 6

π / 3

0

Choose an answer

Principle of equality of fractions

Rule for product of fraction

Rule for quotient of fraction

Golden rule of fractions

A die is thrown 100 times. If getting an odd number is considered a success, the variance of the number of successes is

Choose an answer

50

25

10

100

Period of sin 3x is ______

Choose an answer

none of these

Choose an answer

Latus rectum = 4 x ______________

Choose an answer

focal distance of the vertex

Chord

Focus

1/2

Range of cotθis

Choose an answer

(+∞to -∞)

(-1 to +1)

(-5 to +5)

Set of even numbers only

A polynomial P(x)has a factor (x-a)if P(a) =

Choose an answer

a

x

1

0

Every relation, which can be represented by a linear equation in two variables, represents a

Choose an answer

Relation

Cartesian product

Function

Graph

If f(x) = (-x)²then f(-2) is

Choose an answer

0

2

-4

4

If b²- 4ac is positive then the roots of the equation are

Choose an answer

Real

Imaginary

Positive

Negative

The three consecutive numbers a,√ab,b are in

Choose an answer

G.P

H.P

G.M

None of these

The square of the distance between two points P(x₁, y₁) and Q(x₂, y₂) is

Choose an answer

f(x) = ax + b will be a constant function if

Choose an answer

a = 1 , b = 1

a = 1 , b = 0

A key ring is an example of

Choose an answer

Permutation

Circular permutation

Combination

None

In the expansion of (x+y)ⁿ the coefficient of 5th and 12th terms are equal then n=

Choose an answer

12

n=14

17

n=15

The set (Z, +) forms a group

Choose an answer

Forms a group w.r.t addition

Forms a group w.r.t multiplication

Non commutative group w.r.t multiplication

Doesn't form a group

√23 is

Choose an answer

A rational number

A irrational number

An even integer

A factor of 36

If A∩B=B, then n(A∩B) is equal to

Choose an answer

n(a)

n(a)+n(c)

n(c)

None of these

Choose an answer

4x + 1

4x

2x³

none of these

Choose an answer

Every natural number is

Choose an answer

A prime number

An irrational number

An integer

An even number

Choose an answer

x = 3

x = 1/5

x = 0

None of these

Domain of 1+cot²θ =csc²θ is

Choose an answer

[0,π]

R-{x/x=nπ,n∈ z}

(-∞,+∞)

[-1,1]

Choose an answer

None of these

Choose an answer

If u =[3,-4],then modulus of uis:

Choose an answer

5

5i

-5

√5

Three consecutive terms of a progression are 30, 24, 20. The next terms of the progression is

Choose an answer

A

0

Unit vector

None

Choose an answer

sin h x

cos h x

tan h x

cot h x

Choose an answer

none of these

If n is any positive integer ,t hen 2+4+6+......+2 n=

Choose an answer

2ⁿ-1

2ⁿ+1

n²+1

n(n+1)

Choose an answer

I quadrant

II quadrant

III quadrant

IV quadrant

If (1+x)ⁿ=C₀+ C₁x +C₂x²+ ......+C_nx¹then C₀C₂+ C₁C₃+ C₂C₄+ .....+C_n-2C_n=

Choose an answer

For different values of k equation 4x+5y =k represents

Choose an answer

Parallel lines

Lines parallel to x -axis

Perpendicular lines

Lines parallel to y -axis

Three integers are chosen at random from the first 20 integers. Then probability that their product is even, is

Choose an answer

2 / 19

3 / 29

17 / 19

4 / 19

Choose an answer

Even

Odd

Prime

None of these

The number of values of x in the interval [0, 5π] satisfying the equation 3 sin²x - 7 sinx + 2 = 0 is

Choose an answer

0

5

6

10

Vector i =

Choose an answer

[1,0]

[0,1,0]

[0,0,1]

None of these

If G is a G.M between a and b then a,G,b are in

Choose an answer

A.P

H.P

G.P

None of these

Choose an answer

In order of A is m x n and order of B is n x p then order of AB is

Choose an answer

m x m

n x n

m x p

p x m

Which of the following function form 1 to itself are bi-jective

Choose an answer

F(x) = x + 3

F(x) = x⁵

F(x) = 3x + 2

F(x) = x²+ x

Let A,B, and C be any sets such that A∪B = A∪C and A∩B = A∩C then

Choose an answer

A ≠ C

B = C

A = B

A ≠ B

The period of cos(7x-5) is

Choose an answer

π/7

7π/2

π/2

2π/7

f(x) = 2x²+ 3x + 5 is a

Choose an answer

trigonometric function

algebraic function

exponential function

logarithmic function

Two circles x² +y² +8x -9= 0 and x²+y²+6y +k =0 touch internally if the value of k is

Choose an answer

k = 9

k = ±9

k=-9

k=11

The set of points {(x,y)|y = f(x),∀x∈} is called

Choose an answer

Relation

Graph of f

Function

All are correct

A square matrix all of whose elements except the main diagonal are zeros is called a

Choose an answer

Null matrix

Singular matrix

Symmetric matrix

Diagonal matrix

w¹¹= ______

Choose an answer

0

1

w

w²

For any set X, X∪x is

Choose an answer

X

X'

Φ

Universal Set

Choose an answer

Identity matrix

Diagonal matrix

Null matrix

Hermitian matrix

A∪(A∪B)= --------------------

Choose an answer

B

A

A∪B

None of these

Choose an answer

A.P.

G.P.

H.P.

None of these

Choose an answer

In(x²- x + 1) + c

In(2x - 1) + c

How many numbers are there between 103 and 750 which are divisible by 6

Choose an answer

125

107

108

113

Group of none-singular matrices under multiplication is

Choose an answer

None-Abelian group

Semi group

Abelian group

None of these

The additive inverse of 2/3 is

Choose an answer

3/2

-2/3

-3/2

0

Choose an answer

If a,b,c are unit vectors then |a + b|² +|a - b|²

Choose an answer

4

8ab

9cos

4(a,b)

In one hour the minute hand of a clock turns through

Choose an answer

For all points (x,y) in third quadrant

Choose an answer

x > 0 , y < 0

x > 0 , y > 0

x < 0 , y < 0

x < 0 , y > 0

The st. lines whose direction cosines satisfy al + bm + cn = 0, fmn + gnl + hlm=0 are perpendicular if

Choose an answer

The harmonic mean between a and b is

Choose an answer

The set X is

Choose an answer

Proper Subset of X

Not A subset of X

Improper Subset of X

None of these

Choose an answer

Sin h^-1x = _________

Choose an answer

If x³+ 4x³- 2x +5 is divided by x - 1, then the reminder is

Choose an answer

8

6

4

None of these

Choose an answer

2, 3

3, 3

2, 6

2, 4

The exponent of x in 10^th term in the expansion of (a+x)ⁿ

Choose an answer

10

12

11

9

The set R is ______ w.r.t subtraction

Choose an answer

Not a group

A group

No conclusion drawn

Non commutative group

The symbol of irrational is

Choose an answer

W

N

Q

Q'

If there is one-one correspondence between A and B, then we write.

Choose an answer

A = B

A

⊆ B

A⊇ B

A - B

Choose an answer

A bag contains 3 white, 4 black and 2 red balls. If 2 balls are drawn at random, then the probability that both the ball are white is

Choose an answer

1/18

1/12

1/36

None of these

Choose an answer

If n is a negative integer n! is

Choose an answer

1

0

Unique

Not defined

If x,y are two positive distinct numbers then

Choose an answer

A>G>H

A<G<H

A=G=H

None of these

If a polynomial p(x) is divided by x-c, then the remainder is

Choose an answer

p(x)

x-c

c

P(c)

Choose an answer

πis ______

Choose an answer

A complex number

A rational number

A natural number

An irrational number

Second derivative of y = x⁹+ 10x²+ 2x - 1 at x = 0 is

Choose an answer

10

20

12

1

The horizontal distance between the two towers is 60 m. the angular elevation of the top of the taller tower as seen from the top of the shorter one is 30°. If the height of the taller tower is 150 m, the height of the shorter one is

Choose an answer

116 m

200 m

216 m

None of these

Choose an answer

1/3

1

3

None of these

Choose an answer

One minute is denoted by

Choose an answer

1⁰

1'

1"

None of these

Choose an answer

The surface generated by lines, consists of two parts, called:

Choose an answer

vertex

apex

nappes

axis

Choose an answer

A parabola

An ellipse

A hyperbola

A circle

The sum of all 2 digit number is

Choose an answer

4750

3776

4895

4905

∀x,y,z ∈ R and z 0,then

Choose an answer

x > y ⇒ xz > yz

x<y ⇒ xz < yz

x < y ⇒ xz > yz

None of these

Choose an answer

A circle passing through the vertices of any triangle is called

Choose an answer

Circumcirle

Incircle

Escribed circle

Unit circle

Choose an answer

n!/(n-1)=

Choose an answer

n

n!

(n-1)!

0!

Choose an answer

A natural number

A rational number

An irrational number

A whole number

If n is any positive integer then 4ⁿ>3ⁿ+ 4 is true for all

Choose an answer

b = c

a = c

b = 0

Choose an answer

The angle AOP which the ray from an observer's eye at O to an object at P at a lower level makes with horizontal ray OA through O is called the

Choose an answer

Angle of depression

Angle of elevation

Acute angle

Obtuse angle

Period of cos 2x is ______

Choose an answer

If A = {x / x ∈ R ∧ x² - 16 = 0} then A =

Choose an answer

- x

Infinite set

Φ

{-4,4}

Choose an answer

1

-1

Choose an answer

A

B

A'B'

B'A

The real number system contains.

Choose an answer

Positive Numbers

Negative numbers

Zero

(option a and c)

The set which has no proper subset is

Choose an answer

{0}

{}

{∅}

None of these

Which of the following ordered pair is a solution of the inequality x+2y<6?

Choose an answer

(2,3)

(2,2)

(6,0)

(1,1)

Area of inscribed circle is

Choose an answer

π R²

π η²

π r²₂

π r²

If for the matrix A,A⁵ = 1,then A^-1=

Choose an answer

A²

A³

A

None of above

Choose an answer

The graph of y> 0 is the upper - half of:

Choose an answer

y-axis

x-axis

1st and 4th quandrant

2nd and 3rd quadrant

The square matrix A is skew Hermitian when (A)'=

Choose an answer

A

A'

-A

A

A matrix with a singly column is called

Choose an answer

Column matrix

Row matrix

Identity matrix

Null matrix

For≥ -2 , 1+3+5+......+(2n+5)

Choose an answer

(n+2)²

(n-2)²

2n+1

(n+3)²

The points A(3,1),B(-2,-3),C(2,2) are vertices of an (an)

Choose an answer

Right triangle

Equilateral triangle

Isosceles triangle

Scalene triangle

Choose an answer

sin h x

cos h x

tan h x

cot h x

Choose an answer

1

5

7

9

A and B be two square matrices and if their inverse exist the (AB)^-1 =

Choose an answer

A^-1 B^-1

AB^-1

A^-1B

B^-1A^-1

Choose an answer

¹⁰C₆

¹⁰C₅

¹⁰C₄

None

x = ________ is in the solution of 2x - 5 > 0

Choose an answer

0

2

-2

3

If a (p + q)²+ bpq +c = 0 and a (p + r)²+ 2 bpr + c = 0, then qr equals

Choose an answer

p²+ c/a

p²+ a/c

p²+ c/a

p²- c/a

Sec^-1x =

Choose an answer

Cos^-11/x

cosec^-11/x

Cos^-1(-x)

Tan^-1x

Choose an answer

0

1

If Cosθ=0, thenθ= ______

Choose an answer

nπ/2

(2n + 1)π/2

(2n - 1)π/2

(4n + 1)π/2

The general value ofθsatisfying the equation 2 sin²θ- 3 sinθ-2 = 0 is

Choose an answer

The matrix A is Hermitian when (A)' =

Choose an answer

A

-A

A

A'

The centre of the circle x²+y² -2fx-2gy+x=0 is

Choose an answer

(-g,-f)

(g,f)

(f,g)

(-f,-g)

The inclination of a line parallel to y-axis is

Choose an answer

5x³+ 3x - is a ______

Choose an answer

Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 1

Polynomial of degree 0

Six boys and 3 girls are to be seated at random, in a row, for a photograph. The probability that no two girls will sit together is

Choose an answer

1/12

1/6

5/12

7/12

The domain of f(x) = log x is

Choose an answer

[0,∞]

(0,∞)

[0,∞[

[∞,∞]

Choose an answer

a f(x) + c

f(x) + a

Choose an answer

none of these

Choose an answer

a = -1/2, b = -1

a = 1, b = 2

a = 2, b = 3

None of above

Choose an answer

0

1

-1

2

Circumcentre of the triangle, whose vertices are (0, 0), (6, 0) and (0, 4) is

Choose an answer

(2, 0)

(3, 0)

(0, 3)

(3, 2)

Choose an answer

The general term of the A.P. is

Choose an answer

a₁+ (n - 1) d

n + (a₁- 1) d

d + (n - 1) a₁

None of these

The number of divisors of 1029, 1547 and 122 are in

Choose an answer

A.P.

G.P.

H.P.

None of these

In quadratic equation y=ax³+bx+c, if b and c are both zero then the graph is

Choose an answer

Symmetric w.r.t.y-axis

Symmetric w.r.t.x-axis

Straight Line

Circle

In ΔABC if y = 90° then the Pythagoras theorem is

Choose an answer

b² + c² =a²

a² + b² = c²

a² +c² = b²

None of these

If #n = (n-5)² + 5, then find #3 x #4.

Choose an answer

54

12

4

9

(1 + 2x)⁴= ______

Choose an answer

1 + 4x + 6x²+ 4x³+ x⁴

1 - 4x + 6x²- 4x³+ x⁴

1 - 8x + 24x²- 32x³+ 16x⁴

1 + 8x+ 24x²+ 32x³+ 16x⁴

Archimedes approximate the function by horizontal function and the area under f by the sum of small

Choose an answer

Parallelograms

Squares

Retangles

Polygons

The 6th term of the sequence 7,9,12,16......is

Choose an answer

27

32

20

19

In quadratic equation, if the replacement of y with -y leaves the equation unchanged, then the graph is

Choose an answer

Straight line

Circle

Hyperbola

Symmetric w.r.t.0

The square root of 2i - 20i is

Choose an answer

±(5 - 2i)

±(5+ 2i)

(5 - 2i)

None of these

If one root of the equation ix²- 2(i + 1) x +(2 - i) = 0 is 2 - i, then the other root is

Choose an answer

-i

2 + i

i

2 - i

Choose an answer

The mid point of the line segment joining the points (3,-1) and (-3,1) is

Choose an answer

(3,-1)

(0,0)

(2,2)

(4,4)

Projection of vector u along v is

Choose an answer

|v| cosθ

|u| cosθ

|v| sinθ

|u| sinθ

If a,β are the roots of ax²+bx+c=0,the equation whose roots are doubled is

Choose an answer

ay² +2by+c=0

ay²+2by+4c=0

ay²+2by+c=0

ay²+by+4c=0

Choose an answer

(2x4)

(2x7)

(2x3)

(7x2)

If A and B are two matrices such that AB = B and BA = A then A² + B² =

Choose an answer

2 AB

2 BA

A + B

AB

The sum of all positive integral multiple of 5 less than 100 is

Choose an answer

950

760

1230

875

Choose an answer

Polynomial of degree 0

Polynomial of degree 1

Polynomial of degree 2

Polynomial of degree n

Which one is a pair of allied angles

Choose an answer

(180° -θ)

(180° -θ,180° +θ)

(180° +θ)

None of these

Any point, where f is neither increasing nor decreasing and f(x) = 0 at that point, is called a

Choose an answer

Minimum

Maximum

Stationary point

Constant point

The vertex of the equation y² = 4ax is:

Choose an answer

(2, -2)

(1,1)

(0 , 0)

(2 , 2)

If Z = (1,2), then Z^-1= ?

Choose an answer

(0.2, 0.4)

(-0.2, 0.4)

(0.2, -0.4)

(-0.2, -0.4)

E-radius corresponding to < B is

Choose an answer

The last term of (1+2x)^-2

Choose an answer

(-1)^-2 (2x)^-2

(-1)^-4 (-2x)^-2

(-1)^-3 (2x)^-3

Does not exist

Choose an answer

sin h x

cos h x

sec h x

cosec h x

Range of cot x is ______

Choose an answer

[-1, 1]

R

Negative real numbers

R - {x | - 1 < x < 1}

The span of a standard parabola depends upon

Choose an answer

x

a

y

y²

Name the property used in 4 x (5 x 8) = ( 4 x 5) x 8

Choose an answer

Associative property of addition

Associative property of multiplication

Additive identity

Multiplicative identity

The number of ways of arranging the letter AAAAA BBB CCC D EE F in a row when no two C's are together is

Choose an answer

ⁿC₂= exists when n is ______

Choose an answer

3

6

0

None of these

The range of function f(x)=-x²+2x-1 is

Choose an answer

R

(-∞,0]

(-∞,1]

[0,∞)

Three numbers are chosen random without replacement from {1, 2, 3, ...., 10}. the probability that minimum of the chosen numbering is 3 or their maximum is 7

Choose an answer

7 / 40

5 / 40

11 / 40

None of these

If the angle between two vectors u and v is 0 orπ, then the vectors u and v are:

Choose an answer

Orthogonal

Collinear

Perpendicular

None of these

The point lying on the terminal rat of -270° is

Choose an answer

(1,0)

(0,-1)

(0,1)

(-1,0)

If -1 < x < 0, which of the following statements must be true?

Choose an answer

x < x²< x³

x < x³< x²

x²< x³< x

x²< x < x³

The distance between two points P(x₁, y₁) and Q (x₂, y₂) is

Choose an answer

If the 4th term in the expansion of (px + x^-1)^mis 2.5 for all x∈ R, then

Choose an answer

2 b

2 a

2 ab

a + b

Choose an answer

If the sum of two unit vectors is a unit vector the the magnitude of their difference is

Choose an answer

√2

√3

1

None of these

Conic sections or simply conics are the curves obtained by cutting a right circular cone by

Choose an answer

a line

two lines

a plane

two planes

A machine operates if all of its three components function. The probability that the first component fails during the year is 0.14, the second component fails is 0.10 and the third component fails is 0.05. the probability that the machine will fail during the year is

Choose an answer

0.2647

0.2692

0.3647

None of these

Choose an answer

cos2a=______;

Choose an answer

cos² a-sin² a

2cos² a-1

1-2 sin² a

All of these

The distance between the points A(-8,3) and B(2,-1) is

Choose an answer

116

none of these

A line segment whose end points lie on a circle is called

Choose an answer

the secant of the circle

the arc of the circle

the chord of the circle

the circumference of the circle

The exact value of cos-1 (0) is

Choose an answer

π/2

-π/2

3π

π-π/6

Choose an answer

I quadrant

II quadrant

III quadrant

IV quadrant

When rational fraction is separated into partial fractions, the result is

Choose an answer

an identity

A fraction

A partial sum

Improper fraction

The transport of a null matrix is

Choose an answer

Row matrix

Column matrix

Square matrix

Null matrix

Choose an answer

7

5

6

None of these

A function in which the variable appears as exponent is called:

Choose an answer

An identity function

A logarithmic function

an exponential function

A rational function

The multiplicative inverse of -1 in the set {1-,1} is

Choose an answer

1

-1

±1

0

Does not exist

x = -1 is in the solution of the inequality

Choose an answer

x + 5 < 0

2x + 3 < 0

x > 0

2x + 3 > 0

Choose an answer

The maximum value of the quadratic function f(x) = -2x2+20x,is

Choose an answer

4

3

5

7

The point ________ is in the solution of the inequality 2x - 3y > 5

Choose an answer

(1, -1)

(2,2)

(0,0)

(3,0)

The line l is horizontal if

Choose an answer

m is undefined

m=0

m=1

m=0-1

There are n seats round a table numbered 1, 2, 3 .... n. The number of ways in which m person can take seats is

Choose an answer

ⁿP_m

ⁿC_mx (m - 1) !

^n-1P_m

None of these

1/2,1/3,1/4,1/5.........is

Choose an answer

a geometric sec

an arithmetric series

finite sequence

an infinite sequece

Choose an answer

1

-1

5

2

Choose an answer

Lies between 4 and 7

Lies between 5 and 9

Has no value between 4 and 7

Has no value between 5 and 9

{0} is a

Choose an answer

Empty set

Singleton set

Zero set

Null Set

If one root of 5x² + 13x + k = 0 be the reciprocal of the other root the value of k is

Choose an answer

0

2

1

5

The maximum value of 12 sinθ-9 sin²θis x

Choose an answer

3

4

5

None of these

Choose an answer

parallel vectors

perpendicular vectors

concurrent vectors

collinear vectors

60° = ______

Choose an answer

Period of 3 sin x is ______

Choose an answer

A circle drawn inside a triangle and touching its sides is called

Choose an answer

In-circle

Circum circle

Escribed circle

None of these

Choose an answer

The axis of the parabola x² = 4ay is:

Choose an answer

y = 0

x = 0

x = -a

y = a

Choose an answer

f(x) = x²

f(x²) = x

f(x) = x

none of these

graph of sine function is bounded between lines

Choose an answer

y ± 1 = 0

x ± 1 = 0

x ± y - 0

None of these

If a,b,c are in arithmetic progression, then 1/a,1/b.1/c are in

Choose an answer

A.M

G.M

H.M

G.P

Choose an answer

The sum of the odd coefficients in the expansion of (a + x)⁴is

Choose an answer

14

12

8

4

Choose an answer

(a - c)²= b²- c²

(a - c)²= b²+ c²

(a + c)²= b²- c²

(a + c)²= b²+ c²

Choose an answer

K/6

2K

3K

6K

sin 540° =

Choose an answer

0

1

2

3

Choose an answer

The magnitude of vector a=i-3j+5k is:

Choose an answer

3

√35

√17

√35

Choose an answer

2 x 2

2 x 3

3 x 2

3 x 3

The symbol ______ shall be used both for equation and identity

Choose an answer

Sum of n terms of a geometric series if | r | < 1 is

Choose an answer

-sinθ

cosθ

sinθ

-cosθ

Choose an answer

0

3

9

-3

Choose an answer

A variable

A constant

0

None of these

Choose an answer

I quadrant

II quadrant

III quadrant

IV quadrant

A chimney is such that on walking towards it 50 m in a horizontal line through its base the angular elevation of its top changes from 30° to 45°. The height of the chimney is

Choose an answer

A function f(x) is said to be the periodic function if for all x in the domain of f, there exists a smallest positive number p such the f(x + p) = ______

Choose an answer

f(p)

f(x)

f(o)

None of these

(ABC)' =

Choose an answer

CBA'

CBA

C' B' A'

None of these

In a quadratic equation with leading co-efficient 1, a student reads the co-obtain the roots as - 15 and -4. The correct roots are

Choose an answer

6, 10

-6, -10

8, 8

-8, -8

(51)⁴is equal to

Choose an answer

7065201

8065201

6765201

6565201

Let a₁, a₂, a₃, a₄and a₅be such that a₁, a₂, and a₃are in A.P., a₂, a₃and a₄are in G.P and a₃, a₄and a₅are in H.P. Then, a₁, a₃and a₅are in

Choose an answer

G.P.

A.P.

H.P.

None of these

Choose an answer

0.9

0.74

0.2016

None of these

2cos² a/2 =______;

Choose an answer

1+sina

1-sina

1+cosa

1-cosa

The angle of depression of the point at a distance 70 meters from the foot of the tower from the top of the tower is 45^𝜊.The height of the tower is

Choose an answer

37m

97m

101m

70m

There are 16 point in a plane, in which 6 are collinear. how many lines can be drawn by joining these points?

Choose an answer

10

66

71

106

4/√49 is a

Choose an answer

Irrational Number

Prime Number

Rational number

Whole number

Choose an answer

x³⁹

40x³⁹

40x⁴¹

none of these

The liner equation ax + by = c is called _________ of the inequality ax +by > c.

Choose an answer

Associatedequation

Non-associated equation

disjoint equation

Feasible equation

Choose an answer

8

9

10

11

Choose an answer

I quadrant

II quadrant

III quadrant

IV quadrant

Choose an answer

A

B

A'

None of these

The latus rectum of the ellipse 5x²+ 9y²= 45 is

Choose an answer

10 / 3

5 / 3

3 / 5

3 / 10

Choose an answer

If aand bare two vectors then a+b =

Choose an answer

b + a

b - a

ab

a^ b

Two circle x² + y²+2x - 8 = 0 and x² + y² -6 + 6x -46 =0:

Choose an answer

touch internally

do not intersect

touch externally

None of these

202.04 is an example of

Choose an answer

Recurring decimals

Non-recurring decimals

Terminating decimals

None of above

When we expand (a + 2b)⁵then

Choose an answer

a⁵+ 10a⁴b + 40a³b²+ 80a²b³+ 80ab⁴+ 32b⁵

a⁵+ a⁴b + a³b²+ a²b³+ ab⁴+ b⁵

5a⁵+ 4a⁴b + 3a³b²+ 2a²b³+ 1 ab⁴+ b⁵

None

tan h x = _________

Choose an answer

If A and B are two sets then any subset R of B x A is called

Choose an answer

relation on A

relation on B

relation from A to B

relation from B to A

If x+y+z+......+2ⁿ = 2ⁿ⁺¹-1 ∀n∈W,then cube root of xyz is equal to

Choose an answer

1

4

2

8

Choose an answer

The law of sines

The law of consines

The law of tangents

None of these

Multiplicative inverse of 0 is

Choose an answer

0

1

±1

Does not exist

Choose an answer

1 + tan²x + c

tan x + c

-tan x + c

cot x + c

Unit vector in the positive direction of x-axis is

Choose an answer

The set {-1,1} is closed under the binary operation of

Choose an answer

Addition

Multiplication

Subtraction

Division

cos(a + β)-cos(a-β) = _______;

Choose an answer

2cosa cosβ

2sina cosβ

-25 in a cosβ

-2sin a sinβ

The proposition S(n) for any n∈ N is only true if k ∈ N and

Choose an answer

S(k +1) is true

S(1) is true and S(k+1) is true whenever S (k) is true

S(k+1) is true whenever S (k) is true

S(k) is true

In one hour, the hour hand of a clock turns through

Choose an answer

For all points (x,y) in first quadrant

Choose an answer

x > 0 , y < 0

x > 0 , y > 0

x < 0 , y < 0

x < 0 , y > 0

The differential equations of all conis whose axes coincide with the co-ordinate axis is

Choose an answer

The study conics, pappus used the method of:

Choose an answer

analytic geometry Euclidean

solid geometry

Greek mathmaticians

None of these

In a country 55% of the male population has houses in cities while 30% have houses both in cities and in villages find the percentage of the population that has houses only in villages

Choose an answer

45

30

25

50

The number z so that the triangle with vertices A(1,-1,0),B(-2,2,1)and C(0,2,z) is a right triangle with right angle at vertex C

Choose an answer

1,2

-1,-2

2,-1

-2,1

If (0, 0) and (-1, 0) are end points of a diameter, then the equation of the circle is

Choose an answer

Zero is

Choose an answer

An irrational number

A rational number

A negative integer

A positive number

Choose an answer

If f(x) = x²then f(0) is

Choose an answer

0

1

2

none of these

The sample space for tossing a coin once is

Choose an answer

{T, T}

{H, H}

{H, T}

None of these

Associative law of multiplication

Choose an answer

ab = ba

a(bc) = (ab) c

a(b+c) = ab + ac

(a + b)c = ac + bc

The point of concurrency of the angle bisectors of a triangle is called

Choose an answer

incentre

circumcentre

e-centre

centroid

Choose an answer

a

2a

3a

4a

The central angle of an arc of a circle whose length is equal to the radius of the circle is called one

Choose an answer

Degree

Second

Minute

Radian

If distance between (a,2) and (0,0) is 2 then a = _______

Choose an answer

0

2

4

Probability of an impossible event is

Choose an answer

0

-1

1

∞

Choose an answer

c = 0

c = -1

c = -2

c = 1

Choose an answer

15

15 i

-15 i

-15

Tangent is ...............function

Choose an answer

Inverse

one-one

in-to

Periodic

Period of sec x is ______

Choose an answer

An indicated sum of terms of a sequence is represented by

Choose an answer

S_n

a_n

S(n)

{S_n}

There is no integer n for which 3ⁿis

Choose an answer

Odd

even

Natural

Prime

The square matrix A is skew-symmetric when A^t= 0

Choose an answer

-B

-C

-A

-D

A fixed point which lies on the axis of the cone is called its:

Choose an answer

axis

apex

plane

diameter

If a tangent line touches the function y = f (x) in more than one point then y = f (x) is

Choose an answer

Periodic

Surjective

Bijective

Injective

If distance of (a,b) from origin is 5 then

Choose an answer

a²+ b²=5

a = 5

b = 5

The domain the function : f(x) = x² is given by

Choose an answer

R

Set of all non-negative Real numbers

R^-1

None of these

If A is a symmetric matrix them A^t= ______

Choose an answer

-A

A²

2A

A

Choose an answer

What is the conjugate of -6 -i

Choose an answer

-6 +i

6 + i

-6 -i

6 -i

If f(x) = cos x then f(0) is

Choose an answer

0

1

1/2

Choose an answer

w¹⁵= ______

Choose an answer

0

1

w

w²

The general equation of a circle is

Choose an answer

The lines l1and l2intersect. The shortest distance between them is

Choose an answer

Positive

Negative

Zero

Infinity

If 4 - x >5, then

Choose an answer

x > 1

x > -1

x < 1

x < -1

The two lines y = 2x and x =2y are

Choose an answer

Parallel

Perpendicular

Equally inclined with axes

Congruent

Choose an answer

The coefficient of x¹⁸ in (ax⁴-bx)⁹ after expansion is

Choose an answer

84a³ b⁶

22a³b⁶

27a⁴b⁵

28a³b⁶

Choose an answer

2x + 2y

4 - x²

-x/y

x/y

The term independent of x is the expansion (x³+1/x)¹²

Choose an answer

295

495

395

722

The measure of the angle subtended at the centre of the circle by an arc, whose length is equal to the radius of the circle is

Choose an answer

1⁰

1'

1"

1 rad

Choose an answer

Conclusion

Implication

Antecedent

Hypothesis

Choose an answer

4

6

8

10

The angle between the vectors u = [-3 , 5] and v = [6 , -2] is:

Choose an answer

π/2

-3π/2

π

None of these

How many 6-Digit number can be formed without repairing any digit from the digits 0,1,2,3,4,5

Choose an answer

720

600

120

6-5!

If A and B are two matrices such that AB = B and BA =A, then A²+ B²=

Choose an answer

2 AB

2 BA

A + B

AB

The negation of given number is a

Choose an answer

Binary operation

Unary operation

Relation

None of these

The range of y = cot x = ______

Choose an answer

-∞> y > +∞

-∞> x > +∞

-∞ <y < +∞

None of above

Choose an answer

2²- n - 1

1 - 2^-n

n + 2^-n-1

2ⁿ- 1

If a and b are real numbers then a+b is also real number this law is called

Choose an answer

associative law of addition

closure law of addition

Distributive law of addition

Commutative law of addition

The point of concurrency of the medians of the ΔABC is called its

Choose an answer

Orthocenter

Centriod

Circumcentre

Incentre

30° = ______

Choose an answer

1

2

3

Choose an answer

For all positive integral value of n,3ⁿ< n! , when

Choose an answer

n> 6

n< 6

n<11

n>11

The graph of a quadratic function is

Choose an answer

Circle

Ellipse

Parabola

Hexagon

f(x)g(x)- ∫g(x) f′(x) dx is equal to

Choose an answer

∫f(x)g′(x)dx

∫f′(x)g (x)dx

∫f′(x)g(x)′dx

∫f(x)g(x)dx

Choose an answer

[0, 0, 0]

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

ᵨ is a

Choose an answer

variable

Positive constant

Positive variable

Directrix

Choose an answer

The zero vector is

Choose an answer

[0, 0, 0]

[1, 1, 1]

[0, 1, 0]

[0, 0, 1]

A square matrix A = [aij] is lower triangular matrix when

Choose an answer

aij = 0 for all i<j

bij = 0

cij = 0

dij = 0

Choose an answer

A = x, B = 1

A = 0, B = 2

A = -1, B = 1

A = x-1, B = x + 1

Matrices A = [aij] 2 x 3 and B =[bij] 3 x 2 are suitable for

Choose an answer

BA

A²

AB

B²

The formula a_n = a +(n-1)d for an A.P is called

Choose an answer

nth term of an A.P

Sum of first n terms

A,M between a and b

None of the above

Choose an answer

Symmetric

Skew-symmetric

Hermitian

Skew hermitian

Choose an answer

If the points (a,2b):(c,a+b):(2c-a,h) lie on the same line then

Choose an answer

h=2a

h=a+b

h=ab

h=ac

Choose an answer

3K

K²

K³

K

What is the period of 6 sin x=?

Choose an answer

π

-π

π/2

2π

Choose an answer

Z is the set of integers (Z.*) is a group with a * b = a +b +1, a,b ∈ G.then inverse of a is

Choose an answer

-a

a +1

-2-a

None of these

Choose an answer

The ellipse and hyperbola are called

Choose an answer

Concentric conics

Central conics

Both a b

None

The value of n, when ⁿP₂= 20 is

Choose an answer

3

4

6

5

The function ø(x) is an anti derivative of function f (x),x∈D_f if

Choose an answer

ø′(x) =∫f(x)dx

ø(x) =∫f(x)dx

ø′(x) =f(x)

ø(x) =∫′(x)dx

Choose an answer

n(A)

n(B)

0

1

If m and n be two scalars, then (m+n) g =

Choose an answer

0

m+n

m▁a+n▁a

ma - m▁a

The set { {a, b} } is

Choose an answer

Infinite set

Singleton set

Two points set

Empty set

Choose an answer

If y = e^ax sin bx and y₂ - 2ay₁ + (a²+b²) y=0 the for what values of a and b we have y₂+10y₁+34y =0

Choose an answer

a = -10,b=34

a=-5,b=3

a=5,b=3

a=10,b=34

The distance s of a particle in time t is given by s = t³- 6t²- 4t - 8. Its acceleration vanishes at t =

Choose an answer

1

2

3

4

Choose an answer

none of these

A function in which the second elements of the order pairs are distinct is called

Choose an answer

Onto function

One-one function

Identity function

Inverse function

Choose an answer

If P is a whole number greater than 1, which has only P and I are factors. Then P is called

Choose an answer

Wholw number

Prime number

Even number

Odd number

sin(3π/2 -θ)=_______;

Choose an answer

sinθ

cosθ

-sinθ

-cosθ

Which of the following is a quadrantal angle

Choose an answer

30°

45°

60°

90°

O is ______

Choose an answer

A positive integer

A negative integer

A natural number

An integer

The set {-1, 1} is

Choose an answer

Group under the multiplication

Group under addition

Does not form a group

Contains no identity element

Choose an answer

1

0

3

-3

The fifteenth term of (3-a)¹⁵ is

Choose an answer

-17a¹²

-945a¹³

-941a¹³

-515a¹²

Choose an answer

5

20

9

4

The equation of line passing through intersection of line x = 0 and y = 0 and the point (2,2) is

Choose an answer

y = x

y = x - 1

y = x + 1

Choose an answer

The set {-1, 1} is closed under the binary operation of

Choose an answer

Addition

Multiplication

Subtraction

Division

The coefficient of the second term of (a+b)⁴ is

Choose an answer

1

9

3

5

If tan^-13 + tan^-1x = tan^-18, then x=

Choose an answer

5

1/5

5/14

14/5

Choose an answer

The probability that the sum of dots appearing in two successive thrown of two dice, in every time 7 is

Choose an answer

1/5

1/36

1/7

1/63

If the sum of co-efficient in the expansion of (a+b)ⁿis 4096, then the greatest co-efficient in the expansion is

Choose an answer

1594

792

924

2924

If|a| =|b|=|a + b|=1, then|a+ b| = 5, then|a-b| =

Choose an answer

4

6

5

3

If n is any positive integer then n! > n²for

Choose an answer

Onto function is also called

Choose an answer

Binjective function

Injective function

Surjechive function

None of these

The corner point of the boundary lines, x- 2x

x+2y=10 is:

Choose an answer

(8,1)

(1,8)

(6,10)

(3,5)

Choose an answer

0

1

Choose an answer

cotθ= sin 2θifθ=

Choose an answer

Period of Contangent function is

Choose an answer

π

-π

0

-2π

The measure of the acute angle between the lines represented by x² -xy -6y² =0 is

Choose an answer

120°

30°

130°

45°

If the elevation of the sun is 30°, then the length of the shadow cast by a tower of 150 ft height is

Choose an answer

184

none of these

Choose an answer

The set {1, 2, 3, 4, ....} is called

Choose an answer

Set of Natural numbers

Set of whole numbers

Set of rational number

Set of irrational numbers

Choose an answer

y/x

x/y

y/z

None

The points A(+1,-1),B(3,0),C(3,7),D(1,8) are vertices of

Choose an answer

Square

Parallelogram

Rectangle

Trapezium

If (1+x-2x³)⁶= 1+a₁x + a₂x²+ a₃x³+ ..... the the value of a₂+ a₄+ a₆+ .....+a₁₂will be

Choose an answer

32

31

64

1024

Choose an answer

x =0, y =4

x = -1, y = 2

x = 2, y = 3

x = 3, y = 4

Choose an answer

additive property

multiplicative property

additive inverse

additive identity

Choose an answer

The many subset can be formed from the set {a,b,c,d}

Choose an answer

8

4

12

16

If x,y are two -ve distinct numbers then

Choose an answer

A>G>H

A<G<H

A=G=H

None of these

A tower subtends an angle of 30° at a point distant d from the foot of the tower and on the same level as the foot of the tower. At a second point, h vertically above the firs, the angle of depression of the foot of the tower, is 60°. The height of the tower is

Choose an answer

h/3

h/3d

3h

3h / d

The standard form of the quadratic function f(x) = -x² +4x+2, is

Choose an answer

(x-2)²+6

-(x-2)² + 6

(x-3)²+5

(x+4)²-7

A - B = ______

Choose an answer

G = {e, a, b, c} is an Abelian group with e as identity element. The order of the other elements are

Choose an answer

2, 2, 2

3, 3, 3

2, 2, 4

2, 3, 4

Choose an answer

0

-1

1

2

∀a,b, c ε R,a +c = b + c = > a = b

Choose an answer

Reflexive property

Symmetric property

Cancellations property w.r.t. addition

Transitive property

Choose an answer

2

-3/2

1

0

Choose an answer

Area ofΔABC=

Choose an answer

ab sinα

1/2 ab sinα

1/2 ac sinγ

1/2 ac sinβ

Choose an answer

The null vector is regarded to be perpendicular to

Choose an answer

Every vector

In some cases

Both a b

None

i²=

Choose an answer

1

2

-1

0

sin (α +β)=

Choose an answer

sinαcosβ- cosαsinβ

sinαcosα- cosβsinβ

sinαcosα+ cosβsinβ

A fraction in which the degree of the numerator is greater than or equal to the degree of the denominator is called

Choose an answer

A proper fraction

An improper fraction

An equation

An identity

Choose an answer

Cos 2x = sin 4y

Cos 4y = cos 2x

Cos 3y = sin 4x

None of these

Choose an answer

1 / 2

1 / 3

1 / 4

None of these

Choose an answer

∫sin(ax+b) dx is equal to:

Choose an answer

1/2a cos (ax + b)

-1/a cos (ax +b)

1/a cos (ax +b)

1/a ln (ax + b)

A kite flying at a height of 67.2 m is attached to a fully stretched string inclined at an angle of 53^{𝜊 to thehorizontall, the length of the string is}

Choose an answer

62m

82m

73m

57m

If x - 1 is a factor of x⁴ - 5x² + 4 then other factor is

Choose an answer

(x + 2)²(x - 1)

(x + 2)(x - 1)²

(x+2)(x²- x- 2)

(x + 2)²(x - 1)²

Choose an answer

0

1

-1

none of these

If a polynomial P(x) is divided by x + a, then the remiander is

Choose an answer

P(a)

P(-a)

P(0)

None of these

Which shape of the following objects are approximately parabolic ares?

Choose an answer

Light reflectors

Force

Weight of the pendul

None of these

The centre of the conic x² +16x +4y² -16y +76 =0 is

Choose an answer

(0,10)

(-8,2)

(-8,-2)

(1,1)

The line through the intersection of the lines x+ 2y+ 3= 0 : 3x +4y +7 =0 and making equal intercepts on the axes is

Choose an answer

x+ y+ 1= 0

x+ y- 2= 0

x+ y+ 2= 0

2x +y +2 =0

Order (or sense) of an inequality is changed by multiplying or dividing its each side by a:

Choose an answer

Zero

one

negative constant

Non negative constant

The set {1,-1, i, -i} form a group under

Choose an answer

Addition

Multiplication

Subtraction

None

Choose an answer

A

B

U

None of these

Choose an answer

xy

y

0

x

Choose an answer

If the st. line 3x + 4y = K touches the circle x²+ y²- 10x = 0 then the value of K is

Choose an answer

-1 or 20

-10 or 40

-2 or 20

2 or 20

Which of the following is a scalar.

Choose an answer

force

frequency

weight

acceleration

Choose an answer

1.5

1.2

8

None of these

∛8.6 is approximately equal to

Choose an answer

2.488

2.48

2.0488

2.05

The number of x-intercepts of y= sin x in his period

Choose an answer

0

1

2

3

Choose an answer

none of these

The set of complex numbers forms a group under the binary operation of

Choose an answer

Addition

Multiplication

Division

Subtraction

Choose an answer

If the sum of even coefficients in the expansion of (1+x)ⁿ is 128 then

Choose an answer

n=7

n=9

n=8

None

Find the sum of the infinite geometric series 2 + 1 + 0.5 + ....

Choose an answer

3.5

3

4

None of these

πis the period of the function

Choose an answer

|sin x| + |sin x|

sin⁴x + cos x

sin (sin x) + sin (cos x)

None of these

Choose an answer

0

1

A square is inscribed in the circle x²+ y²- 2x + 4y + 3 =0. Its sides are parallel to the co-ordinate axes. Then one vertex of the square is

Choose an answer

If distance of (a,b) from x-axis is 2 then

Choose an answer

a = 2

b = 2

a = b

b = 4

The unit vector along z-axis is

Choose an answer

none of these

In quadratic equation f(x) = ax²,if a >0, then the graph of parabola

Choose an answer

Opens up

Opens down

close up

symmetric w.r.t.x.axis

Choose an answer

Another name of quadratic equation is

Choose an answer

Polynomial

2nd degree polynomial

Linear equation

simaltaneous equations

If the sum of co-efficient in the expansion of (a+b)ⁿis 4096, then the greatest co-efficient in the expansion is

Choose an answer

1594

792

924

2924

The centroid of a triangle divides each median in the ratio

Choose an answer

2 : 1

3 : 1

3 : 2

1 : 1

Which one represents a sequence

Choose an answer

a_n

S_n

a(n)

{a_n}

For non-trival solution |A| is

Choose an answer

A = 0

|A| = 0

A^t = 0

The set of integers is a subset of

Choose an answer

The set of natural numbers

The set of whole numbers

The set of prime numbers

The set of rational numbers

If z₁ = 2 + 6i and z₂ = 3 + 7i then which expression defines the product of z₁ and z₂

Choose an answer

36 +(-32)i

-36+32i

6+(-11)i

0, +(-12)i

The process of finding a function whose derivative is given is called a

Choose an answer

Differentiation

Integration

Differential

None

A function of the form p(x)/Q(x) is called:

Choose an answer

Rational function

Logarithmic function

Exponential function

Hyperbolic function

Choose an answer

The second degree equation of the form Ax² +By² +Gx +Fy +C =0 represent hyperbola if

Choose an answer

A = B ≠ 0

A ≠ B and both are of same sign

A ≠ B both are of opposite sign

Either A = 0 or B =0

The constant distance of all points of the circle from its centre is called the

Choose an answer

Radius of the circle

Secant of the circle

Chord of the circle

Diameter of the circle

6 is

Choose an answer

A prime integar

An irrational number

A rational number

An odd integer

Choose an answer

If S is a sample space and event set E = Φ then P(E) is

Choose an answer

>0

1

<1

0

The identity element with respect to subtraction is

Choose an answer

0

-1

0 and 1

None of thes

sin (α -β)=

Choose an answer

sinαcosβ- cosαsinβ

sinαcosβ+ cosαsinβ

sinαcosα- cosβsinβ

tan (π-θ) = ______

Choose an answer

- sinθ

- tanθ

- cosθ

- cotθ

If f(x) = x²-x then f(0) is

Choose an answer

0

1

2

3

The 7th term of the A.P 7,11,15,is

Choose an answer

24

31

26

23

Which of the following sets has closure property w.r.t. addition

Choose an answer

{ 0 }

{ 1 }

{ 0, -1}

{ 1, -1}

How many terms of the A.P 3,6,9,12,15...........must be taken to make the sum 108

Choose an answer

8

6

7

36

Choose an answer

An upper triangular matrix

A lower triangular matrix

A diagonal matrix

A null matrix

The quadratic equation 8 sec²θ - 6 secθ +1 =0 has

Choose an answer

Infinitely many roots

Exactly two roots

Exactly four roots

No roots

Choose an answer

Natural numbers

Whole numbers

Integers

Rational numbers

The area under the curve y = 1/x² between x = 1 and x =4 is:

Choose an answer

-25

0.75

-0.35

-10

The slope of the normal at the point (at², 2at) of the parabola y²= 4ax is

Choose an answer

1/t

t

-t

-1/t

If 4 sin²θ=1, then values ofθare

Choose an answer

The point on y²= 4ax nearest to the focus has its abciassae equal to

Choose an answer

-a

a

a/2

0

Choose an answer

The vector i = [1,0] is called unit vector along:

Choose an answer

x-axis

y - axis

z- axis

Botha a and y-axis

The middle term of [1/x-x]¹⁰is

Choose an answer

-152

-252

371

-421

The square root of every incomplete square is an

Choose an answer

Rational numbers

Even numbers

odd numbers

Irrational numbers

If A and B are skew-symmetric then (AB)^t is

Choose an answer

A^t B^t

AB

-AB

BA

f(x) = 3x⁴ -2x² + 7 is:

Choose an answer

an even function

an odd function

an even and implicit function

neither even nor a odd

Choose an answer

The key for opening a door is in a bunch of 10 keys. A man attempts to open the door by trying the keys at random discarding the wrong key. The probability that the door is opened in the 5th trial is

Choose an answer

1 / 10

2 / 10

3 / 10

4 / 10

Choose an answer

A rational number

A irrational number

An even integer

A factor of 36

∫f(x) is known as:

Choose an answer

Definite itegral

Indefinite integral

Fixed integral

Multiple integral

If one end of the diameter of the circle x² + y²- 5x = 3y -22 = 0 is (3,4) the other end is:

Choose an answer

(2,7)

(-2,-7)

(-2,7)

(2,-7)

Name the property used in a (a-c) = ab - ac

Choose an answer

commutative property of multiplication

distributive property of multiplication

associative property of multiplication

multiplicative inverse

Choose an answer

The equation of the sphere thro' the origin and making intercepts a, b, c on co-ordinate axes is

Choose an answer

x²+ y²+ z²+ ax + by + cz = 0

x²+ y²+ z²- 2ax - 2 by - 2 cz = 0

x²+ y²+ z²= a + b + c

x²+ y²+ z²- ax - by - cz =0

Choose an answer

a + b + c

0

1

none of these

Choose an answer

The sum of co-efficient in (1+x-3x²)⁴¹⁶³is

Choose an answer

0

1

-1

None

The sum of indicated terms of a sequence is called

Choose an answer

Arithmetic series

Series

Harmonic series

None of these

Choose an answer

1

-1

w⁷³= ______

Choose an answer

0

1

w

w²

Union of the sets of rational and irrational numbers is called 6th set of

Choose an answer

Natural numbers

Real numbers

Whole numbers

Prime numbers

Choose an answer

The law of consines

The law of sines

The law of tangents

None of these

An expression involving any of the symbols <,>,< or > is called

Choose an answer

equation

inequality

linear equation

identity

If 6th term of a series in A.P, is -2 and 8th term is -8, the first term of the serie is

Choose an answer

13

-13

18

-10

Choose an answer

9/4

4/9

1

None of these

Choose an answer

The fixed point from which all the points of a circle are equidistant is called the

Choose an answer

chord of the circle

centre of the circle

diameter of the circle

radius of the circle

tan270° =__________;

Choose an answer

0

1

-1

Undefined

Sine is a periodic function and its period is ______

Choose an answer

π

s

2π

4π

Roots of the equation x²- x = 2 are

Choose an answer

{2, -1}

{1, 0}

{2, 1}

{-2, 1}

x =r cosθ,y= sinθ are the parametric equations of

Choose an answer

Circle

Ellipse

Parabola

Hyoerbola

Choose an answer

a^xIn a + c

a^x+ c

x a^x+ c

Derivative of strictly increasing function is always

Choose an answer

Zero

Positive

Negative

Both (A) and (B)

Choose an answer

all are correct

Choose an answer

sec h x = ________

Choose an answer

With usual notations b² = a² + c² -2ac cos is called______;

Choose an answer

Law of sines

Law of consines

Law of tangents

None of these

The square root of 2i - 20i is

Choose an answer

+-(5 - 2i)

+-(5 + 2i)

(5 - 2i)

None of these

A diagonal matrix is always

Choose an answer

Identity

Triangular

Scalar

Non-singular

Choose an answer

0

1

2

3

cos 3a =_______;

Choose an answer

3sin a - 4sin³ a

4sin a - 3sin³ a

3cos³ a - 4cos a

4cos³ a - 3cos a

Choose an answer

none of these

The area of sector with central angle of 1 radian in a circular region whose radius is 2m is

Choose an answer

0.5m²

2m²

1m²

4m²

sin -1(sin2π/3) =

Choose an answer

π/2

-2π/3

-3π/2

π/3

Choose an answer

The set of the first elements of the ordered pairs forming a relation is called its

Choose an answer

Function on B

Range

Domain

A into B

Range of sec x is ______

Choose an answer

[-1, 1]

R

Negative real numbers

R = {x | -1 < x < 1}

Choose an answer

sec x tan x

cos²x

sin²x

sec²x

3x + 4 = 0 is

Choose an answer

not inequality

equation

identity

inequality

Sequence also called..............

Choose an answer

Series

Function

progressions

Elements

A chord passing through the centre of the circle is called

Choose an answer

the secant of the circle

the tangent of the circle

the arc of the circle

the diameter of the circle

Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

Choose an answer

14 / 29

20 / 39

1 / 2

n

Choose an answer

In one hour, the hour hand of a clock turns through

Choose an answer

16

None of these

Which of the following is a vector.

Choose an answer

distance

temperature

energy

acceleration

The decimal fraction in which we have finite number of digits in its decimal part is called.

Choose an answer

recurring decimal fraction

Non terminating faction

Non recurring fraction

terminating decimal fraction

Choose an answer

Q∪ Q' =

Choose an answer

Q

Q'

N

R

If the terminal rays of an angle falls on any axis then the angle is called

Choose an answer

Allied angle

Acute angle

Standard position

Quadrantal angle

Choose an answer

A matrix in which the number of rows is not equal to the number of columns is called a

Choose an answer

Diagonal matrix

Rectangular matrix

Square matrix

Scalar matrix

Choose an answer

(a + b)c = ac + bc

a + b = b + a

(a + b) + c = a + (b + c)

a(b +c) = ab + ac

Choose an answer

a cos(ax + b) + c

- a cos(ax + b) + c

Range of 3 sin x is ______

Choose an answer

[ -3, 3]

[-1, 1]

R

None of these

θ and 2kπ+θ are the ________ angles

Choose an answer

Quadrantal angles

Coterminal

Allied

None

If z₁= 2 + 6i and z₂= 3 + 7i, then which expression defines the product of z₁and z₂?

Choose an answer

36 + (-32)i

-36 + 32i

6 + (-11)1

0, +(-12)i

2x + 3y > 4 is a linear inequality in

Choose an answer

one variable

two variables

three variables

none of these

The position vector of a point (x, y) in xy plane is

Choose an answer

none of these

A sequence is a functions whose domain is a subset of the set of

Choose an answer

Natural numbers

Real numbers

Whole numbers

Rational numbers

The domain of a finite sequence is a

Choose an answer

Set of natural numbers

R

Subset of N

Proper subset of N

1⁰= ______

Choose an answer

The area of the circle centred at (1,2) and passing through (4,6) is

Choose an answer

30 πsq.units

5π sq.units

15π sq.units

25π sq.units

Choose an answer

cos x

sec x tan x

sec²x

-cosec²x

(2 + w) (2 + w²) = ______

Choose an answer

1

2

3

0

Choose an answer

There may be ______ feasible solution in the feasible region

Choose an answer

Infinite

Finite

Defined

None of above

Choose an answer

If l, m, n are the d.c.'s of a line, then

Choose an answer

l2+ m2+ n2= 0

l2+ m2+ n2= 1

l + m + n = 1

l = m = n = 1

The period of the function f(x) = sin⁴x + cos⁴x is

Choose an answer

π

π/2

2π

None of these

Which of the following integrals can be evaluated

Choose an answer

Maximum value of z =15x +20y subject to 3x+ 4y ≤ 12,x,y ≥ 0 is given by

Choose an answer

46

60

50

70

Choose an answer

0

1

1/2

(n + 2) (n + 1)n in factorial form is

Choose an answer

If three unequal numbers p, q, r are in H.P. and their squares are in A.P., then the ration p : q : r is

Choose an answer

√25 is a number

Choose an answer

Rational

Irrational

Natural

Odd

Choose an answer

2C

C³

1

0

Choose an answer

0 (zero) is

Choose an answer

An irrational number

A rational number

A negative integer

A positive number

Choose an answer

The point which divides the line segment joining the points (a, b) and (c, d) in the ratio 2 : 3 internally is

Choose an answer

none of these

The approximate percentage increase in the volume of a cube if the length of its each edge changes from 5 to 5.02 is

Choose an answer

1.2%

1.5%

0.16%

100.16%

Choose an answer

If x⁴- 10x²- 2x + 4 is divided by x + 3, then the reminder is

Choose an answer

1

0

4

None of these

The law of sines is

Choose an answer

2

4

6

8

The triangle that does not have a right angle is called.

Choose an answer

Isosceles triangle

right angle triangle

equivalent triangle

oblique triangle

For n€ N,2^n>2 > n is to only when

Choose an answer

n<2

n≤ 4

n≥ 4

Choose an answer

sin[cot^-1{cos(tan^-1x)}]=

Choose an answer

The Principal value of sin-1 (-1/1/2)

Choose an answer

π/2

-π/2

π

-π

If x + y + 1 = 0 touches the parabola y²=λx, thenλis equal to

Choose an answer

2

4

6

8

Every whole number is

Choose an answer

A real number

An irrational number

A prime number

A negative integer

If A and B are non singular matrices then (AB)^-1= ______

Choose an answer

A^-1

B^-1

A^-1B^-1

B^-1A^-1

Choose an answer

9

-9

0

1

Choose an answer

6

360

120

24

Choose an answer

In a triangle ABC, if angle A = 72° , angle B = 48° and c = 9 cm then Ĉ is

Choose an answer

69°

66°

60°

63°

The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant is

Choose an answer

A parabola

A circle

An ellipse

A st. line

Choose an answer

0

-2

1

4

Choose an answer

2

4

3

16

Choose an answer

Associative law of addition

Commutative law of addition

Additive identity

Closure law of addition

sin² π/6 + sin² π/3 + tan² π/4 =______;

Choose an answer

1

2

3

4

If w+w² is a root of (x+1)(x+2)(x+3)(x+4) = k, then

Choose an answer

k=0

k=1

k=w

k=w²

graph of trigonometric function y = sec x does not meet

Choose an answer

x - axis

y -axis

both axis

None of these

Multiplicative inverse of "1" is

Choose an answer

0

-1

1

{0, 1}

sin²αcos²α=

Choose an answer

-1

0

1

None of these

Choose an answer

The law of of sines

The law of tangents

The law of consines

None of these

No term of a harmonic sequence can be

Choose an answer

0

1

2

3

Choose an answer

The distance of the point (1.1) from the origin is

Choose an answer

0

2

Choose an answer

5x^{4 + c}

1/6 x⁶+ c

5x²+ c

1/5 x⁶+ c

Tan^-11/x = ______

Choose an answer

sin x

sec^-1X

cot^-1X

None of these

If the cutting plane is slightly tilted and cuts only one nappe of the cone, the intersection is

Choose an answer

an ellipse

a hyperbola

a circle

a parabola

The value of the expression 3 cos + 4 sinθlie between

Choose an answer

-7 and 7

-25 and 25

-1 and 1

-5 and 5

w⁴= ______

Choose an answer

0

1

w

w²

It is not possible to find the exact value of

Choose an answer

π

√9

∛27

√1

(√3+√5)+√7 = √3 +(√5 +√7) property used in above is

Choose an answer

Commutative property of addition

Closure property of addition

Additive inverse

Associative property w.r.t to adition

If p and q are two statements then their biconditional 'p if q' is denoted by

Choose an answer

a chord passing through the focus of a parabola is called a:

Choose an answer

Focal chord

Latus rectum

Tangent

Directrix

Which of the following is not a quadrantal angle

Choose an answer

90°

100°

180°

270°

Roots of the equation x²+ 5x - 1 = 0 are

Choose an answer

Rational

Irrational

Complex

None of these

Choose an answer

If 2 and 2 are x and y components of vector then its angle with x-axis is

Choose an answer

30°

45°

60°

90°

Choose an answer

a = 4, b = 1

a = 1, b = 4

a = 0, b = 4

a = 2, b = 4

The set of whole numbers is subset of

Choose an answer

The set on integers

The set of natural numbers

{1, 3, 5, 7, ....}

The set of prime numbers

cotθ= sin 2θifθ=

Choose an answer

The number of arbitrary constants in the general solution of a differential equation is equal to the different equation

Choose an answer

Order

Degree

Variables

All are correct

If there are m rows and n columns in a matrix then its order is

Choose an answer

m x n

m x m

n x n

n x m

0! = ______

Choose an answer

0

1

2

Not defined

Choose an answer

Closure law of addition

Closure law of multiplication

Commutative law of addition

Commutative law of multiplication

The value of sin^-1 5/13 is equal to

Choose an answer

Cos 5/13

Tan^-1 5/12

cos^-15/12

2 cos^-14/5

Choose an answer

(x + 3) (x + 4) = x²+ 7x + 12 is ______

Choose an answer

Quadratic equation

Linear equation

Cubic equation

Identity

sin (α+β) - sin (α -β) =

Choose an answer

4 cosαsinβ

2 cosαsinβ

4 cosαcosβ

4 sin αsinβ

Choose an answer

The projections of a line segment on x, y, z axes are 12, 4, 3. The length and the direction cosines of the line segment are

Choose an answer

f(x) = x3-x/x2+1 is :

Choose an answer

an even function

an odd function

an even and implicit function

neither even nor a odd

The 8th term of (1+2x) ^-1/2is

Choose an answer

-221/16 x⁷

-225/18 x⁷

-407/9 x³

-429/16 x⁷

Choose an answer

range of f

domain of f

both (a) and (b)

none of these

The range of the principle cos function is

Choose an answer

A onto B

both a & c

A into B

none of these

The direction cosines of y-axis are

Choose an answer

1, 0, 0

0, 1, 0

0, 0, 1

1, 1, 1

Choose an answer

1

7

4

None of these

Which of the following us a scalar

Choose an answer

displacement

velocity

acceleration

density

What is the value of cos-1(1/2)?

Choose an answer

2π/3

π/4

3π/2

π/6

Choose an answer

If a > 0, b > 0, c > 0, then the roots of the equation ax²+ bx + c = 0 are

Choose an answer

Real and negative

Non-real with negative real parts

Real and positive

Nothing can be said

Choose an answer

If z₁ = (a,b), z₂=(c,d), then z₁ z₂ = -------------------

Choose an answer

(ac,bd)

(ac+bd, ad-bc)

(ac-bd , ad+bc)

(ac-bd , ad-bc)

Choose an answer

Right angled

Obtuse angled

Isosceles

Equilateral

A matrix in which the number of rows is equal to the number of columns is called a

Choose an answer

Diagonal matrix

Rectangular matrix

Square matrix

Scalar matrix

The general equation of circle x³ + y³ + 2gx + 2fy + c = 0 , contains:

Choose an answer

Three independent variables

Two independent conntants

Three indepentent parameters

Three independent constants

A line segment whose end points lie on a circle is called

Choose an answer

The secant of the circle

The arc of the circle

The chord of the circle

The circumference of the circle

The foot of perpendicular from (α,β,γ) only y-axis is

Choose an answer

(α, 0, 0)

(0,β, 0)

(0, 0, γ)

(0, 0, 0)

Choose an answer

Power set of difference set N-W is

Choose an answer

Empty set

Infinite set

Singleton set

{0,∅}

The identity element with respect to subtraction is

Choose an answer

0

1

-1

Does not exist

p, q, r and s are integers. If the A.M. of the roots of x²- px + q²= 0 and G.M. of the roots of x²- rx + s²= 0 are equal, then

Choose an answer

q is an odd integer

r is an even integer

p is an even integer

s is an odd integer

Choose an answer

Cos (cos4π/3)=

Choose an answer

π/2

π/3

2π/3

-π/3

Choose an answer

quadrant I

quadrant II

quadrant III

quadrant IV

Range of cosec x is ______

Choose an answer

{-1, 1}

R

Negative real numbers

R - { x | - 1 < x < 1}

∀x∈(a,b),f(x) is increasing if

Choose an answer

f^′(x) >0

f^′(x) <0

f^′′(x) >0

f^′′(x) =0

Choose an answer

The distance of the points (3, 4, 5) from y-axis is

Choose an answer

y + 1 = Ae^x

y + 1 = Axe^x

xe^x= C

y + xe^x= C

The eccentricity of ellipse becomes zero, then it takes the form of:

Choose an answer

a parabols

a straight line

a circle

None of these

The coefficient of x¹⁰in the expansion (x³+3/x²)¹⁰is

Choose an answer

1700

17023

17027

17010

Choose an answer

A combination lock on a suitcase has 3 wheels each labeled with nine digits from 1 to 9. If an opening combination is a particular sequence of three digits with no repeats, the probability of a person guessing the right combination is

Choose an answer

1 / 500

1 / 504

1 / 252

1 / 250

An open sentence formed by using the sign of equality "=" is called

Choose an answer

Equation

In equation

True sentence

False sentence

Choose an answer

The range of the principal sine function is

Choose an answer

Range of 2 tan x is ______

Choose an answer

[-2, 2]

-1 < x < 1

R

None of these

Choose an answer

Additive property of inequality

Commutative property

Additive inverse

Additive identity

Choose an answer

2

6

We also the system of non-homogeneous linear equations by

Choose an answer

a and b

b and c

c and a

a, b and c

A non-terminating non_recurring decimal represents an

Choose an answer

Irrational no

Both a & c

Rational no

None of these

Choose an answer

0

1

2

None of these

a vertical pole is 8m high and the length of its shadow is 6 m. The angle of elevation of the sun of the moment is

Choose an answer

57^𝜊

-48^𝜊

27^𝜊

53^𝜊

Choose an answer

The conjugate of √5 i is

Choose an answer

√5

-√5 i

i

5i

45° = ______

Choose an answer

Which of the following sets in infinite

Choose an answer

The set of students of your class

The set of all schools in Pakistan

The set of natural numbers between 3 and 10

The set of rational numbers between 3 and 10

Digit in the unit place of the number 183! + 3¹⁸³

Choose an answer

7

6

3

0

The order axioms are satisfied by set of

Choose an answer

C

C and R

R

None of these

Choose an answer

Which one is not defined ∀n∈Z⁺

Choose an answer

-n!

n!

(-n)!

n!+0!=n!+1

Choose an answer

If n is any positive integer then 3 + 6 + 9 + ....+ 3n = ______

Choose an answer

A is proper subset of B

A is an improper subset of B

A is equivalent to B

B is subset of A

A die is rolled. What is the probability that the dots on the top are greater than 4?

Choose an answer

1/4

1/2

1/3

1/33

System of linear equation is inconsistent if

Choose an answer

System has no solution

System has one solution

System has two solution

None of above

Choose an answer

sec 5x + c

- sec 5x + c

the curve of the parabola y² = -4ax is symmetric with respect to

Choose an answer

x -axis

y - axis

Botha x and y- axis

None of thes

Which of the following has the same value as i¹¹³

Choose an answer

i

-1

-i

1

If the exponent in the binomial expansion is 6, then the middle term is

Choose an answer

2nd term

3rd term

4th term

5th term

The direction cosines of any normal to the xy-plane are

Choose an answer

<1, 0, 0>

<0, 1, 0>

<1, 1, 0>

<0, 0, 1>

The number of tangents to the circle x²+ y²+ -8x -6y +9 =0 which pass through the point (3,-2) is

Choose an answer

2

1

0

None of these

The trid of a G.P. is 4, The product of first five terms is

Choose an answer

4³

4⁵

4⁶

None of these

The equation ax²+ 2hxy + by²+2gx + 2fy + c =0 represents an ellipse if

Choose an answer

The first three terms in the expansion of (1 + x)^-1are

Choose an answer

1 + x + x²

1 - x - x²

-1 -x + x²

1 - x + x²

Tan 2θ=

Choose an answer

Two coins are tossed twice each. The probability that the head appears on the first toss and the same forces appear in the two tosses is

Choose an answer

1/4

1/2

1/3

1/7

The Domain of y = sin x is ______

Choose an answer

Set of real numbers

Rational

Irrational no.

None of above

The set of natural is a semi group w.r.t

Choose an answer

Addition

Division

Subtraction

None of these

If a particle moves according to the law s = t³- t², then its velocity at time t = 1.5 is

Choose an answer

9/2

15/4

5

None

The line Ax + By + C = 0 will touch the circle x²+ y²=λ when

Choose an answer

C²=λ(A²+ B²)

A²=λ(A²+ C²)

B²=λ(A²+ C²)

None of these

Choose an answer

For any set B,B∪B' is

Choose an answer

Is set B

Set B'

Universal set

If A and B are two sets then intersection of A and B is denoted by

Choose an answer

If five triangles are constructed having sides of the lengths indicated below, the triangle that will NOT be a right triangle is

Choose an answer

8, 15, 17

3, 4, 5

12, 15, 18

5, 12, 13

How many different 5-digit even numbers are possible form digit 1,2,4,6,8

Choose an answer

4 : 4!

4!

5!

4!+4!

If f(x) = ax², and a>0, then the lowest point on the parabola is called.

Choose an answer

Vertex of parabola

Co-ordinates of parabola

Roots of the equation

Coefficient of the equation

f (x) = | x | is a/an

Choose an answer

Injective function

Bijective function

Surjective function

Implicit function

Choose an answer

π

π / 2

π / 3

π / 4

The order of the matrix [1 2 3] is

Choose an answer

1 x 1

3 x 3

3 x 1

1 x 3

If Z = (1,2), then Z^-1 =?

Choose an answer

(0.2, 0.4)

(-0.2 ,0.4)

(0.2,-0.4)

(-0.2,-0.4)

If a cone is cut by a plane perpendicular to the axis of the cone, then the section is a

Choose an answer

Parabola

Circle

Hyperbola

Ellipse

Choose an answer

If a² = b² then

Choose an answer

a = b

a + b = 1

|a + b| =0

None

The geometrical representation of a linear function is

Choose an answer

Circle

Parabola

Straight lie

None of these

The unit vector along y-axis is

Choose an answer

none of these

n(n - 1) (n - 2) in factorial form is

Choose an answer

(1, 2) is in the solution of the inequality

Choose an answer

2x + y > 8

2x + y < 6

2x - y > 1

2x + 3y < 2

Choose an answer

The function f{(x, y) | y = ax²+ bx + c} is

Choose an answer

One-one function

Constant function

Onto function

Quadratic function

The n numbers A₁,A₂,A₃,.....A_nare called an arithmetic means between a and b if a.A₁,A₂,A₃.....A_n, b is ______

Choose an answer

An arithmetic series

An arithmetic sequence

A geometric sequence

A harmonic sequence

n(n - 1) (n - 2) .... (n - r + 1) = ______

Choose an answer

(x + 2)²= x²+ 4x + 4 is

Choose an answer

A linear equation

A cubic equation

A quadratic equation

None

(x + 2)²= x²+ 4x + 4 is

Choose an answer

A linear equation

A cubic equation

A quadratic equation

None

In-radius is denoted by

Choose an answer

r

η

r₂

R

Every irrational number is

Choose an answer

A real number

A prime number

A natural number

An integer

Choose an answer

p(x) = 2x⁴- 3x³+ 2x - 1 is polynomial of degree

Choose an answer

1

2

3

4

Choose an answer

2π+θwill have terminal side in Quad

Choose an answer

I

II

III

IV

Choose an answer

0

1

2

Choose an answer

Closure law of addition

Associative law of addition

Additive inverse

Additive identity

Which of the following is the definition of singleton

Choose an answer

The objects in a set

A set having no element

A set having no subset

None of these

The distance between the points (0 , 0) and (1, 2) is

Choose an answer

5

0

3

Choose an answer

0

1

-1

none of these

The distance of the plane 2x - 3y + 6z + 14 = 0 from the origin is

Choose an answer

14

2

-2

11

Choose an answer

If t is the parameter for one end of a focal chord of the parabola y²= 4ax, then its length is

Choose an answer

A = x, B = 1

A = 0, B = 2

A = -1, B = 1

A = x-1, B = x+1

Choose an answer

if a₁ =3, d=7 and a_n =59 , then the number of terms in A.P is

Choose an answer

7

9

11

13

If f (x) is defined and continuous then f (x) is always

Choose an answer

Rational function

Trigonometric function

Logarithmic function

All are correct

The sum of the squares of three distinct real numbers, which are in G.P., is S². if their sum isαS then

Choose an answer

The transpose of a row matrix is a

Choose an answer

Column matrix

Row matrix

Scalar matrix

Null matrix

Choose an answer

Improper rational fraction

Proper rational fraction

Polynomial

Equation

The series obtained by adding the terms of a geometric sequence is called

Choose an answer

Infinite series

Arithmetic series

Geometric series

Harmonic series

Choose an answer

Zero matrix

Diagonal matrix

Column matrix

Scalar matrix

(7, 9) + (3, -5) =

Choose an answer

(4, 4)

(10, 4)

(9, -5)

(7, 3)

Choose an answer

ab=-1

ab = 1

ab = 2

None

The vertices of the ellipse x²+ 4y²= 16 are

Choose an answer

The 10th common term between the series 3+7+11+....... and 1 + 6 +11 + ....... is

Choose an answer

191

193

211

None of these

What is the conjugate of -7 -2i?

Choose an answer

-7 + 2i

7 + 2i

7 -2i

None of these

The coordinates of the point that divides the join of A(-6,3) and B(5, -2) in the ratio 2:3 internally

Choose an answer

(a,0) x (c,0) =

Choose an answer

(0,ac)

(ac,0)

(0,0)

(a,c)

(7,9) +(3,-5) =

Choose an answer

(4,4)

(10,4)

(9,-5)

(7,3)

Choose an answer

x³

3x²

3x

3

The probability that a slip of number divisible by 4 is picked from the slips bearing numbers 1, 2, 3, ...10 is

Choose an answer

1/5

1/4

1/3

1/2

Sin^-1(-x)=

Choose an answer

Cos^-11/x

- Sin^-1X

Cot^-1X

None of these

G = {e, a, b, c} is an Abelian group with e as identity element The order of the other elements are

Choose an answer

2,2,2

3,3,3

2,2,4

2,3,4

(1+w)(1+w²)(1+w⁴)(1+w⁸)....50 factors

Choose an answer

0

-1

1

2

I is not

Choose an answer

Real number

Natural number

Prime Number

Whole Number

Geometrically, the modulus of a complex number represents its distance from the

Choose an answer

Point (1, 0)

Point (0, 1)

Point (1, 1)

Point (0, 0)

The sum of infinite numbers of terms of an arithmetic series is

Choose an answer

Finite

Infinite

May or may not finite

None of these

Choose an answer

Commutative property of addition

Closure property of addition

Additive inverse

Associative property w.r.t. to addition

A quadratic equation in x is an equation that can be witten in the form

Choose an answer

ax²+ b = 0

ax³ +b²+c=0

ax² +bx+c=0

ax³ +bx³+cx=0

Choose an answer

1

2

3

None of these

Choose an answer

0

-1

1/2

1

Choose an answer

The towers each 120 meters high are 800 meters apart. The measure of the angle of elevation from the base of one tower to the top of the other is

Choose an answer

12^𝜊

9^𝜊

7^𝜊

-120^𝜊

The negation of a number

Choose an answer

a relation

a function

unary operation

binary operation

If you are looking a bird in the tree from the ground then the angle formed is called angle of______;

Choose an answer

Elevation

Depression

Right angle

None of these

Choose an answer

12

6

8

none of these

The minimum value of the quadratic function f(x) = 5 x 2-11,is

Choose an answer

7

-7

6

-11

In the expansion of (a + x)ⁿthe general term T_{r + 1}is

Choose an answer

In R, the multiplicative identity is

Choose an answer

0

1

-1

None

Choose an answer

If a≠ , b≠ 0 and|a=b|=|a-b|,then vectors a and b are:

Choose an answer

Parallel to each other

Perpendicular to each other

Inclined at 60^o

neither parallel nor perpendicular

A line joining two distinct points on a parabola is called

Choose an answer

Axis

Directrix

Chord

Tangent

Cos^-1 12/13 =

Choose an answer

tan^-1 3/5

cot^-1 13/12

Sec^-1 13/12

sin^-1 5/13

Choose an answer

Ifπ≤x≤2π, then cos-1 (cos x)=

Choose an answer

cos x

-x

1/x

-x

A circle which touches one side of a triangle externally and the other two sides produced is called ______

Choose an answer

In-circle

Circum cirle

Escribed circle

None of these

The multiplicative inverse of -1 in the set {1-, 1} is

Choose an answer

1

-1

+-1

0

The solution set of x < 4 is

Choose an answer

-∞< x < 4

-∞> x > 4

-∞< x < 2

-∞> x > 2

If the roots of ax²+ b = 0 are real and distinct then

Choose an answer

ab > 0

a = 0

ab < 0

a > 0, b > 0

A sequence of number whose reciprocals form an arithmetic sequence is called

Choose an answer

Geometric sequence

Arithmetic series

Harmonic sequence

Harmonic series

The process of finding the unknown elements in triangle is called the

Choose an answer

solution of the triangle

Mean differnece

Engineering distance

angle of depressin

If a +b +c =0 then which of the following is true

Choose an answer

a =b =c =0

a,b =b,c =c,a

a xb =b xc =c xa

None

Period of 2 cos x is ______

Choose an answer

x^-2+ c

not possible

Choose an answer

Which of the following is a scalar.

Choose an answer

electric field

magnetic field

weight

mass

Choose an answer

0

1

-1

A committee consists of 9 experts taken from three institutions A, B, and C, of which 2 are from, A, 3 form B and 4 from C. If three experts resign, then the probability that they belong to different institutions is

Choose an answer

1 / 729

1 / 24

1 / 21

2 / 7

Choose an answer

1

-1

0

I

If A and B are two sets then any subset R of A x B is called

Choose an answer

relation on A

relation on B

relation from A to B

relation from B to A

General solution of 1 + cos x = 0 is

Choose an answer

Imaginary

Rational

Irrational

Real numbers

Choose an answer

0

abc

1/abc

None of these

The distance of the point (2, -3) from x-axis is

Choose an answer

-2

-3

2

3

If a, b, c, d, e, f are in A.P.,then e-c is equal to

Choose an answer

2(c - a)

2(f - d)

2(d - c)

d - c

The next term of the sequence 1, 2, 4, 7, 11, ..... is.

Choose an answer

15

16

17

18

The distance of a moving particle at any instant t is x = 3t² +1 then velocity of particle at t = 10 is

Choose an answer

50 cm/sec

60 cm/sec

61 cm/sec

None of these

Choose an answer

x = 1 is in the solution of the inequality

Choose an answer

x + 1 > 0

x - 2 > 0

3x - 1 < 0

x + 2 < 0

A quadratic equation has two

Choose an answer

roots

degree

variables

constants

If the flag-staff 6 meters high placed on the top of a tower. Makes the shadow 2√3 m on the ground, then the angle of elevation of the sun is

Choose an answer

30^ο

35^ο

45^ο

60^ο

Which of the vectors have opposite direction?

Choose an answer

A triangle which is not right is called an ______ triangle

Choose an answer

Acute

Obtuse

Oblique

None of these

Choose an answer

The equation of the circle with centre (5, -2) and radius 4 is

Choose an answer

(x-5)²+ (y+2)²= 16

(x-5)²+ (y+2)²= 4

(x-5)²+ (y-2)²= 16

(x-5)²+ (y-2)²= 4

∀x,y∈R and x> 0 , y>0, if x > y

Choose an answer

None of these

An open sentences formed by using the sign of equality '=' is called ______

Choose an answer

An identity

An equation

A polynomial

None of these

Choose an answer

none of these

Choose an answer

real part of z

imaginary part of z

conjugate of z

modulus of z

The value of x.and y when (x + iy)² = 5 + 4i

Choose an answer

x = 2,y = 1

x = -2,y =1

x = 2,y = -i

x = 2,y= 2

Choose an answer

If 5,7 and 9 are A.Ms between a and b, then a and b is equal to

Choose an answer

2 and 12

1 and 10

3 and 11

-7 and 2

Choose an answer

None of these

For what value of k, 3x -2y+ k= 0 is tangent to the circle x² +y² +6x -4y =0

Choose an answer

k=0

k=0 or 26

k = 26

k=-13

Choose an answer

x²+ 2x + c

(x²+ 2x -1)⁴+ c

In how many ways can 5 persons be seated at a round table

Choose an answer

5!

4!

3!

120

ax + by < c is linear inequality in

Choose an answer

four variables

three variables

two variables

one variable

The polynomial x - a is a factor of the polynomial f(x) if and only if

Choose an answer

f(a) is positive

f(a) is negative

f(a) = 0

None of these

Choose an answer

real number

complex number

rational number

irrational number

The value of sin [ arc cos (-1/2)] is

Choose an answer

If the angle between two vectors u and v is 0 orπ, then the vectors u and v are:

Choose an answer

Orthogonal

Collinear

Perpendicular

None of these

The sum of the cubes of three consecutive natural number is divisible by

Choose an answer

9

6

5

10

The four fourth roots of unity are

Choose an answer

none of these

The sum if 1,3,5,7,9........ up to 20 terms is

Choose an answer

400

472

563

264

How many 3 digit numbers can be formed by using each one of the digit 2, 3, 5, 7, 9 only once?

Choose an answer

15

24

60

120

Choose an answer

none of these

If f(x) = x²- x then f(-2) is

Choose an answer

4

6

2

0

The roots of the equation 2^2x- 10.2^x+ 16 = 0 are

Choose an answer

2, 8

1, 3

1, 8

2, 3

Choose an answer

Associative law of multiplication

Commutative law of addition

Commutative law of multiplication

Associative law of addition

The product of complex numbers (a,b) and (c,d) is

Choose an answer

(ac, bd)

(ac-bd, ad+bc)

(ab,cd)

(ac+bd,ad-bc)

Choose an answer

0

1

2

3

Choose an answer

405 / 256

504 / 259

450 / 263

None

Choose an answer

1/2

2

1/4

4

The contra positive of p → q is

Choose an answer

q → p

~q→~q

~p→~q

None of these

For trival solution |A| is

Choose an answer

A

|A| = 0

A = 0

|A| ≠ 0

Choose an answer

A

A'

U

None of these

Choose an answer

3 sec²x

3 sec²3x

sec²3x

sec²x

Choose an answer

No solution

One real solution

Choose an answer

If 0 = R, thenthe additive inverse of a is

Choose an answer

1/9

^1/-9

a

-a

The directrix of y² =-4ax is

Choose an answer

y =-a

y = a

x = a

x = -a

Which conjunction is not true ?

Choose an answer

Two matrices A and B are conformable for the product AB if

Choose an answer

Both A and B are square

Both A and B are symmetric

Number of rows of A = number of columns of B

Number of columns of A = number of rows of B

The magnitude of vector a 2i-7j is

Choose an answer

√23

√43

3

√53

Choose an answer

The transpose of a column matrix is a ______

Choose an answer

Zero matrix

Diagonal matrix

Column matrix

Row matrix

Choose an answer

A positive integer

A negative integer

A natural number

An irrational number

i is equal

Choose an answer

(1 , 0)

(0 , 1)

(1 , 1)

(0 , 0)

The vertex of the standard position angles lies on

Choose an answer

(0,0)

(0,1)

(1,0)

(1,1)

Choose an answer

X = 100 sinθ

X = 10 sinθ

X = 100 secθ

None of these

What is the conjugate of -6 -i?

Choose an answer

-6 +i

6+i

-6 -i

6 -i

Choose an answer

A

A'

U

i² =

Choose an answer

1

2

-1

0

Choose an answer

The number of 5-digit number that can be formed from the digits 1,2,4,6,8, when 2 and 8 are never together is

Choose an answer

72

48

144

20

tan(2π+θ) = ________;

Choose an answer

tanθ

-tanθ

cotθ

-cotθ

Choose an answer

A = B

B = C

A = C

None of these

xy= 2 is:

Choose an answer

a constant function

an identity function

an improper function

implicit function

The general solution of tan 3x = 1 is

Choose an answer

the latus rectum of the parabola x³= -4ay is:

Choose an answer

x = a

y = -a

x = -a

y = 0

If a₁, r are first term and the common ratio respectively then the sum of an infinite geometric series is

Choose an answer

(1,7/3)

(1, 7/5)

(1, 11/7)

(1, 3/5)

Choose an answer

The angle between lines xy =0 is

Choose an answer

45°

60°

90°

180°

Choose an answer

The angle of elevation of a tower from a point A due south of it is x and from a point B due east of A is y. If AB = 1, then the height h of the tower is given by

Choose an answer

n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

Choose an answer

I andII quadrants

II andIII quadrants

II andIVquadrants

none of these

Choose an answer

The period of cosec 10x is _______

Choose an answer

Which of the following is a vector

Choose an answer

length

momentum

volume

speed

If z₁ = 1 + 2i, z₂ = 3 + 4i then

Choose an answer

z₁ > z₂

z₁ = z₂

z₁ < z₂

None of these

Choose an answer

How many arrangements of the letters of the word PAKISTAN cab be made

Choose an answer

Matrices A = [aij] 2 x 3 and B = [bij] 3 x 2 are suitable for

Choose an answer

BA

A²

AB

B²

The number of standard parabolic functions are is

Choose an answer

4

2

3

1

If f(x) = x²- x then f(2) is

Choose an answer

4

6

2

0

Which symbolic notation represent unary operation ?

Choose an answer

-

∨

∧

⇔

Choose an answer

0

-1

1

1/2

Choose an answer

Write down the power set of {9, 11}

Choose an answer

(x, y)

(kx, y)

(x, ky)

(kx, ky)

In an A.P,a +(n-a)d is

Choose an answer

1^st term

General term

Last term

None of these

The second degree equation 2x² -xy+ 5x -2y +2 =0 represents

Choose an answer

Circle

Hyperbola

Ellipse

Pair of straight lines

The nth term of an A.P is (3n+5) Its 75^thterm is

Choose an answer

26

7

21

Cannot be determined

Choose an answer

1, 1/2, 0

1, 2, 1

1, 2, 3

1, 2, 0

The positive integer just greater than (1+0.0001)¹⁰⁰⁰⁰is

Choose an answer

4

5

2

3

The conic ax²+2hxy+by²+2gx+2fy+c= 0 never represent a circle if

Choose an answer

a ≠ b,h≠0

a=b

h≠0

h=0

(a +bi) -c (c +di) =

Choose an answer

(a +b) = (c +d)

(a +c) + i(b +d)

(a -c) + (c -d)i

(a -c) +(b -d) i

Choose an answer

Free vector

Null vector

Unit vector

None of these

Which of the following is a vector.

Choose an answer

work

time

density

electric field

Choose an answer

none of these

The statement that a group can have more than one identity elements is

Choose an answer

True

False

Ambiguous

Some times true

A dice is rolled. The probability that the dots on the top are greater than 4 is

Choose an answer

1/6

1/3

1/2

1

If A is any matrix then its additive inverse is

Choose an answer

A

A^-1

A^t

-A

If sided of𝜟ABC, are 16,20,and 33, then the value of thegreatests angle to

Choose an answer

150^𝜊20'

132^𝜊35'

101^𝜊25'

160^𝜊 50'

The eccentricity e of an ellipse is always

Choose an answer

Rational

Real

Irrational

Integer

Choose an answer

3, -3, 11

3, 3, 11

-3, 3, -11

-3, -3, 11

Which of the following is factor of p(x) =2x³ +3x²+3x^-2?

Choose an answer

x+1

2x+1

3x+1

2x-1

The line through the centre and perpendicular to the transverse axis is called the

Choose an answer

Major axis

Minor axis

Focal axis

Conjugate axis

Choose an answer

Addition

Multiplication

Division

Both addition and multiplication

Choose an answer

The set R is ........w.r.t subtraction

Choose an answer

Not a group

A group

No conclusion drawn

Non commutative group

Choose an answer

1/8

1/2

1/4

1/6

What is the period of tan 4/3 x =?

Choose an answer

π/4

4π/3

7π/4

3π/4

If a₁= 3, r = 2, then the nth term of the G.P. is

Choose an answer

2.3^n-1

3.2ⁿ

3.2ⁿ⁺¹

3.2^n-1

Choose an answer

The domain and range of a trigonometric function can be allocate by their

Choose an answer

graph

Continuity

Discontinuity

Periods

if f(x) = x³ -3x² +5x -1, then f(-√2)=

Choose an answer

7+7√2

3+3√2

-7-7√2

-3-3√2

Choose an answer

The transpose of a row matrix is a ______

Choose an answer

Zero matrix

Diagonal matrix

Column matrix

Row matrix

If distance of (a,b) from y-axis is 2 then

Choose an answer

a = 2

b = 2

a = b

a = 4

The roots of (b-c)x²+(c-a) x+a-b=0 are equal if

Choose an answer

2b = a+c

2a = b+c

2c = a+b

a + b + c =0

Choose an answer

A = B iff

Choose an answer

All elements of A also the elements of B

A and B should be singleton

A and B have the same number of elements

If both have the same element

3x + 4 < 0 is

Choose an answer

not inequality

equation

identity

inequality

The coordinates of a point P(x,y) referred to XY-system are

Choose an answer

(x+y,y+k)

(x-h,y-k)

(x,y)

(x-h,y-k)

The law of sines can be used to solve

Choose an answer

Right angle triangle

Isosceles triangle

oblique triangle

haxagon

A card is drawn from a pack of cards numbered 1 to 52, the probability that the number on the card is a perfect square is

Choose an answer

1/13

2/13

7/52

None of these

Choose an answer

The 31 term of the A.P 5,2,-1.....is

Choose an answer

-82

82

85

-85

We solve the system of non-homogeneous linear equations by

Choose an answer

a and b

b and c

c and a

a,b and c

If ΔABC is right triangle then the law of Cosines reduces to

Choose an answer

The Pythagoras Theorem

The law of Sines

The law of cosines

The law of tangents

Choose an answer

When a selection of object is made without paying regard to the order of selection, it is called

Choose an answer

Sequence

Series

Combination

Permutation

Choose an answer

1

12

5

29

Choose an answer

If a = {2m/2m < 9 ,m€ p} , the n A =

Choose an answer

{2,3,4,5,6,7,8}

{2,4,6,8............16}

{ 4, 6}

{2,3,5,7}

Choose an answer

(1, 3)

(-1, -3)

(1, -3)

(-1, 3)

Two cards are drawn at random from a well shuffled pack of cards. The probability that at least one of them is a face card is

Choose an answer

3 / 17

5 / 17

7 / 17

9 / 17

Choose an answer

100

99

0

none of these

Choose an answer

2

4

8

12

f(x) = C is

Choose an answer

identity function

constant function

linear function

quadratic function

The identity elements with respect to subtraction is

Choose an answer

0

1

-1

Does not exist

1 + 2 + 3 + ...... + n = ______

Choose an answer

Sin-1(-x)=

Choose an answer

x

-x

-sin^-1 x

cos^-1 x

Period of tan 4x is ______

Choose an answer

The function f(x) =|x| is a/an_______function

Choose an answer

Even

Odd

Both even as well as odd

Neither even nor odd

If origin is the mid point of (a, -3) and (-5, b) then

Choose an answer

a = -5 , b = -3

a = 5 , b =3

a = -5 , b = 3

a = 5 , b = -3

The roots of the equation x³ +6x-7=0,are

Choose an answer

1

2

1 and -7

-7

Choose an answer

The range of the function f : x → y is defined by

Choose an answer

{x| y = f (x) ∀x∈ X ∧y∈y}

{(x,y) |y = f (x) ∀x∈ X}

{y| y = f (x) ∀x∈ X ∧y∈y}

Y

Choose an answer

The roots of the equation will be irrational if b²- 4ac is

Choose an answer

Positive and perfect square

Positive but not a perfect square

Negative

Zero

The distance between the points (2, 2) and (3, 3) is

Choose an answer

10

5

2

Choose an answer

The constant distance of all points of the circle from its centre is called the

Choose an answer

radius of the circle

secant of the circle

chord of the circle

diameter of the circle

Range of sin x is ______

Choose an answer

[-1, 1]

R

Negative real numbers

None of these

Choose an answer

5

25

3

∀a,b ε R, ab = be is a

Choose an answer

Commutative law of multiplication

Closure law of multiplication

Associative law of multiplication

Multiplicative identity

If order of A is m x n, then order of A^tis

Choose an answer

m x m

n x n

m x n

n x m

A series consisting of an unlimited number of terms is termed as an

Choose an answer

Finite sequence

Infinite sequence

^{Infinite series}

geometric sequence

Choose an answer

16 / 7

6 / 17

7 / 16

None of these

Choose an answer

0

90°

180°

360°

The number of real tangents that can be drawn to the ellipse 3x²+ 5y²= 32 passing thro. (3, 5) is

Choose an answer

0

1

2

Infinite

Graph of the question x²+ y²= 4 is

Choose an answer

A circle

An ellipse

A parabola

A square

Choose an answer

[i,j,k]

Choose an answer

0

2

1

-2

Choose an answer

A square matrix A = [aij] is upper triangular when

Choose an answer

cij = 0

bij = 0

aij = 0 for all i > j

dij = 0

The circle (x - 2)²+ (y + 3)²= 4 is not concentric with the circle

Choose an answer

(x - 2)²+ (y + 3)²= 9

(x + 2)²+ (y - 3)²= 4

(x + 2)²+ (y - 3)²= 8

(x - 2)²+ (y + 3)²= 5

Choose an answer

Which of the following is a quadrantal angle

Choose an answer

100°

200°

170°

270°

Let the equation ax²- bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be

Choose an answer

(5, 3, 1)

(4, 3, 2)

(5, 5, 1)

(6, 4, 1)

Choose an answer

I and II quadrants

I and III quadrants

II and III quadrants

II and IV quadrants

Choose an answer

Linear equation

Quadratic equation

Cubic equation

None of these

Choose an answer

Gooch crucible is made of :

Choose an answer

Brass.

Porcelain.

Bronze.

Gold.

Choose an answer

If cosα= 4/5, then cosα/2

Choose an answer

If (0,4) and (0,2) are vertex and focus of the parabola respectively, the the equation of the parabola is:

Choose an answer

x² = 4y -32

x² =8y -32

y³ = 16 x

x2 + 8y =32

Choose an answer

Associate law of addition

Commutative law of addition

Additive identity

Closure law of addition

Choose an answer

The fifth term of an A.P. Whose first term is 5 and common difference is 3,is

Choose an answer

20

17

25

30

Choose an answer

cos 2x + c

- cos 2x + c

tan 2x + c

cot 2x + c

In common logarithm the base is

Choose an answer

1

0

10

e

A man of height 6 ft observes the top of a tower and the foot of the tower at angles of 45° and 30° of elevation and depression respectively. The height of the tower is

Choose an answer

A statement which is either true or false is called

Choose an answer

Induction

Deduction

Propositicon

Logic

A monoid (G, _*) is said to be group if

Choose an answer

have identity element

is commutative

have inverse of each element

None of these

An equation of the form ax + by = k is homogeneous linear equation when:

Choose an answer

If x is an image of y under the function f. This can be written as

Choose an answer

y = f(x)

f(x) = 0

x = f(y)

f(y) =0

The tangents drawn from the point P to a circle are imaginary if

Choose an answer

P is on the circle

P is inside the circle

P is outside the circle

none of these

If the angle between two vectors with magnitude 6 and 2 is 60° when their scalar product is

Choose an answer

12

6

3

0

Choose an answer

- cot 4x + c

cot 4x + c

tan 4x + c

- tan 4x + c

The expression x² - x + 1 has

Choose an answer

One proper linear factor

No proper linear factor

Two proper linear factors

None of these

The multiplicative inverse of -1 in the set {1-, 1} is

Choose an answer

1

-1

0

Does not exist

Choose an answer

e^x+ c

e^-x+ c

x e^x+ c

not possible

cos(3π/2 +θ) = _____;

Choose an answer

sinθ

cosθ

-sinθ

-cosθ

The mid point of the line segment joining the points A(3,1) and B(-2,-4) is

Choose an answer

(1, -3)

Choose an answer

Only one real solution

Exactly three real solution

Exactly one rational solution

Non-real roots

Choose an answer

If eccentricity of ellipse becomes zero then it takes the form of

Choose an answer

A parabola

A circle

A straight line

None of these

Choose an answer

none of these

The solution set of the equation 4 cos²x - 3 + 0 is

Choose an answer

none of these

Choose an answer

Tangent is a periodic function and its period is ______

Choose an answer

2π

3π

π

4π

Choose an answer

If u = 2ai + i - k and v = i +ai + 4k are perpendicular then a =

Choose an answer

4

1/2

3

4/3

Choose an answer

none of these+

x²+ x - 6 = 0 is

Choose an answer

An equation

An identity

A polynomial

None of these

The function sine and Cosine have the closed internal as their range

Choose an answer

[1, 0]

[-1, 1]

[0, 1]

[-1, 2]

The number of terms in the expansion of (a + b)⁹is

Choose an answer

10

11

9

12

The value of x, and y, when (x + iy)²= 5 + 4i

Choose an answer

X = 2, y = -1

X = -2, y=1

X = 2, y = -1

X = 2, y = 2

The sum of even coefficient in the binomial expansion is

Choose an answer

2ⁿ⁺¹

2ⁿ

2^n-1

2n

Choose an answer

-x

Infinite set

{-4, 4}

None of these

Choose an answer

additive property

multiplicative property

additive identity

multiplicative identity

A diagonal matrix in which the diagonal elements are equal is called a

Choose an answer

Null matrix

Identity matrix

Scalar matrix

Row matrix

Choose an answer

none of these

The matrix A = [a_ij]_mxn with m≠n is

Choose an answer

Rectangular

Symmetric

Square

None

Choose an answer

6x + 2 + c

6x + x²+ c

6x³+ x²+ x

The range of y = sin x is ______

Choose an answer

[1, -1]

[-1, 1]

[0, -1]

[-∞+∞]

Choose an answer

0

-1

1

2

Choose an answer

Multiplying each side of an inequality by (-1) will:

Choose an answer

Not effect

Change the sign

Become zero

Not defined

Choose an answer

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

Choose an answer

24

25

9

13

The slope of the tangent at the point (h,h) of the circle x² +y² =a² is

Choose an answer

0

1

-1

h

If u = x and dv = -sin x, the∫ x cos dx is equal to:

Choose an answer

x cos x + sin x

cos x + x sin x

x cos x + x sin x

x sin x - cos x

∀ z ∈ C, multipliucative is

Choose an answer

(1,1)

(1,0)

(0,1)

None of these

Choose an answer

The period of tan x/7 is

Choose an answer

3π

7π

15π

5π

sin(180° -θ)=

Choose an answer

cosθ

-cosθ

Tanθ

Sinθ

The set of rationals numbers between 0 and I is

Choose an answer

Finite

Null set

Infinite

None of these

If the matrices A and B have the order 1 x 10 and 10 x 1 then order of AB is

Choose an answer

1 x 1

1 x 10

10 x 10

10 x 1

Choose an answer

The equation of the chord of the circle x²+ y²- 4x = 0 whose mid-point is (1, 0) is

Choose an answer

y = 2

y = 1

x = 2

x = 1

Choose an answer

1

-1

-1/2

1/2

Find the geometric mean between 4 and 16

Choose an answer

I and III quadrants

II and III quadrants

I and II quadrants

II and IV quadrants

If one end of the diameter of the circle 2x²+ 2y²-8x - 4y = 2 = 0 is (2 ,3), the other end is:

Choose an answer

(2,1)

(-2,1)

(2,-1)

(1,-1)

Choose an answer

A²- 5A + 7I = 1

2A²- 3A + 7I = 0

A²- 5A + I = 0

A²- 5A + 7I = 0

Choose an answer

Commutative law of addition

Associative law of addition

Additive identity

Additive inverse

If a,βare the roots of the equation x² - 8x + p = 0 and a² + β²= 40,then value of p is

Choose an answer

8

12

10

14

Choose an answer

π

2π

π/2

None of these

The are of the circle centred at ( 1 , 2) and passing through ( 4 , 6) is:

Choose an answer

10π

25π

5π

25/2π

Choose an answer

If d₁is the distance between (0,0) and (1,2) and d₂is the distance between (0,0) and (-1,-2) the

Choose an answer

d₁< d₂

d₁> d₂

d₁= d₂

none of these

The sum of the focal distance from any point on the ellipse 9x² +16y2 =144 is

Choose an answer

32

16

18

8

For all points (x,y) on x-axis

Choose an answer

x is positive

x is negative

y = 0

y is negative

Choose an answer

The sum of all even numbers less than 100 is

Choose an answer

2450

2352

2272

2468

x²+ x - 6 = 0 is a conditional equation and it is true for

Choose an answer

2, 3

2, -3

-2, -3

-2, 3

Choose an answer

All letters of the word "AGAIN" are permuted in all possible ways and the words so formed (with or without meaning) are written as in dictionary, then the 50th word is

Choose an answer

NAAGI

NAAIG

IAANG

INAGA

Three unbiased coins are tossed. Then the probabilities of getting two heads is

Choose an answer

3/8

1/8

1/4

None of these

Arithmetic mean between 14 and 18 is

Choose an answer

16

17

15

32

If A is a set then any subset R of A x A is called

Choose an answer

relation on A

relation on B

relation from A to B

relation from B to A

The difference of two consecutive terms of an A.P is called the

Choose an answer

Common difference

Common ratio

Geometric series

Geometric mean

2x³+ 3x + 9 is a ______

Choose an answer

Polynomial of degree 3

Quadratic equation

Cubic equation

Polynomial of degree 2

F(x) = x^xdecreases in the interval

Choose an answer

(0, e)

(0, 1)

(-∞,0)

None

Choose an answer

cos x + c

-sin x + c

-cos x + c

sin x + c

Choose an answer

all

If Z₁= 1 + i, Z₂= 2+3i, then |Z₁- Z₂| = ?

Choose an answer

The additive inverse of 0 is

Choose an answer

1

-1

0

Does not exist

The product of cube roots of unity is

Choose an answer

Zero

1

-1

None of these

Which of the following represents a vector

Choose an answer

(x, y)

Choose an answer

Additive property in R

Multiplication property in R

Cancellation property in R

Distribution property in R

1⁰= ______

Choose an answer

1.5 rad

0.5 rad

0.175 rad

None of these

The fifth term of the sequence a_n= 2n + 3 is ______

Choose an answer

13

-13

8

3

f(x) = ax + b will be an identity function if

Choose an answer

a = 1 , b = 1

a = 1 , b = 0

Cos-1(x)=

Choose an answer

cos x

x

tan^-1(-x)

Sec-1 (1/x)

Choose an answer

Principle of equality of fractions

Rule for product of fractions

Golden rule for fractions

Rule for quotient of fractions

Which is not a half plane

Choose an answer

ax + by < c

ax + by > c

Both A and B

None

Choose an answer

tan 294° =______;

Choose an answer

tan 24°

-tan 24°

cot 24°

-cot 24°

Choose an answer

k³

0

3k

k⁶

Choose an answer

Singleton set

A set with two points

Empty set

None of these

The line y= 4x +c touches the hyperbola x² = y² =1 if and only if

Choose an answer

c =±√2

c =0

c=±√17

c=±√15

r + 3 >5 then which is true

Choose an answer

r + 2 > 4

r + 2 < 4

r + 2 = 4

None

Choose an answer

The velocity of a particle moving along a straight line is given by v = 3t + t². The acceleration of the particle after 4 seconds from the start is

Choose an answer

4

11

26

None

f(x) = x³is:

Choose an answer

an odd function

an even function

an implicit function

a quadratic funtion

Choose an answer

-1

1

2

-2

An A.P. consists of n(odd terms) and its middle term is m. then the sum of the A.P. is

Choose an answer

2 mn

1/2 mn

mn

mn²

The period of 3 sin x is

Choose an answer

2π

9π

3π

5π

An equation containing at least one derivative of a depends variable with respect to independent variable is a (an)

Choose an answer

Implicit equation

Differential equation

General equation

None of these

The middle term of (x-y)⁸is

Choose an answer

25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

The range of y=x² + 1 is the set of non-negative real numbers except

Choose an answer

0 ≤ y < 1

0 < y < 1

0 ≤ y ≤ 1

0 < y ≤1

Name the property used in 100 + 0 = 100

Choose an answer

Additive inverse

Multiplicative inverse

Additive identity

Multiplicative identity

If the graph of f is entirely below the x-axis, then the value of definite integral is

Choose an answer

= 0

< 0

> 0

None

sin(^π/2+θ) = _______;

Choose an answer

sinθ

cosθ

-sinθ

-cosθ

If the roots of x²+ ax + b = 0 are non-real, then for all real x, x²+ ax + b is

Choose an answer

Negative

Positive

Zero

Nothing can be said

Period of cosec x is ______

Choose an answer

Total number of subsets that can be formed out of the set {a,b,c} is

Choose an answer

1

4

8

12

Let A and B be two sets. If every element of A is also an element of B then

Choose an answer

An airplane flying at height of 300 meters above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60° and 45° respectively. Then the height of the lower plane from the ground is (in meters).

Choose an answer

{1, 2, 3} is _____

Choose an answer

an infinite set

A finite set

A singleton set

Universal set

The period of the function csc x/4 us

Choose an answer

4x

π/4

8π

π/8

If in a set of real no a is additive identity then

Choose an answer

a+a = 2a

a+a = 1

a+a = 0

None of these

Choose an answer

If u =2i +pi + 5k and v = 3i + i +pk are perpendicular , then p=

Choose an answer

1

2

-1

-3

If a, b, c are the measures of the sides of a triangle then

Choose an answer

In the expansion of (a + x)ⁿthe sum of exponents of a and x in each term of the expansion is

Choose an answer

n + 1

n - 1

n

2n

Which is a proper rational fraction

Choose an answer

6

20

0

A fraction in which the degree of the numerator is less the degree of the denominator is called

Choose an answer

Polynomial

Proper fraction

Rational fraction

None

Choose an answer

Diagonal matrix

Scalar matrix

Triangular matrix

Identity matrix

If n(X) = 18, n(X∩Y) = 7, n(X ∪ Y) = 40 then n(Y) =

Choose an answer

1

12

5

29

If cos (2 sin-1 x) = 1/9 , then what is the value of x?

Choose an answer

1/3

-2/3

2/3

2/3 , -2/3

The distance between the points (2,3) and (3,2) is

Choose an answer

5

2

10

Choose an answer

Hermitian matrix

Skew-hermitian matrix

Symmetric matrix

Identity matrix

The element range of sequence are called

Choose an answer

Series

progression

Members

Terms

1 radian = _____

Choose an answer

60°

57.296°

57.2°

180°

Choose an answer

1

2

0

4

At a point 15 meters away from the base of a 15 meters high house, the angle of elevation of the top is

Choose an answer

90°

60°

30°

45°

A box containing 10 mangoes out of which 4 are rotter. Tow mangoes are taken together from the box. If one of them is found to be good, the probability that the other is also good is

Choose an answer

1 / 3

8 / 15

5 / 13

5 / 9

The set of all antiderivaties of f(= ∫f(x)dx) is the

Choose an answer

Definite integral

Indefinite integral

Integral

Area

Choose an answer

Always negative

Zero

Always positive

Infinity

Every subset of a finite set is

Choose an answer

Disjoint

Null

Finite

Infinite

If the focus lies on the y-axis with coordinates f(0,a) and directrix of the parabola is y = -a, the equation of parabola is:

Choose an answer

y² = -4 ax

x² = 4ay

x² = -4ay

y² = 4ax

Choose an answer

15

9

7

8

Choose an answer

The center of the sphore which passes thro' (a, 0, 0), (0, b, 0), (0, 0, c) and (0, 0, 0) is

Choose an answer

Form a group of 5 men and 3 women, a committee of 4 persons is to be selected randomly. The probability that there is a majority of men is

Choose an answer

1/4

1/3

1/2

1/6

The sum even binomial coefficient of (3+2x)⁵ is ______term

Choose an answer

16

30

8

32

The sum of an indicated number of terms in a sequence is called

Choose an answer

sequence

progression

Series

Mean

What is range of the function g (x) =|x-3|?

Choose an answer

[0 ,∞ )

(0 ,∞)

(-∞ ,3]

[0,∞)

9. 8. 7. 6= ______

Choose an answer

If A and B are two disjoint events then

Choose an answer

P(A∪B)=P(A)+p(B)

P(A∪B)=P(A)-P(A∪B)

P(A∪B)=P(A)or P(B)

None

The value of x and y when (x + iy)² =

Choose an answer

x = 2, y = -1

x = -2, y = 1

x = 2, y = -i

x = 2, y = 2

If A, G, H are the arithmetic, geometric and harmonic means between a and b respectively then A, G, H are in

Choose an answer

A. P.

G. P.

H. P.

None of these

The upper 3/4 the portion of a vertical pole subtends an angle tan^-13/5 at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is

Choose an answer

20 m

40 m

60 m

80 m

tan(π-θ)=_____;

Choose an answer

tanθ

cotθ

-tanθ

-cotθ

Choose an answer

π / 3

π / 4

π / 6

0

(ABC)' =

Choose an answer

CBA'

CBA

C'B'A

C'B'A'

If X = 1/x for X ∈ R then the value of x is

Choose an answer

±1

0

2

4

The distance of the point (2,3) from origin is

Choose an answer

5

2

3

Choose an answer

1

-1

0

None of these

Choose an answer

a constant function

linear function

quadratic funtion

none of these

If either A = 0 or B =0,then Ax² +By² +2Gx +2Fy +c =0 represents a

Choose an answer

Circle

Hyperbola

Ellipse

Parabola

Tan(α-β)=

Choose an answer

The number of non zero rows in echelon form of a matrix is called

Choose an answer

Order of matrix

Rank of matrix

Row operation

None of these

Two positive integers whose sum is 30 and their product will be maximum are

Choose an answer

12,18

10,20

15,15

14,16

120°=______

Choose an answer

The solution set of trigonometric equation contains

Choose an answer

one element

two elements

three elements

Infinite elements

A sequence is a function whose domain is

Choose an answer

N

Subset of N

R

None of these

Choose an answer

Sec 30° = ______

Choose an answer

0

1

undefined

The corner point of the boundary lines, x-2y

2x + y = 2 is:

Choose an answer

(2,6)

(6,2)

(-2,2)

(2,-2)

Every prime number is also

Choose an answer

Rational number

Even number

Irrational number

Multiple of two numbers

The central angle of an arc of a circle whose length is equal to the radius of the circle is called the

Choose an answer

degree

radian

minute

second

The period of tan [x/3] is ______

Choose an answer

2π

4π

3π

5π

Corner point of the system x - y ≤ 2,x + y ≤ 4,2x -y ≤ 6,x ≥ 0,y ≥ 0

Choose an answer

(1,4)

(4,2)

(3,1)

(4,1)

The multiplicative inverse of x such that x = 0 is

Choose an answer

-x

Does not exist

1/x

±1

If A = {2m/m³= 8 , m€ Z} then A =

Choose an answer

{1,8,27}

{4}

(2,4,6}

{2,16,54}

If sinαand cosαare the roots of the equation px²+ qx + r =0, then

Choose an answer

p²- q²+ 2pr = 0

(p + r)²= q²- r²

p²+ q²- 2pr = 0

(p - r)²= q²+ r²

Choose an answer

For an A.P common difference d

Choose an answer

Can be zero

May or may not zero

Cannot be zero

None of these

Choose an answer

An equation which hold good for all values of the variables is called

Choose an answer

Identity

fraction

mixed form

Partial equation

The set of the first elements of the ordered pairs forming a relation is called its

Choose an answer

Function on B

Range

Domain

A into B

sin5θ+sin3θ = _______;

Choose an answer

2sin 4θ cosθ

2cos 4θ sin θ

2cos 4θ cosθ

-2sin 4 θ sinθ

The equation of vertical asymptotes of y = cos ecx is

Choose an answer

x = 0

y = 0

x = ∞

y = ∞

If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then the probability that the drawn balls are of different colours is

Choose an answer

1 / 66

3 / 66

19 / 66

47 / 66

Choose an answer

tanθ/2

Choose an answer

If θ be angle between u,v and u,v determine the sides of a triangle then the third side opposite to angle θ has length

Choose an answer

|u+v|

|u|+|v|

|u-v|

|u|-|v|

Choose an answer

20

10

0

None of these

Choose an answer

If origin is the mid point of (a,3) and (5,b) then

Choose an answer

a = -5 , b = -3

a = 5 , b =3

a = -5 , b = 3

a = 5 , b = -3

Choose an answer

0

-4

none of these

The point _________ is in the solution of the inequality 2x + 3y < 5

Choose an answer

(1,1)

(2,2)

(0,1)

(0,2)

The distance between the points A(3,1) and B(-2,-4) is

Choose an answer

5

25

10

If line through (4,3) and (2,k) is perpendicular to y =2x +3, then k =_______

Choose an answer

-1

1

-4

4

Choose an answer

0

1

Roots of the equation x²+ 7x + 12 = 0 are

Choose an answer

{3, -4}

{-3, 4}

{3, 4}

{-3, -4}

The multiplicative inverse of 2/3 is

Choose an answer

3/2

-2/3

-3/2

1

Cot 45° = ______

Choose an answer

x³+ 2x²- 3x + 5 is ______

Choose an answer

An equation

A polynomial

Proper rational fractions

Improper rational fractions

The term involving x⁴in the expansion of (3 - 2x)⁷is

Choose an answer

120

1512

1250

15120

The angle between the vectors u =2i - i + k and v = -i + i is:

Choose an answer

3π/2

2π/3

5π/6

π/3

The velocity and acceleration at any point t of a particle which moves along straight line x = 5r-3

Choose an answer

5,3

5,-3

5,0

10,0

Matrix multiplication is

Choose an answer

Commutative

Not commutative

Not associative

Not distributive

∀a,b,c∈R, a >b ∧ b>c ⇒ a >c is

Choose an answer

Trichotomy property

Transitive property

Symmetric property

Additive property

Choose an answer

N

r

2r

π

Choose an answer

In R the number of identity element w.r.t '+' is

Choose an answer

One

Two

Three

Four

x = ________ is in the solution of 2x - 3 < 0

Choose an answer

2

-2

3

4

E-radius corresponding to < A is

Choose an answer

Associative property of addition

Associative property of multiplication

Commutative property of addition

Commutative property of multiplication

Apollonius was a:

Choose an answer

Rocket

Muslims scientist

Greek mathematicians

Method of finding conics

x is a member of the set [-1, 0, 3, 5] y is a member of the set {-2, 1, 2, 4} which is possible?

Choose an answer

x - y = -6

x - y < -6

x - y > -6

None

The behavior of trigonometric function is called

Choose an answer

Continuity

Discontinuity

Periodicity

Smoothness

(1, 1) is the in the solution of the inequality

Choose an answer

3x + 4y > 3

2x + 3y < 2

4x = 3y > 5

2c - 3y > 2

Choose an answer

Associative law of addition

Commutative law of addition

Additive identity

Closure law of addition

Choose an answer

2

-2

none of these

A disjunction of two statement p and q is true

Choose an answer

p is false

q is false

Both p and q are false

One of p and q is true

A card is drawn from a pack of cards numbered 2 to 53. the probability that the number on the card is prime number less than 20 is

Choose an answer

2 / 13

4 / 13

5 / 13

8 / 13

In ladder leaning against a vertical well makes an angle of 24^𝜊with the wall, Its foot is 5m from the wall, its length is

Choose an answer

5.47m

2m

7m

6.29m

2π is the period of

Choose an answer

sin𝜽

tan𝜽

cot𝜽

all circular function

Choose an answer

0

1

-1

(x3-1/x)¹²

Choose an answer

295

495

395

722

For which of the following ordered pairs (s, t) is s + t > 2 and s - t < -3?

Choose an answer

(3, 2)

(2, 3)

(1, 8)

(0, 3)

If z = (x,y) , then z ̅ =

Choose an answer

(-x,y)

(x,-y)

(-x, -y)

None of these

A square matrix A for which A^t= A is called a

Choose an answer

Column matrix

Symmetric matrix

Skew-symmetric matrix

Row matrix

sin^-1 x =

Choose an answer

tan^-1 x

Cosec^-1 x

Cosec x

cosec^-1(1/x)

H.M. between 3 and 7 is

Choose an answer

2 x 2

2 x 3

3 x 2

3 x 3

If f(x) = x²then f(-2) is

Choose an answer

-2

2

4

-4

Choose an answer

Range of cosθis

Choose an answer

The equation of the sphere passing thro' (0, 0, 0), (a, 0, 0), (0, b, 0), (9, 0, c) is

Choose an answer

x²+ y²+ z²+ 2 ax +2 by + 2cz = 0

x²+ y²+ z²- 2ax - 2 by - 2cz = 0

x²+ y²+ z²- ax - by - cz = 0

x²+ y²+ z²+ ax + by + cz = 0

Choose an answer

What is the period of sin 2x/3 cos 4x=?

Choose an answer

π

2π

π/2

π/3

Choose an answer

f(x) = sin x + cos²x is

Choose an answer

trigonometric function

algebraic function

exponential function

logarithmic function

The angles with some initial and terminal sides are called

Choose an answer

Quadrantal angles

Coterminal angles

Allied angles

None

The negative square root of 9 can be written as:

Choose an answer

-√9

√9

√18

-√18

64.A point (x, y, z) moves parallel to xy plane. Which of the three variables x, y, z remain fixed?

Choose an answer

z

x

y

x and y

For an arithmetic series to be convergent it is necessary that the series has

Choose an answer

Finite terms

d<0

Infinite terms

None of these

The straight line passing through the focus and perpendicular to the directrix of the conic is known as its

Choose an answer

Tangent

axis

Focal chord

major or manor axis

Choose an answer

none of these

The third term in the expansion of (1+2x) is

Choose an answer

-2x²

-4x²

2x²

4x²

The formula an = ar^n-1represents

Choose an answer

nth term of G.P

Sum of the first n terms

G.M between a and b

None of these

Choose an answer

cos x

- sin x

- cos x

tan x

y=-a is the equation of the directrix of

Choose an answer

y² =4ax

x² =-4ay

x² =4ay

y² =-4ax

Choose an answer

1

2

-2

Choose an answer

-1

0

1

Undefined

The law of tangents is ______

Choose an answer

If the cutting plane is slightly tilted and cuts only one nappe of the cone, the resulting section is:

Choose an answer

an ellipse

Circle

a hyperbola

a parabola

The maximum value of sinθcosθis

Choose an answer

1

1/2

1/4

1/6

Choose an answer

1

-1

0

None of these

The number of terms in the expansion of (a + x)¹²is

Choose an answer

13

12

11

10

Choose an answer

2

1

5

0

Choose an answer

-8

8

8i

32

∀ a ε R ∃ o ε R such that a + v = 0 + a = a is property of

Choose an answer

Commutative law of addition

Associative law of addition

Additive identity

Additive inverse

Four cards are drawn at random from a pack of 52 playing cards. The probability of getting all the four cars of the same suit is

Choose an answer

44/4165

22/4165

11/4165

None of these

(a,b) +(-a,-b) =

Choose an answer

(0,0)

(a,b)

(-a,-b)

(1,1)

Choose an answer

The sum of first 60 natural numbers is

Choose an answer

1830

3660

1640

1770

√-1 b=

Choose an answer

b

2

2b

None of these

The common point to four standard parabolas

Choose an answer

Focus

Centre

Vertex

P(x,y)

If y=f(x) is a function then y is called

Choose an answer

dependent variable

independent variable

constant

none of these

Choose an answer

(0.90)^1/2is equal to

Choose an answer

0.99

0.90

0.80

0.88

A non-terminating, non-recurring decimal represent

Choose an answer

A natural number

A rational number

An irrational number

A prime number

Choose an answer

100x ⁹⁹

100x ¹⁰¹

-99x ⁹⁹

-100x ¹⁰¹

If n is odd then the middle terms in the expansion of (a + x)ⁿare

Choose an answer

What is the number of elements of the power set of {0, 1}

Choose an answer

1

2

3

4

Choose an answer

A,. B, C are coincident

A, B, C are collinear

Both A and B

None of these

(1 - x)³= ______

Choose an answer

1 + 3x + 3x²+ x³

1 + x + x²+ x³

1 - x + x²- x³

1 - 3x + 3x²- x³

The tangents drawn from the point P to a circle are real and coincident if

Choose an answer

P is on the circle

P is inside the circle

P is outside the circle

none of these

Choose an answer

Which of the following is a scalar

Choose an answer

weight

force

speed

momentum

The conic is a parabola if

Choose an answer

e < 1

e > 1

e = 1

None of these

Choose an answer

What is the period of cos 6x =?

Choose an answer

π/2

π/3

π/4

π

If Z₁ = 1+ i, Z₂ = 2+3i , then |Z₁ -Z₂| =?

Choose an answer

√5

√7

-1-2i

√3

If A = |a_ij| is (m x n) matrix then transpose of A is of the order

Choose an answer

m x m

m x n

n x n

n x m

If the intersecting plane is parallel to a generator of the cone, but intersects its one nappe only, the curve obtained is

Choose an answer

an ellipse

a hyperbola

a circle

a parabola

A person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is 45°. then which of the following statements is correct?

Choose an answer

Breadth of the river is twice the height of the tower

Breadth of the river an the height of the tower are the same

Breadth of the river is half of the height of the tower

None of these

Which of the following is a factor of x³- 3x²+ 2x - 6

Choose an answer

x + 2

x + 3

x - 3

x - 4

The point R dividing externally the line joining the points P(x₁, y₁) and Q(x₂, y₂) in the ratio k₁: k₂has the coordinates

Choose an answer

sin (α+β) + sin (α-β)

Choose an answer

2 sinαcosβ

sin (2αβ)

sinαcosα

None of these

The radius of the circle 2x²+ 2y²- 4x + 12 y+11=0 is:

Choose an answer

√4.5

√11

√29

√15

Choose an answer

a^x

a^xIn a

For two vector a and b, a+b = _______

Choose an answer

a b

b +a

b -a

None

The point of contact of the circles x²+ y² - 6x -6y+10 = 0 and x² + y² =2 is

Choose an answer

(-3 ,2)

(1 , 3)

( -2 , -1)

None of these

The line through the focus and perpendicular to the directrix is called ______ of the parabola

Choose an answer

axis

focal chord

tangent

latus rectum

Choose an answer

2x + 3

x²+ 3 + c

Two quadratic equation in which xy term is missing and the coefficients of x²and y²are equal, give a linear equation by ______

Choose an answer

Addition

Subtraction

Multiplication

Division

Area of the triangle whose vertices are (2,3),(0,1),(0,0) is

Choose an answer

6

2

4

1

If S = {3,6,9,12.......}, then

Choose an answer

S = Four multiples of 3

S = Set of even numbers

S = Set of prime numbers

S = All multiples of 3

Five engineering, four mathematics, two chemistry books are placed on a table at random.The probability that the books of each kind are all together is

Choose an answer

If A = [a_ij]_mxp and B = [a_ij]_pxn then order of BA is

Choose an answer

m x n

p x n

n x m

None of these

Choose an answer

trigonometric equation

conditional equation

identity

None

The number of subset of {0} is

Choose an answer

1

2

3

None

The points (x, y) which satisfy a linear inequality in two variables x and y from its

Choose an answer

domain

range

solution

none of these

If the domain of the function f: x⟶ 2x³+ 1 is {-1,2,3}, the range of the function is

Choose an answer

{3,2,5}

{1,3,9}

{-1,-2,-3}

{3,9,19}

The multiplicative inverse ofx^(-1) is

Choose an answer

1/a

a^-2

0

1

The difference of two consecutive terms of an A.P. is called ______

Choose an answer

General term

Common ratio

Common difference

None of these

Out of 10, 000 families with 4 children each, the number of families all of whose children are daughters is

Choose an answer

375

500

625

150

If x < y, 2x = A, and 2y = B, then

Choose an answer

A = B

A < B

A < x

B < y

1⁰= ______

Choose an answer

360'

60"

60'

3600'

i¹⁰¹ =

Choose an answer

i

i²

-i

-1

Choose an answer

0

1

none of these

The set of all positive even integers is

Choose an answer

Not a group

A group w.r.t subtraction

A group w.r.t division

A group w.r.t multiplication

If n is a positive integer then n! is

Choose an answer

(n - 1) (n - 2) .....3,.2.1

n(n - 1) (n - 2) ...3.2.1

n(n - 1 ) ( n -2) ... 3

None of these

The 5th term of (3a-2b)^-1is

Choose an answer

77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

Sin 90° = ______

Choose an answer

-1

0

1

Undefined

The set (Z, +) forms a group

Choose an answer

Forms a group w.r.t. addition

Non commutative group w.r.t. multiplication

Forms a group w.r.t multiplication

Doesn't form a group

Under multiplication, solution set of is

Choose an answer

Groupoid

Abelian group

Semi group

All of these

If A(a,b) lies on 3x +2y =13 and point B(b,a) lies on x-y =5 then equation of AB is

Choose an answer

x- y= 5

x+ y+ =5

x+ y= -5

5x +5y =21

Choose an answer

Null matrix

Triangular matrix

Unit matrix

Rectangular matrix

Choose an answer

Trival solution of homogeneous linear equation is

Choose an answer

(1, 1, 1)

(1, 2, 3)

(1, 3, 5)

a.b and c

Choose an answer

Associative property of addition

Commutative property of addition

Distributive property

Additive identity

Choose an answer

In school there are 150 students Out of these 80 students enrolled for mathematics class 50 enrolled for English class and 60 enrolled for Physics class The student enrolled for English cannot attend any other class but the students of mathematics and Physics can take two courses at a time Find the number of students who have taken both physics and mathematics.

Choose an answer

40

30

50

20

Matrices are represented by

Choose an answer

Natural numbers

Real numbers

Small letters

Capital letters

If S and P are the sum and the product of roots of a quadratic equation, then the quadratic equation is

Choose an answer

x²+ Sx - P = 0

x²- Sx + P = 0

x²- Sx - P = 0

X²+ Sx + P = 0

Period of tan x is ______

Choose an answer

-2, 1, 4, 7,.... is ______

Choose an answer

Harmonic sequence

Arithmetic sequence

Geometric sequence

Arithmetic series

The points (5, 0, 2), (2, -6, 0), (4, -9, 6) and (7, -3, 8) are vertices of a

Choose an answer

Square

Rhombus

Rectangle

Parallelogram

Choose an answer

2x

2

A = [3] is a/an

Choose an answer

Square matrix

Scalar matrix

Diagonal matrix

Identity matrix

Given two numbers a and b. Let A denote the single A.M. between these and S denote the sum of n A.M.'s between them. Then S/A depends upon

Choose an answer

n, a, b

n, a

n, b

n

Which of the following is not a solution of system of inequalities 2x- 3y ≤6,2x +y ≥ 2,x +2y ≤ 8, x ≥ 0,y ≥ 0

Choose an answer

(1,0)

(0,4)

(3,0)

(8,0)

The function f : x → y defined as f (x) = α ∀x∈ X,α∈ y is called

Choose an answer

Constant function

Polynomial function

Identity function

Linear function

If A is a skew-symmetric matrix of order n and P, any square matrix of order n.prove that P' AP is

Choose an answer

Skew-symmetric

Symmetric

Null

Diagonal

w²⁸+ w³⁸= ______

Choose an answer

0

1

w

-1

Both the roots of the equation (x -b) (x - c ) + (x -c) (x-a) +(x-a) (x-b) = 0 are always

Choose an answer

Positive

Negative

Real

None of these

Choose an answer

square root function

identity function

linear function

quadratic function

The points (5, 2, 4)(6, -1, 2) and (8, -7, k) are collinear if k is equal to

Choose an answer

-2

2

3

-1

The distance of the point (2,-3) from y-axis is

Choose an answer

2

-3

1

5

Derivative of a w.r.t x is

Choose an answer

0

1

x

sin h x = ___________

Choose an answer

∀a,b,c∈R and c>0,then

Choose an answer

a>b ⇒ ac < bc

a>b ⇒ ac > bc

a<b ⇒ ac > bc

None of these

Choose an answer

Reflexive property

Symmetric property

Cancellations property w.r.t. addition

Transitive property

The exact value of cos^-1 (-1) + cos^-1(1) =

Choose an answer

π

-π

π/2

π/3

2x = 3 is a conditional equation it is true for

Choose an answer

2

3

3/2

2/3

The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8) is

Choose an answer

x + y + z - 15 = 0

x - y + z - 15 = 0

x - y - z - 15 = 0

x + y + z + 15 = 0

Name the property used in 1000 x 1 = 1000

Choose an answer

additive inverse

multiplicative inverse

additive identity

multiplicative identity

How many arrangements of the letter of the word PAKPATTAN can be made

Choose an answer

The degree of differential equation is the power of the

Choose an answer

Lowest order derivative

Highest order derivative

Integral

All are correct

Inverse of the function y-10^x is

Choose an answer

y=lgx

y=lnx

x=10^y

Choose an answer

An expression

Rational fraction

Equation

Identity

x²+ x - 5 = 0 is

Choose an answer

A polynomial

An inequality

An identity

None

The number of words that can be formed out of the letters of the word ASSASSINATION is

Choose an answer

Optimize means ______ a quantity under certain constraints

Choose an answer

Minimize

Maximize

Maximize or minimize

None of these

Choose an answer

none of these

Which of the following integrals can be evaluated

Choose an answer

Tan 360° = _______

Choose an answer

-1

0

1

Undefined

Choose an answer

The period of cot 8x is

Choose an answer

π/10

9π/7

π/9

π/8

Optimal solution is found by evaluation the objective function at

Choose an answer

All point of feasible region

Corner point

Origin

None

If f(x) = x²-x then f(1) is

Choose an answer

0

1

2

3

If ax + bx + c =0 is satisfied by every value of x,then

Choose an answer

b = 0,c = 0

c = 0

b = 0

a = b = c = 0

The period of|sin⁡2x| is

Choose an answer

π/2

-π/2

π

π/3

The roots of (x - a)(x - b) = ab x² are always

Choose an answer

Real

Depends upon a

Depends upon b

Depends upon a and b

Choose an answer

Rational

Irrational

Even

Odd

Choose an answer

0

U

u/2

log u

A stationary point x is a relative exterma of y= f(x) is

Choose an answer

f^′′ (x) > 0

f^′′ (x) < 0

f^′′ (x) ≠ 0

f^′′(x) = 0

Choose an answer

x

y

Choose an answer

The remove the term involving xy, from 7x² -6√3xy+ 13y² -16 =0 the angel of rotation is

Choose an answer

θ = 30°

θ = 45°

θ = 60°

θ = 75°

The period of 2 cos x is

Choose an answer

30π

7π

5π

2π

Choose an answer

x-axis

y-axis

z-axis

None of these

AB is a vertical pole and C is its middle point. The end A is on the level ground and P is any point on the level ground other than A. the portion CB subtends and angleβat P. If AP : AB = 2 : 1 thenβ=

Choose an answer

n if n is even

0 for any natural number n

1 if in odd

None of these

Choose an answer

What is the axis of the parabola y²= 4ax?

Choose an answer

x = 0

y = 0

x = a

y = 0

The set of integer is

Choose an answer

Finite group

A group w.r.t addition

A group w.r.t multiplication

Not a group

For f(x) = x² + px +1, if f(3) = 3 then P =

Choose an answer

3/7

-2/5

-7/5

-7/3

If w is a cube root of unity then 1 + w + w²= ______

Choose an answer

1

2

0

-1

If ab > 0 and a < 0, which of the following is negative?

Choose an answer

b

-b

-a

(a - b)²

If the vector 2i + 4j - 7k and 2i + 6j + xk are perpendicular then x = ?

Choose an answer

0

2

4

7

If the lowe. limit of an integral is a constant and the upper limit is a variable, then the integral is a

Choose an answer

Constant function

Variable value

Function of upper limit

All

The equation of the normal to the circle x²+ y²= 25 at (4, 3) is

Choose an answer

3x - 4y =0

3x - 4y =5

4x + 3y = 5

4x + 3y = 25

To each element of a group there corresponds ............. inverse element

Choose an answer

Two

One

No

Three

Distance between A(3, 8), B(5, 6) is

Choose an answer

The length of the tangent from (2, 1) to the circle x²+ y²+ 4y + 3 = 0 is

Choose an answer

The point ________ is in the solution of the inequality 2x - 3y < 4

Choose an answer

(0, -2)

(1, -3)

(2, 2)

(3, 0)

The roots of ax² + bx + c = 0 are always unequal if

Choose an answer

b² - 4ac = 0

b² - 4ac ≠ 0

b² - 4ac > 0

b² - 4ac ≥ 0

A tower subtends an angleαat a point on the same level as the root of the tower and at a second point, b meters above the first, the angle of depression of the foot of the tower isβ. The height of the tower is

Choose an answer

b cotαtanβ

b tanαtanβ

b tanαcotβ

None of these

The function discontinuous at x = 0 is (1) tan x (II) cot x (III) sec x (iv)cosec x)

Choose an answer

I & III

I & IV

II & IV

II & III

cos 2α=

Choose an answer

sin²α+ cos²α

-cosθ

tanθ

None of these

What is the number of elements of the power set of { }

Choose an answer

0

1

2

3

What is the circular measure of the angle between the hands of a watch at 4 O'clock

Choose an answer

If you are looking someone on the ground from the top of a hill the angle formed is called angle of _______;

Choose an answer

Elevation

Depression

Right angle

None off these

How many arrangements of the letters of the word MATHEMATICS can be made

Choose an answer

The equation of the circle witch centre (-3, 5) and radius 7 is

Choose an answer

(x-3)²+ (y+5)²= 7²

(x-3)²+ (y-5)²= 7²

(x+3)²+ (y+5)²= 7²

(x+3)²+ (y-5)²= 7²

Choose an answer

quadrant I

quadrant II

quadrant III

quadrant IV

If a variable y dependents on a variable x is such a way that each value of x determines exactly one value of y, then we say that

Choose an answer

x is function of y

y is a function of x

y is independent variable

x is real valued function

(2, 1) is in the solution of the inequality

Choose an answer

2x + y > 7

x - y > 2

3x + 5y < 6

2x + y < 6

Sin 50°-sin 70°+sin 10° is equal to

Choose an answer

1

0

1/2

2

If b²- 4ac = 0 then the roots of the equation are

Choose an answer

Real and distinct

Real and equal

Imaginary

None of these

Choose an answer

120

5

4

6

(a, b) + (-a, -b) =

Choose an answer

(0,0)

(a, b)

(-a, -b)

(1, 1)

u,v,w and u x (v.w) are

Choose an answer

Equal

Parallel

Additive immense of each other

Meaningless

The coefficient of the third term of (8a-b)^1/3, after simplification is

Choose an answer

-228

1/288

1/220

-1/177

Choose an answer

- cos x

sin x

- sin x

sec x

cos h²x + sin h² x

Choose an answer

an even function

an odd function

an even and implicit function

neither even nor a odd

Choose an answer

sin x + c

-sin x + c

cos x + c

-cos x + c

Choose an answer

I andII quadrants

II andIII quadrants

III andIVquadrants

none of these

Choose an answer

36

360

24

6

The area between the x-axis the curve y -4x-x²is :

Choose an answer

32/2

15

18

21

The distance of the point (-2,3) from x-axis is

Choose an answer

-2

2

3

1

Choose an answer

none of these

f(x) = 1 is

Choose an answer

identity function

constant function

linear function

quadratic function

The periods of the function f(x) = x[x] is

Choose an answer

1

2

Non periodic

None of these

Choose an answer

-cosec²x

-sec²x

- cosec x cot x

cosec x

probability of a certain event is

Choose an answer

0

-1

1

∞

If s = 2t³- 3t²+ 15t - 8 is the equation of motion of a particle, then its initial velocity is

Choose an answer

8

15

-6

None

Choose an answer

The value of cos(cos-1 1/2) is

Choose an answer

1/2

√3/2

-1/2

1/√2

Number of combination of zero or more things out of n different things

Choose an answer

ⁿP_n

ⁿP_r

ⁿC_r

2ⁿ

If S_n is a definite number as n → ∞,then the geometric series is

Choose an answer

Convergent

Divergent

Oscillatroy

None of these

Choose an answer

0

Independent of a

Independent of b

Independent of c

In set builder notation the set {0,1,2,........100} can be written as

Choose an answer

{x / xε B ∧ x ≤ 100}

{x / x ∈ W ∧ x < 101}

{x / x ∈ Z ∧ x < 101}

The set of first 100 whole numbers

If n € N , then n(n+3) is always

Choose an answer

Multiple of 3

Multiple of 6

odd

even

Choose an answer

An empty set

Universal set

A singleton set

None of these

Choose an answer

By expressing sin 125° in terms of trigonometrical ratios, answer will be

Choose an answer

sin 65° = 0.9128

sin 55° = 0.8192

sin 70° = 0.5384

sin 72° = 0.1982

{x : x ε Z and x < 1} is

Choose an answer

Singleton set

A set with two points

Empty set

None of these

The no of term is the expansion of (a+x)^n-1 is

Choose an answer

n+1

n-1

n

n-2

The probability of getting a number between 1 and 100 which is divisible by 1 and itself if only is

Choose an answer

1 / 4

1 / 2

3 / 4

25 / 98

Choose an answer

f(x)g(x)- ∫g(x) f′(x) dx is equal to

Choose an answer

∫f(x)g′(x)dx

∫f′(x)g (x)dx

∫f′(x)g(x)′dx

∫f(x)g(x)dx

G is geometric mean between a and b if a, G, b is

Choose an answer

A.P.

G.P.

H.P.

None of these

cot(3π/2 -θ)=______;

Choose an answer

tanθ

cotθ

-tanθ

-cotθ

The value of i⁴ⁿ⁺¹

Choose an answer

1

-1

i

i²

If x-2 and x-1 both are factors of x³-3x³+2x-4p, then P must equal to

Choose an answer

1

2

0

-2

Choose an answer

Does not exist because f is unbounded

Is not attained even though f is bounded

Is equal to 1

Is equal to -1

(fog)′(x) =f′ (g(x))g′(x) is derivative by

Choose an answer

Chain rule

Reciprocal rule

Power rule

Product rule

Choose an answer

The law of sines

The law of consines

The law of tangents

None of these

Which is not included in the domain of cos^-1x

Choose an answer

0

1

-1

2

Which of the following is the subset of all sets?

Choose an answer

The point R dividing internally the line joining the points P(x₁, y₁) and Q(x₂, y₂) in the ratio K₁: K₂has the coordinates

Choose an answer

Number of terms in the expansion of (a+x)ⁿis

Choose an answer

n - 1

n + 1

n + 2

n + 3

The principal value of sin^-1[-√(√3) /2] is

Choose an answer

5π/3

-2π/3

-

π/3

If y = sin (ax + b), then fourth derivative of y with respect to x =

Choose an answer

a⁴cos (ax + b)

a⁴sin (ax + b)

-a⁴sin (ax + b)

a⁴tan (ax + b)

Choose an answer

Y = -x log x -x + c

Y = x log x + x

Y = x log x - x + c

None of these

If c = 2i+j+k and d= -1 + 4j +2k, then [c-d]=

Choose an answer

√7

√41

√19

√(2&7)

If D = {a} , the P(D) =

Choose an answer

{a}

∅

{∅,{a}}

{∅,a}

A farmer possesses 100 hectometers of land and wants to grow corn and wheat. Cultivations of corn requires 3 hours per hectometer while cultivation of wheat requires 2 hours per hectometer. Working hours cannot exceed 240. If he gets a profit of Rs. 20 per hectometer for corn and Rs. 15 per hectometer for wheat. The profit function for the farmer is

Choose an answer

P(x, y) = 20x + 15y

P(x, y) = 2x + 3y

P(x, y) = x + y

P(x, y) = 3x + 2y

If a,b,c are three non-coplanar vector then [a +b,b +c,c +a] = _____

Choose an answer

[a.b.c]

2[a,b,c]

[abc]^-2

2[abc]²

What is the conjugate of -7 -2i ?

Choose an answer

-7 + 2i

7 +2i

7 -2i

√53

The slope of x-axis is

Choose an answer

0

undefined

1

The root of the quadratic equation are

Choose an answer

3

2

1

4

The area between the x-axis and the curve y = x² + 1 from x = 1 to 2 is:

Choose an answer

15/6

15/4

10/4

10/3

The sixth term of the sequence 1,3,12,60....is

Choose an answer

1500

72

2160

2520

If f(x) = x + 1 then f(z²-1) is

Choose an answer

z²

z²+ 2

z²- 2

none of these

The number of the diagonals of a 6 sided figure is

Choose an answer

15

21

9

6

The identity element of a set X with respect to intersection in P(x) is

Choose an answer

X

Does not exist

∅

None of these

Choose an answer

The first three terms in the expansion of (1 - x)^-1are

Choose an answer

1 + x + x²

1 - x - x²

-1 -x +x²

1 - x + x²

Express as a sum or difference: 2 sin 5θcosθ

Choose an answer

cos 4θ- cos 2θ

sin 4θ+ sin 2θ

cos 4θ+ cos 2θ

sin 4θ- sin 2θ

cos 6θ + cos 2 θ =_______;

Choose an answer

-2sin 4θ sin 2θ

2cos4θ cos2θ

2sin4θ cos2θ

2cos4θ sin2θ

Choose an answer

Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

Choose an answer

3 x 2

2 x 3

3 x 3

2 x 2

The third term of the sequence a_n= (-1)^n-1(n-7) is ______

Choose an answer

8

4

-4

8

Choose an answer

If d₁is the distance between (0,0) and (1,2) and d₂is the distance between (0,0) and (2,1) then

Choose an answer

d₁= d₂

d₁<d₂

d_1>d₂

none of these

The multiplicative inverse of -3i is

Choose an answer

3i

-3i

-1/3i

1/3 i

P∉ A means

Choose an answer

Pis subset of A

Pis an element of A

P does not belongs to A

A does not element of P

Choose an answer

If P = {x/x = p/q where p,q∈ Z and q≠ 0}, then P is the set of

Choose an answer

Irrational numbers

Even numbers

Rational numbers

Whole numbers

Choose an answer

1+3x+6x² +10x³ +....=

Choose an answer

(1+x)^-3

(1-x)^-2

(1-x)^-3

(1+x)^-2

3, 6, 12,.... is

Choose an answer

A.P

G.P.

H.P.

None of these

If f(x) = x³- 2x²+ 4x -1, then f(-2) = ?

Choose an answer

0

-25

5

45

(x³-1/2x)⁶is

Choose an answer

15/16 x²

2/13 x²

17/7 x²

16/15 x²

Choose an answer

3

1

4

A fraction in which the degree of the numerator is less than the degree of the denominator is called

Choose an answer

Polynomial

Equation

Proper fraction

Improper fraction

i =

Choose an answer

1

-1

The sum of complex number (a,b) and (c,d) is

Choose an answer

A square matrix A = [aij] is upper triangular when

Choose an answer

cij = 0

bij = 0

aij = 0 for all i > j

dij = 0

Choose an answer

ⁿC_n-ris equal to

Choose an answer

n!

^n-1C_r

ⁿC_r

None of these

The number of permutation that can be formed from the letters of the word OBJECT is

Choose an answer

700

600

720

620

Choose an answer

25

16

5

0

Choose an answer

0

1

13

A point of a solution regions where two of its boundary lines intersect, is called:

Choose an answer

Vertex of the solution

Feasible point

Point of inequality

Null point of the solution region

Choose an answer

0

1

-2

10

The solution set of x²- 5x + 6 = 0 is

Choose an answer

{1, 3}

{2, 3}

{1, 2}

None of these

cosθ/2=

Choose an answer

0

1

1/2

Choose an answer

I

|A|

|A| I

None of these

Choose an answer

are real no

both are not real

are imaginary no

both are imaginary

The roots of the equation ax²+ bx + c = 0 are real and equal if

Choose an answer

b²- 4ac < 0

b²- 4ac = 0

b²- 4ac > 0

None of these

Choose an answer

A prime number

An integer

A whole number

An irrational number

The period of the trigonometric function y = sin x cos x is

Choose an answer

2π

π

4π

π / 2

Choose an answer

A³+ 3A²+ A - 91₃= 0

A³- 3A²+ A + 9I₃= 0

A³+ 3A²- A + 9I₃= 0

A³- 3A²- A + 9I₃= 0

Choose an answer

Rational fraction

Proper fraction

Improper rational fraction

None of these

i⁹ =

Choose an answer

i²

-1

1

i

If the roots of ax²+ bx + c =0 are equal in magnitude but opposite in sign, then

Choose an answer

a = 0

b = 0

c = 0

None of these

Domain of sin x is ______

Choose an answer

The transpose of a zero matrix is a ______

Choose an answer

Column matrix

Zero matrix

Row matrix

Scalar matrix

Period of sin x is

Choose an answer

3.5+5.4=5.4+3.5 =8.9 this property of addition is called

Choose an answer

additive identity

assoclative property

commulative property

closure property

The set {Z\ {0} } is group w.r.t

Choose an answer

Addition

Multiplication

Division

Subtraction

For three consecutive terms in A.P middle term is called

Choose an answer

A.M

nth term

Central term

None of these

The period of sin x/2 = Cos x/3 is

Choose an answer

2p

12p

13p

7p

1 radian = ______

Choose an answer

180°

90°

57.296°

60°

Choose an answer

A function which is to be maximized or minimized is called an

Choose an answer

Explicit function

Implicit function

Objective function

None

Choose an answer

Area of the circle with ends of a diameter at (-3,2) and (5,-6)

Choose an answer

128π sq. units

64π sq. units

32π sq.units

None of these

Which is the proper rational function

Choose an answer

The quadratic formula is

Choose an answer

The statement that a group can have more than one identity elements is

Choose an answer

True

False

Fallacious

Some times true

The 6th term of an arithmetic sequence whose first term is 3 and common difference in zero is

Choose an answer

18

6

3

0

If we have a statement "if p then q" then q is called

Choose an answer

Conclusion

Implication

Unknown

Hypothesis

The solution set of the equation 1 + Cos x = 0 is __________

Choose an answer

none of these

Co-ordinate of a point on the parabola y² = 8x whose focal distance is 4 are:

Choose an answer

(2 , 4)

(-2 ,-4)

(-2, 4)

(2,-4)

The law of sines can be used to solve oblique triangle when fooowing information is given:

Choose an answer

Two angles and a side

Two sides and an angle opposite one of the given sides

Two sides and the angle between two sided

Option a and b

tan^-1x > cot^-1x holds for

Choose an answer

x > 1

x < 1

x = 1

All values of x

Number of selections of n different things out of n

Choose an answer

1

ⁿP_r

n!

ⁿP_r

The point (1,3) is one solution of

Choose an answer

3x + 5y > 29

3x + 5y < 7

x + 2y < 4

x + 4y > 3

The polar form of complex number x ≠ I y =

Choose an answer

r cos θ+ r sin θ

r cos θ+ is sin θ

cos θ+ r sin θ

i cos θ+ i sin θ

Choose an answer

Two circles are said to be concentric if they have

Choose an answer

same radius

same chord

same centre

same diameter

x = r2, y = 1 are the parametric equation of

Choose an answer

Circle

Hyperbola

Ellipse

Parabola

The equation of the directrix of the parabola x²= 4ay is

Choose an answer

x + a = 0

x - a = 0

y + a = 0

y - a = 0

Choose an answer

The 60th part of one minute is called

Choose an answer

Degree

Second

Radiam

None of these

The number of different ways of describing a set is

Choose an answer

One

Two

Three

Four

If sin (πcosθ) = cos (πsinθ), then which of the following is correct?

Choose an answer

An integer is chosen at random from the number ranging from 1 to 50. the probability that the integer chosen is a multiple of 2 or 3 or 10 is

Choose an answer

3 / 10

5 / 10

7 / 10

9 / 10

A function from X to X is denoted as

Choose an answer

f : X to Y

f : Y to Y

Choose an answer

The point where the axis meets the parabola is called

Choose an answer

Directrix

Foucu

Chord

Vertix

(0,0) is in the solution of the inequality

Choose an answer

x + y > 3

x - y > 2

3x + 2y > 5

3x - 2y < 2

Choose an answer

The vertex of the parabola (xsin a -ycos a)² =4a(xcos a +ysin a) lies at

Choose an answer

(acos a,asin a)

(a,0)

(cos a,sin a)

(0,0)

Arithmetic mean between x - 3 and x + 5 is

Choose an answer

x + 1

x + 2

x + 3

x + 4

The area of the rhombus whose vertices are A(0,0),B(2,1),C(3,3),D(1,2) is

Choose an answer

36 square units

3 square units

6 square units

18 square units

3/2 is

Choose an answer

An irrational number

Whole number

A positive integer

A rational number

A square matrix A = [aij] is lower triangular matrix when:

Choose an answer

aij = 0 for all i < j

bij = 0

cij = 0

dij =0

If (x₁, y₁) and (x₂,y₂) are the end points of a diameter then the centre of the circle is

Choose an answer

The probability to get an odd number in a dice thrown once is

Choose an answer

6

1

1/6

1/2

Name the property used in 4 + 9 = 9 + 4

Choose an answer

Associative property of addition

Commutative property of addition

Distributive property

Additive identity

A conditional is regarded as false only when the antecedent is true and consequent is

Choose an answer

True

False

Known

Unknown

Choose an answer

1

2

3

4

If n is any positive integer then 2ⁿ> 2(n + 1) is true for all

Choose an answer

0

1

The range of the tangent function is

Choose an answer

all real numbers

-1 ≤ x ≥ 1

natural number

z⁺

If f(x) = x³- 2x²+ 4x -1 then f(2) is

Choose an answer

7

-16

16

-9

If x³- x²+ 5x+ 4 is divided by x - 2, then the reminder is

Choose an answer

0

2

18

14

A non-homogeneous linear system AX = B has no solution if

Choose an answer

|A| = 0

|A| ≠ 0

Rank (a) = no of variables

Rank > no of variables

Two unbiased dice are thrown. The probability that the total score is > 5 is

Choose an answer

1 / 18

7 / 18

13 / 18

11 / 18

The parametric equations of a circle are

Choose an answer

none of these

If n(A) = n then n(P(A)) is

Choose an answer

2n

n²

n/2

2ⁿ

3x + 4 > 0 is

Choose an answer

equation

inequality

identity

none of these

Choose an answer

The set (Q..)

Choose an answer

Forms a group

Does not form a group

Contains no additive indentity

Contains no additive inverse

Which of the following sets is finite

Choose an answer

The set of natural numbers between 3 and 10

The set of rational numbers between 3 and 10

The set of real numbers between 0 and 1

The set of rational numbers between 0 and 1

Which of the following has the same value as i¹¹³?

Choose an answer

i

-1

-i

1

A function from X to Y is written as

Choose an answer

f : X to Y

f : Y to Y

i¹⁰¹=

Choose an answer

i

i²

-i

-1

The set of the first elements of the orders pairs forming a relations is called its

Choose an answer

Relation in B

Range

Domain

Relation in A

Choose an answer

For graphing a linear inequality, solid line is drawn if the inequality involves the symbols:

Choose an answer

> or <

= or≠

= or >

The group of the quadratic equation is

Choose an answer

Straight line

Circle

Parabola

elipse

Choose an answer

The additive inverse of a matrix A is

Choose an answer

None of these

Domain of sinθis

Choose an answer

Set of real numbers

Set of complex numbers

Set of natural numbers

Set of even numbers

y=0 of the parabola y² = 4ax is the

Choose an answer

equation of directirx

Equatio of the tangent

Equation of axis

equation of latus rectum

The set of the first elements of the orders pairs forming a relation is called its

Choose an answer

Relation in B

Range

Domain

Relation In A

Choose an answer

π/ 2

π/ 3

π/ 4

π

sin 3a = ______;

Choose an answer

3sin a - 4sin³a

4sin a -3 sin³ a

3 cos³ a -cosa

4cos³ a - 3cos a

Choose an answer

1

-1

A function f is said to be an even if f(-x) =

Choose an answer

0

1

f(x)

-f(x)

Choose an answer

Three right angles is the angle of measure

Choose an answer

270°

180°

90°

270'

Let the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, ..... where n consecutive terms have the value n, then 1025th term is

Choose an answer

2⁹

2¹⁰

2¹¹

2⁸

Choose an answer

-1

0

2

1

Choose an answer

If 4 > b or a < b than a = b is a

Choose an answer

Additive property

Transitive property

Trichotomy property of inequality

None of above

1st four terms of the expansion (1-x)^-2are

Choose an answer

1 + 2x + 3x²+ 4x³

3x²+ 2x + 1

1 + 3x + 4x²+ 5x³

None of these

Domain of cosec x is ______

Choose an answer

Cosec 60° = ______

Choose an answer

The number of subsets of B = {1,2,3,4,5}

Choose an answer

10

32

16

5

The domain of y = cos^-1 x is

Choose an answer

-∞ < x < ∞

-1 ≤ x ≤ 1

x ≤ -1 or x ≥ 1

None of these

Domain of cosh x is

Choose an answer

R

R -{0}

[1,∞)

[0,∞)

A function whose range is just one elements is called

Choose an answer

One-one function

Constant function

Onto function

Identity function

Choose an answer

-3

-7

1

0

The real numbers which satisfy an inequality form its

Choose an answer

solution

coefficient

domain

range

The area of a sector with central angle of 0.5 radians in a circular region whose radius is 2m is

Choose an answer

For any equilateral r :R :η :r₁ :r₂ :r₃ =

Choose an answer

1:2:3:4:5

1:2:3:3:3

1:2:4:4:4

2 :1 :2 :2 :2

Each point of the feasible region is called

Choose an answer

Solution

feasible solution

Both a & b

None

Choose an answer

For any integer k, wⁿ= ______ when n = 3k

Choose an answer

1

2

0

-4

The expansion (1 + x)^-3holds when

Choose an answer

|x| > 1

|x| < 1

x < 1

x > 1

Choose an answer

The number of combinations of 10 different objects taken 8 objects at a time is

Choose an answer

90

45

55

50

Choose an answer

The solution of the quadratic equation x³-7x + 10=0, is

Choose an answer

2

5

2,5

7

A number H is said to be the H.M. between a and b if a, H, b are in

Choose an answer

A.P.

G. P.

H. P.

None of these

A second degree equation in which coefficients of x²and y²are equal and there is no product therm xy represents:

Choose an answer

a parabola

a circle

an ellipse

a pair of lines

A class contains nine boys and three girls, in how many ways can the teacher choose a committee of four?

Choose an answer

460

495

272

60

Choose an answer

tan 3x + c

cot 3x + c

- cot 3x + c

Choose an answer

0

1

2

4

Circle x² + y² - 2y -y = 0 and x² + y² - 8y -4 =0:

Choose an answer

Interesect

touch externally

touch internally

do not touch

Choose an answer

none of these

i^-(4n+2)= -------------------------------

Choose an answer

1

i

-1

-i

Choose an answer

8 . 7 . 6. 5 in factorial form is

Choose an answer

If z=(x,y) then z has no multiplicative inverse when

Choose an answer

x ≠ 0, y = 0

x = 0, y = 0

x = 0, y ≠ 0

None of these

The area of sector with central angle of 1 radians in a circular region whose radius is 2 m is

Choose an answer

p < r

p > rr

p + r < 0

p - r < 0

Choose an answer

a = a

a < a

a > a

a²= a

I f the focus is F ( 0,-a) and directrix is the line v=a, then equation of the parabola is:

Choose an answer

x² = 4ay

y² = 4ax

y² = -4ax

x² = 4ax

The seventh term of an A.P whose first term is P and common difference is q. is

Choose an answer

P-6q

P+6q

P-4q

P-nq

Choose an answer

(0.90)^1/2is equal to

Choose an answer

0.99

0.90

0.80

0.88

For each even natural number n (n²-1) is divisible by

Choose an answer

6

3

4

8

(0,1) is in the solution of the inequality

Choose an answer

3x + 2y > 8

2x - 3y < 4

2x + 3y > 5

x -2y < -5

The general term of a sequence is denoted by

Choose an answer

a₁

a_n

n

s_n

An ellipse slides between two lines at right angles to one another. The locus of its centre is :

Choose an answer

a parabola

an ellipse

a circle

a hyperbola

∀x,y∈ R and x < 0, y < 0, which one is true

Choose an answer

xy < o

xy = o

xy > o

None of these

Choose an answer

Domain of cotθis

Choose an answer

2x cos x²

-2x sin x²

- sin x²

2x sin x²

If S_rdenotes the sum of the first r terms of a G.P., then S_n, S_2n- S_n, S_3n- S_2nare in

Choose an answer

A.P.

G.P.

H.P.

None of these

If a statement S(n) is true for n = i where i is some natural number and the truth of S(n) for n = k > i implies the truth of S(n) for n = k +1 then S(n) is true for all positive integers

Choose an answer

Period of Tangent function is

Choose an answer

0°

-π

π

2π

The square matrix A is skew-symmetric when A' = 0

Choose an answer

-B

-C

-A

-D

Choose an answer

none of these

Choose an answer

0

1

-1

None of these

Choose an answer

In f(x) + c

f(x) + c

(a,0) x (c, 0) =

Choose an answer

(0,ac)

(ac, 0)

(0,0)

(a, c)

Choose an answer

8

1/56

56

None of these

Choose an answer

No term of a geometric sequence can be

Choose an answer

0

1

2

3

Choose an answer

A function F(x) is called even if

Choose an answer

F(x) = F (-x)

F(x) = F(-x)

F(x) = -F(x)

2F(x) = 0

The angles of elevation of the top of a tower at the top and the foot of a pole of height 10 m are 30° and 60° respectively. The height of the tower is

Choose an answer

10 m

15 m

20 m

None of these

Choose an answer

Less then 1

Equal to 1

Greater than 1 but less then 2

Greater then or equal to 2

Choose an answer

x = f(y)

y = f(x)

x = f(x)

y = f(y)

Choose an answer

c/a

-c/a

b/a

-b/a

If 3x⁴+4x³+x⁵is divided by x+1 , which of the followign is the remainder

Choose an answer

7

-7

6

1

If y=sin(ax+b) then y₄=________:

Choose an answer

sin⁴(ax+b)

a⁴sin(ax+b)

a⁴cos(ax+b)

None of these

If x, y, z are the pth, qth, rth terms of an A.P. and also of G.P., then x^y-z. y^z-x. z^x-yeqals

Choose an answer

xyz

0

1

None of these

Choose an answer

Polynomial of degree 0

Polynomial of degree 2

Quadratic equation

None of these

If f(x) = -x²then f(-2) is

Choose an answer

-2

2

-4

4

Range of tan x is ______

Choose an answer

[-1, -]

R

Negative real numbers

R - {x | - 1 < x < 1}

Choose an answer

The ratio in which the line y- x+ 2 =0 divides the line joining (3,-1) and (8,9) is

Choose an answer

2:3

-2:3

3:2

-3:2

Choose an answer

The equation |x +4| = x has solution

Choose an answer

x = -2

x = 2

x = -4

x = 4

A Geometric Series is divergent only if

Choose an answer

|r|>1

|r|≥1

|r|=1

None of these

The nth term of an A.P., is 12-4n. Its common difference is

Choose an answer

8

4

16

Choose an answer

for n€ N, 3^{2n + 7 is divisible by}

Choose an answer

7

8

9

10

Choose an answer

Symmetric property

Cancellation property w.r.t. multiplication

Reflexive property

Transitive property

The exterior angle of the interior angle C of he quadrilateral whose vertices are A(5,2),B(-2,3),C(-3,-4),D(4,-5) is

Choose an answer

30°

60°

45°

90°

Choose an answer

none of these

If |a x b|² + (a,b)² = _____

Choose an answer

|a|² + |b|²

|a|² - |b|²

|a|² |b|²

None

5 unbiased coins coins are tossed simultaneously. The probability of getting at least one head is

Choose an answer

1 / 32

31 / 32

1 / 16

None of these

An experiment yields 3 mutually exclusive and exhaustive events, B, C, if P(A) = 2P (B) = 3 P (C). then P(A) =

Choose an answer

1 / 11

2 / 11

3 / 11

6 / 11

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangement is

Choose an answer

⁶C₃x ⁴C₂

⁴C₂x ⁴P₃

⁴P₂x ⁶P₃

None of these

The synthetic division method is only used to divide a polynomial by

Choose an answer

quadratic equation

binomial

linear equation

monomial

The range of the principle cot function is

Choose an answer

______________ invented a symbolic way to write the statement "y is a function of x" as y= f(x)

Choose an answer

Leibniz

Newton

Euler

None of these

Choose an answer

360°

180°

90°

None of these

The extraction of cube root of a given number is a

Choose an answer

Unary Operation

Binary Operation

Relation

None of these

If a > b or a < b than a = b is a

Choose an answer

Additive property

Transitive property

Trichotomy property of inequality

Choose an answer

If n is not natural number, then the expansion (1 + x)ⁿis valid for

Choose an answer

The set {1,2,3,4......} is called

Choose an answer

Set of natural numbers

Set of whole numbers

Set of rational number

Set of irrational numbers

The period sin²θis

Choose an answer

π²

π

2π

π/2

If B⊆ A, then complement of B in A is B^c = -----------------------

Choose an answer

A-B

A∩B

B-A

A∪B

How many comittees of 5 numbers can be chosen from a group of 8 players person when each committee must include 2 particular persons

Choose an answer

8!

5!3!

5!

20

A ________ divides the plane into left and right half planes.

Choose an answer

Vertical line

Horizontal line

Non vertical line

Inequality

The modulus of a vector i-i+ k is:

Choose an answer

√3

1

√2

∞

Any horizontal line divided the plane into

Choose an answer

Left half plane

Upper and lower half planes

Infinite number of horizontal liens

None of these

Choose an answer

Consider the equation px² + qx + r = 0 where p,q,r are real The roots are equal in magnitude but opposite in sign when

Choose an answer

q = 0, r = 0,p ≠ 0

p = 0,qr ≠ 0

r = 0,pq ≠ 0

q = 0, pq ≠ 0

For a square matrix A, if A = A^t, then A is called

Choose an answer

Matrix

Transpose

Symmetric

Non-symmetric

If nis positive integers, then 2ⁿ>2n+1, only when

Choose an answer

n≤ 3

n≥ 3

n≤ 2

n≤ 1

An observer on the top of a cliff 200 m above the sea level, observes the angles of depression of two ships on opposite sides of the cliff to be 45° and 30°, respectively. The distance between the ships if the line joining them points to the base of cliff is

Choose an answer

For a positive integer n

Choose an answer

n! = n(n + 1)

n! = n(n+1)!

n! = n(n - 1 )

n! = n(n - 1)!

Choose an answer

5

10

20

30

The distance of point P(x,y) from focus in a parabola

y² =4ax, is:

Choose an answer

2a

a

x + a

x-a

Choose an answer

Multiplication property

Additive property

Trichotomy property

Transitive property of inequality

Choose an answer

The point of concurrency of the right bisectors of the sides of a triangle is called

Choose an answer

incentre

circum center

e-center

centroid

Choose an answer

2

5

7

None of these

Choose an answer

0

1

2

1/2

Cos 60° = ______

Choose an answer

1

2

1/2

3

Two cards are drawn at random without replacement. the probability that the first is a king and second is not a king is

Choose an answer

48 / 663

24 / 663

12 / 663

None of these

Choose an answer

The slope of y-axis is

Choose an answer

0

undefined

1

Choose an answer

How many necklaces can be made from 6 beads of different colours?

Choose an answer

120

60

24

15

Point ( /2,0) lies on trigonometric function f(x)=______;

Choose an answer

sinx

cosx

tanx

secx

The point (x₁, y₁) lies outside the circle x²+ y²+ 2gx + 2fy + c =0 if

Choose an answer

cos 315° = ______

Choose an answer

If the equation x²+2x-3=0 and x²+3x-k=0 have a common root then the non - zero value of k is

Choose an answer

1

3

2

4

Vector additon is:

Choose an answer

Commutative

Associative

Commutative and Associative

None of these

Choose an answer

The value of sin²20° + sin²70° is equal to

Choose an answer

1

2

-1

1/2

Choose an answer

[0, 0, 0]

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

The maximum value of 12 sinθ-9 sin²θis x

Choose an answer

3

4

5

None of these

Choose an answer

none of these

Choose an answer

none of these

Choose an answer

In a triangle if a > 45°,β > 30° then y cannot be

Choose an answer

90°

100°

10°

120°

Choose an answer

3/8

7/8

1/8

None

The term involving x⁴ in the expansion (3-2x) is

Choose an answer

217x⁴

15120x⁴

313x⁴

-25x⁴

Choose an answer

360°

180°

90°

None of these

(a^-1)^-1 =

Choose an answer

a^-1

a

-a

None of above

if the value of the sphere, v =4/3πr²^, then the which of the following statement is true?

Choose an answer

r is the function of v

v is the function ofπ

π is independent variable

None of these

One root of the equation cos x - x + 1/2 = 0 lies in the interval

Choose an answer

a cot(ax + b) + c

- a cot(ax + b) + c

How many term are there in the A.P, in which a₁ = 11 , a_n =68, d=3

Choose an answer

30

27

20

21

If 0 = {1,3,5.......}, then n (0) =

Choose an answer

99

odd integers

Even numbers

Infinite

If a^x= b^y= c^zand a, b, c are in G.P. then x, y, z are in

Choose an answer

A.P.

G.P.

H.P.

None of these

The approximate increase in the area of a circular disc if its diameter increased form 44cm to 44.4cm is

Choose an answer

0.4cm

8.8πcm

17.6 πcm

35.2πcm

The parabola y² =4ax open up if

Choose an answer

a<0

a≠0

a>0

All are incorrect

The first three terms in the expansion of (1 - x)^-3are

Choose an answer

1 + 3x + 6x²

1 - 3x + 6x²

-3 - 3x - 6x²

1 - 3x - 6x²

Choose an answer

A line joining two distinct points on a parabola is called a ______ of the parabola.

Choose an answer

Chord

Tangent

Lust rectum

directrix

Choose an answer

If α,β are non-real roots of ax2 + bx +c =0 (a,b,c ∈ Q),then

Choose an answer

α = β

αβ = 1

α = β

α = 1

The 7th term of (3⁸ + 6⁴x)^11/4 is

Choose an answer

-19217/3 x⁶

189/2 6⁴x

2227/12 x³

-19712/3 x⁶

Cofactor of an element aij denoted by Aij is

Choose an answer

(-2)^i+j

Mij

(-1)^i+j Mij

None of above

H₁, H₂, H₃, .... H_nare called n harmonic means between a and b if a, H₁, H₂, H₃, ... H_nb are in

Choose an answer

H.P.

G.P.

A.P.

None of these

Choose an answer

If |α i + (α+1)j +2k| =3 then value of α is

Choose an answer

1,2

-1,-2

1,-2

-1,2

Every set is an improper subset of

Choose an answer

Empty set

Equivalent set

Itself

Singleton set

The equation of the circle with centre (h, k) and radius r is

Choose an answer

(x+ h)²+ (y+ k)²= r²

(x+ h)²+ (y - k)²= r²

(x - h)²+ (y+ k)²= r²

(x - h)²+ (y - k)²= r²

If distance between (3,b) and (0,0) is 3 then b = _______

Choose an answer

3

9

0

if A = (x/x€ Q˄ 0 < x < 1}, the A is

Choose an answer

Infinite set

Finite set

Set of rational numbers

Set of real numbers

The conic is a parabola, when:

Choose an answer

ᵨ > 1

ᵨ < 1

ᵨ = 1

ᵨ = 0

Domain of tan x is ______

Choose an answer

If a force F = 2i + j +3k acts at point (1,-2,2) of a body then the moment of F about a pint lying on the line of action of the force is

Choose an answer

5

Equal to the moment of the force about origin

0

Cannot be found

When the angle between the ground and the sun is 30^𝜊,flag pole costss a shadow of 40 mg long. the height of the top of the flag is

Choose an answer

25m

23m

12m

29m

An equation in which at least one term contains dy/dx, d² y /dx²etc, is called.

Choose an answer

Differential equation

Initial condition

General solution

Singular equation

Choose an answer

0

1

-1

None of these

1/3 is a decimal

Choose an answer

Recurring

Terminating

Non-terminating

None of the above

Which of the following statement is true?

Choose an answer

A set is a collection of non-empty object

A set is a collection of only numbers

a set is any collection of things

a set is well-defined collection of objects

If a,β are the roots of the equation x² + kx +12 = 0 such that a - β = 1, the value of k is

Choose an answer

0

±1

±5

±7

The sum of the roots of the equation x² -6x +2 = 0 is

Choose an answer

-6

2

-2

6

A rule or correspondence that assigns to each element x in X a unique element y in Y is called a function from

Choose an answer

X to X

X to Y

Y to X

none of these

If (0, 0) and (0, -1) are end points of a diameter, then the equation of the circle is

Choose an answer

0

undefined

Choose an answer

none of these

Choose an answer

2

4

8

16

There are two middle terms in the expansion of (a+x)ⁿ if n is

Choose an answer

Even +ve integer

+ve integer

Odd +ve integer

All

If a₁, r and a_nare the first term, common ratio and the nth term respectively of a G. P. then a_n=

Choose an answer

a₁rⁿ

a₁r^n-1

a₁rⁿ⁺¹

a₁r

Choose an answer

15

15 i

-15 i

-15

Choose an answer

QUQ'

Choose an answer

If the vertex of the parabola is the origin and directrix is x+5 = 0 . then its latus rectum is:

Choose an answer

10

5

0

20

Roots of the equation x²+ 2x + 3 = 0 are

Choose an answer

Real and equal

Real and distinct

Complex

None of these

If n∈Z⁺ then(a+x)ⁿ is a/an

Choose an answer

Finite series

Convergent series

Infinite series

Divergent series

Choose an answer

Rational

Irrational

Non-real

Zero

The principal value of sin-1√(3/2) is

Choose an answer

-π/3

π/3

2π/3

π/2

Minor of an element a_ijis denoted by

Choose an answer

M_ij

A_ij

|A|

None of these

Choose an answer

The consecutive terms of a progressions are 30, 24, 20. The next term of the progression is

Choose an answer

Number of permutations of n distinct objects taken r(<n - 3) at a time which exclude 3(<n) particular objects is

Choose an answer

3! P(n, r - 3)

P(n, 3) P(n, r - 3)

P(r, r)P(n, r - 3)

P(n - 3, r)

The proposition S(n) is true ∀n∈N,S(k+1) true when ______is true

Choose an answer

S(1)

Both a & c

S(k)

None

The set of rational numbers is subset of

Choose an answer

The set of natural numbers

The set of real numbers

The set of integers

The set of whole numbers

Choose an answer

(a^-1)^-1=

Choose an answer

a^-1

a

-a

None of above

Choose an answer

cot x + c

tan x + c

-cot x + c

-tan x + c

(A ∩ B)^c =

Choose an answer

A ∩ B

(A ∪ B)^c

A^c∪B^c

Φ

If e,e′ be the eccentricities of two conics S=0 and S′ =0 and if e² +e′²=3 then both S and S′ can be

Choose an answer

Hyperbola

Parabolas

Ellipses

None of these

How many arrangements of the letters of the word MI SSI PPI, taken all together can be made?

Choose an answer

The set (Q, .)

Choose an answer

Forms a group

Does not form a group

Contains no additive identity

Contains no additive inverse

i³=

Choose an answer

-1

i

-i

1

Choose an answer

If sinθand cosθare the roots of the equation ax²- bx + c = 0, then a, b, c satisfy the relation

Choose an answer

b²- a²= 2ac

A²- b²= 2ac

A²+ b²= c²

B²+ a²= 2ac

Choose an answer

The lines that form the cone are called its:

Choose an answer

Generation

Circular cone

nappes

conics

The first three terms in the expansion of (1 + x)^-2are ______

Choose an answer

1 - 2x + 3x²

1 - 2x - 3x²

1 + 2x + 3x²

-2 -2x + 3x²

Range of 3 cot x is ______

Choose an answer

[-1, 1]

[-3, 3]

R

None of these

For the equation |x²| + |x| -6 =0, the roots are

Choose an answer

One and only one real number

Real with sum one

Real with sum zero

Real with product zero

Choose an answer

Addition

Subtraction

Multiplication

None of these

If sin A = cos A, 0°<A<90° then A is equal to

Choose an answer

1

1/2

0

None of these

In (x + iy) x is the known as

Choose an answer

Imaginary part of complex number

Real part of complex number

Complex number

None of above

Choose an answer

If A is a subset of B and B contains at least one element which is not an element of A, then A is said to be

Choose an answer

Improper subset of B

Super set of B

Proper subset of B

None of these

Choose an answer

The distance between the points (0,0) and (x,y) is

Choose an answer

x²+ y²

x

y

Choose an answer

The law of sines

The law of tangents

The pythagorus theorem

None of these

Range of sinθis

Choose an answer

The set of all points in the plane that are equally distant from a fixed point to called a

Choose an answer

Parabola

ellipse

Hyperbola

Circle

sinα=

Choose an answer

2 sinαcosα

2 sinαcosβ

2 sinα/2 cosα/2

1+ tan²α/2

Choose an answer

quadratic function

constant function

linear function

exponential function

Choose an answer

Two real roots

Two positive roots

Two negative roots

One positive and one negative root

For a square matrix A, if A = A^t, then A is called

Choose an answer

matrix

Transpose

Symmetric

Non-symmetric

Φset is the ______ of all sets?

Choose an answer

Subset

Union

Universal

Intersection

Choose an answer

Diagonal matrix

Scalar matrix

Triangular matrix

Identity matrix

The coefficient of xⁿ in the expansion of (1-x)^-1 is

Choose an answer

(-1)ⁿ2ⁿ

1

(-1)ⁿ(n+1)

(n+1)

Considering Cosine Rule of any triangle ABC, possible measures of angle A includes

Choose an answer

Angle A is obtuse

Angle A is acute

Angle A is right-angle

All of above

Choose an answer

none of these

Choose an answer

0

1

-1

None

Choose an answer

A conditional "if p then q" is denoted by

Choose an answer

In a country, 55% of the male population has houses in cities while 30% have houses both in cities and in village. Find the percentage of the population that has house only in villages.

Choose an answer

45

30

25

50

If a statement S(n) is true for n = 1 and the truth of S(n) for n = k implies the truth of S(n) for = k + 1, then S(n) is true for all

Choose an answer

Real numbers n

Integers n

Positive integers n

None of these

Every prime number is also

Choose an answer

Rational number

Even number

Irrational number

Multiple of two numbers

Choose an answer

Commutative law of multiplication

Closure law of multiplication

Associative law of multiplication

Multiplication identity

√-1b =?

Choose an answer

b i

-i b

b²

i√b

Choose an answer

Principle of equality of Fractions

Rule for product of fraction

Golden rule of fraction

Rule of quotient of Fraction

Domain of 3 sin x is ______

Choose an answer

[-3, 3]

R

Positive real numbers

None of these

In R, the additive identity is

Choose an answer

0

1

-1

None

Domain of y = scs x is

Choose an answer

R - nπ, nε1

R

All negative integers

None of these

Choose an answer

The sun of the four fourth roots of unity is

Choose an answer

4

3

1

0

Choose an answer

0

1

If the function y=2x -3, what is the preimage of 11?

Choose an answer

11

7

5

2

In the function f: A⟶B, the elements of a are called

Choose an answer

Images

Pre-images

ranges

Parameters

Choose an answer

none of these

Choose an answer

Improper rational fraction

Rational fraction

Proper rational fraction

None of above

If x³+ ax²- a²x - a³is divided by x + a, then the remainder is

Choose an answer

-a³

a³

2a³

0

Choose an answer

Derivative of x³w.r.t x is

Choose an answer

0

1

3x²

x³

Choose an answer

If Proj_vu = Proj_uv, then

Choose an answer

U and v are parallel

|u|=|v|

U and v re perpendicular

One of u or v

Choose an answer

If f(α) = b² and g (c) =d where c=b² then (gof)(a) is

Choose an answer

α

c

b

d

Which of the following is a vector.

Choose an answer

energy

force

work

power

Choose an answer

cos 2x

2 cos 2x

2 sin2x

-2 cos2x

The set of months in a year beginning with S.

Choose an answer

{September, October, November}

Singleton set

Null set

Empty set

In the interval 0≤ x ≤ π, the sine is

Choose an answer

Not a function

Not defined

Infinity

Not one-to-one function

The maximum value of the quadratic function f(x) = 2 x2-4x+7,is

Choose an answer

3

5

-3

-5

Choose an answer

The eccentricity of the parabola y²= -8x is

Choose an answer

-2

2

-1

1

If A is a non singular matrix then A^-1= ______

Choose an answer

The point which is closet to the focus of a parabola is:

Choose an answer

vertex

Chord

Focus

Directix

The multiplicative inverse of 1 - 2i is

Choose an answer

If sin 6θ+ sin 4θ+ sin 2θ, thenθ=

Choose an answer

The total number of subsets that can be formed out of the set {a, b, c} is

Choose an answer

1

4

8

12

Choose an answer

-1

0

1

undefined

The modulus of 12-5i is:

Choose an answer

7

13

√7

119

The system of measurement in which the angle is measured in degrees, minutes and seconds is called the

Choose an answer

circular system

CGS system

sexagesimal system

none of these

The condition for ax² + bx c to be expressed as the product of linear polynomials is

Choose an answer

b⁴ - 4ac =0

b⁴ - 4ac ≥0

b⁴ - 4ac <0

b⁴ = 4ac

The line y = 4x + c touches the hyperbola x²- y²= 1 if

Choose an answer

An equation of the form ax + by = k is homogeneous linear equation when

Choose an answer

b = 0, a = 0

a = 0,b ≠ 0

b = -0,a ≠ 0

a ≠ 0,b ≠ 0, k = 0

Choose an answer

π is the ration of

Choose an answer

Area of a circle to its diameter

Area of a circle to its radius

Circumference of a circle to its diameter

Circumference of circle to its radius

A prime number can be a factor of a square only if it occurs in the square at least

Choose an answer

Once

Thirce

Twice

None of these

A cone is generated by all lines through a fixed point and the circumference of

Choose an answer

a Circle

an ellipse

a Hyperbola

None of these

Every real number is

Choose an answer

a positive integer

a rational number

a negative integer

a complex number

Two sets A and B are said to be disjoint if

Choose an answer

The set of integer is

Choose an answer

Finite group

A group w.r.t addition

A group w.r.t multiplication

Not a group

sin(π+θ)=_______;

Choose an answer

sinθ

cosθ

-sinθ

-cosθ

Two balanced dice are tossed once, the sample space when the integers on the faces of two dice are the same is

Choose an answer

{(1, 1), (2, 2), (3, 3)}

{(4, 4), (5, 5), (6, 6)}

{(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}

None of these

Choose an answer

Singular

Non-singular

Adjoint

None of above

Choose an answer

If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is

Choose an answer

an ellipse

a hyperbola

a circle

a parabola

Choose an answer

Reflexive property

Symmetric property

Transitive property

Additive property

If a=5j + 2j,b=2i -3j, then|a+2b|=

Choose an answer

√21

√97

√39

None of these

Choose an answer

Cofactor of an element a_ijis defined by

Choose an answer

(-1)^i+j|A|

(-1)^i+jM_ij

(-1)^i+jM^-1

None of these

Choose an answer

f(x) = 3x/x² + 1 is:

Choose an answer

an even function

an odd function

an even and implicit function

neither even nor a odd

The expansion of (1 - 3x)^-1is valid if

Choose an answer

| x | < 1

| x | < 3

| x | < 1/3

None of these

Choose an answer

Principle of equality of fractions

Rule for product of fractions

Golden rule of fractions

Rule for quotient of fractions

Choose an answer

image

pre-image

constant

none of these

Z' is a

Choose an answer

Infinite set

Finite set

Singleton set

Set of all integers

For any real numbers x,y,xy=o ⇒

Choose an answer

x ≠ 0 ∧ y ≠ 0

x = 0 ∨ y = 0

x = 0

y = 0

For Cosine Rule of any triangle ABC, b²is equal to

Choose an answer

a²- c²+ 2ab cos A

a³+ c³- 3ab cos A

a²+ c²- 2ac cos B

a²- c²4bc cos A

What is the 26th term of the sequence, if its general term is a_{n = (-1)}ⁿ⁺¹

Choose an answer

2

26

27

1

Sum of two quantities is at least 20 is denoted by

Choose an answer

x +y =20

x +y ≥ 20

x +y ≠ 20

x +y ≤20

The set of first elements of the ordered pairs in a relation is called its

Choose an answer

domain

range

relation

function

A function whose range is just one element is called

Choose an answer

One-one function

Constant function

Onto function

Identity function

14 is not a

Choose an answer

Prime number

Whole number

Even number

Real number

6 is

Choose an answer

A prime integer

An irrational number

A rational number

An odd integer

An infinite sequence has no

Choose an answer

nth term

Last term

Sum

None of these

The set {x|x∈N_∧x-4=0} in tabular form is

Choose an answer

{-4}

{0}

{}

None of these

IfΔABC is right, law of cosine reduce to

Choose an answer

Law of sine

Law of tangent

Phthogorous theorem

Hero's formula

The mid point of the line joining the points P(x₁, y₁) and Q(x₂, y₂) is

Choose an answer

The set {0,-1} hold closure property under

Choose an answer

Addition

Both a & c

Multiplication

None of these

Choose an answer

Number of ways of writing the letters of WORD taken all at a time is

Choose an answer

24

4

12

6

Through how many radians does the minute hand of a clock turn in one hour

Choose an answer

sin^-1[-1/2] = ______

Choose an answer

If a,b c are sides of a triangle taken in order then a x b =

Choose an answer

b x c

b x a

c x a

Both a & b

Domain of y = cot x = ______

Choose an answer

w²⁹= ______

Choose an answer

0

1

w

w²

Choose an answer

The parabola y²= x is symmetric about

Choose an answer

x-axis

y-axis

Both x and y-axis

The line y = x

If a set S contains "n" elements then P (S) has ...... number of elements

Choose an answer

2ⁿ

2²ⁿ

2 . n

n²

Choose an answer

Roots of the equation x²- 7x + 10 = 0 are

Choose an answer

{2, 5}

{-2, 5}

{2,5}

{-2,-5}

The period of|sin⁡2x| is

Choose an answer

π/2

-π/2

π

π/3

In R the right cancellation property w.r.t. addition is

Choose an answer

Power set of X i.e P(X) _______ under the binary operation of union U

Choose an answer

Forms a group

Does not form a group

Has no identity element

Infinite set although X is infinite

Multiplicative inverse of "1" is

Choose an answer

+- 1

0

1

None of these

The 26th term of the A.P -2,-4,10,.............is

Choose an answer

136

-136

148

-148

Choose an answer

A rational number

A natural number

An irrational number

An integer

The equation of the circle wit (-1, 1) and radius 2 is

Choose an answer

The law of consines is

Choose an answer

If (0, 0) and (1, 0) are the end points of a diameter, then the equation of the circle is

Choose an answer

If the cone is cut by a plane perpendicular to the axis of the conec, then the section is a:

Choose an answer

Circle

ellipse

hyperbola

parabola

Choose an answer

An ellipse

A parabola

A circle

A hyperbola

Choose an answer

Reciprocal equation

Exponential equation

Radical equation

None of these

The equation (cos p - 1)x²+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval

Choose an answer

(0, 2π)

(-π, -0)

(0,π)

None of these

The slope of the normal at (5 cos, 0, 5 sin 0) to the circle. x²+y² = 25 is:

Choose an answer

tan𝜽

cos𝜽 /sin𝜽

-cot𝜽

- tan𝜽

Choose an answer

30°

45°

60°

75°

A set having only one element is called

Choose an answer

An empty set

Universal set

A singleton set

A power set

csc(^-π/2) = __________;

Choose an answer

0

1

-1

Undefined

Choose an answer

The point ________ is in the solution of the inequality 4x - 3y < 2

Choose an answer

(0,1)

(2,1)

(2,2)

(3,3)

Choose an answer

a ______quantity is one that possesses both magnitude and direction.

Choose an answer

Scalar

Vector

Segment

None of these

Which one is quadrantal angle

Choose an answer

8181710°

2345°

-8181180°

-2344°

The number of solution of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is

Choose an answer

0

1

2

3

Riaz, Saba. Maria, Shehzad are to give speeches in a class. The teacher can arrange the order of their presentation in

Choose an answer

4 ways

12 ways

256 ways

24 ways

The parabola y2 + 2y + x = 0 lie in _____ quadrant.

Choose an answer

First

Second

Third

Fourth

If a₁= a₂= 2, a_n= a_n-1- 1 (n > 2), then a₅is

Choose an answer

1

0

-1

-2

Choose an answer

1

1/2

0

None

Given two independent event A and B such that P(A) = 0.30 and P(B) = 0.60. Probability of getting neither A nor B is

Choose an answer

0.28

0.13

0.12

0.42

The equation x²+ y²- 8x+ 6y+ 25= 0 represents

Choose an answer

A circle

A pair of straight lines

A point

None of these

Composition of functions is

Choose an answer

Non-commutative (fg ≠ gf)

non-associative [8(fh) ≠ (8f)h]

Commutative (fg = gf)

f of-1 ≠ 1

If B-A≠φ , then n(B-A) is equal to

Choose an answer

n(a)+n(c)

n(c)-n(a)

n(a)-n(c)

None of these

Choose an answer

(2x+a+b+c)

(a+b+c)

(a+b+c+x)

0

I f a =5i + 2j, then|a| =

Choose an answer

√13

√7

1/√13

√29

Choose an answer

Number of lines passing through three non-collinear points is

Choose an answer

2

3

1

0

∞

Choose an answer

none of these

If P is a proposition then its negative is denoted by

Choose an answer

a.a^-1= a^-1.a = 1 is a

Choose an answer

Commutative law of multiplication

Multiplication identity

Associative law of multiplication

Multiplication inverse

Choose an answer

π/ 4

π/ 6

π/ 3

2π/ 3

If a is any real number and a = a is called

Choose an answer

symmetric property

Trichotomy Properties

Transitive Property

Reflexive Properties

The domain of y =√(x^2-9) is

Choose an answer

R

(0 , +∞)

(-∞ , -3 )∪ (3 , +∞)

(0 ,∞)

Which element is the additive inverse of (a, b) in Complex numbers?

Choose an answer

(a, 0)

(0, b)

(a, b)

(-a, -b)

To express a single rational fraction as a sum of two or more single rational fractions which are called

Choose an answer

improper fractions

Partial fractions

mixed form

Polynomials

Choose an answer

(3, 1, -2)

(3, -2, 1)

(2, -1, 3)

(-1, -2, -3)

Choose an answer

(g,f)

(-g,f)

(g,-f)

(-g,-f)

Choose an answer

(x +a)(x +b)(x +c)(x +) = k, k ≠0 is reducible to quadratic form only if

Choose an answer

a+b=c+d

a+c=b+d

a+d=b+c

All are correct

A die is thrown, the probability that the dots on the top are prime numbers or odd numbers is

Choose an answer

1/2

2/3

1/3

2/5

If in the expansion of (1+x)ⁿ, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x=

Choose an answer

4

5

6

7

Choose an answer

Rational number is a number which can be written as a terminating decimal fraction or a

Choose an answer

Non-terminating decimal fraction

Non-recurring

Recurring decimal fraction

a, b and c

Sum of first n terms of an arithmetic series is

Choose an answer

The middle term(s) of (a+x)¹¹ is

Choose an answer

6^th term

6^thor 7^th

7^thterm

6^thand 7^th

Choose an answer

Such fraction which can not be written in the form ofp⁄q where p,q and q≠ 0,such fractions are called.

Choose an answer

Fractinal numbers

Rational Numbers

Even Numbers

Whole Numbers

The distance of the point (2,3) from y-axis is

Choose an answer

2

3

5

The first three terms in the expansion of (1 + x)³are

Choose an answer

1 + 3x +6x²

1- 3x + 6x²\

-3 -3x -6x²

1- 3x -6x²

s > t then

Choose an answer

(s - t)²> (t - s)²

(s - t)²< (t - s)²

(s - t)²= (t - s)²

None

Choose an answer

5

15

10

20

What is the period of 5 cot x=?

Choose an answer

π

-π

π/2

2π

if Z₁ = 1+i, Z₂ = 2 = 2+3i, then |Z₂ -Z₁| =

Choose an answer

√3 i

√7

-2-i

√5

In one hour, the minute hand of a clock turns through

Choose an answer

Rational

Irrational

Natural

Odd

ab > 0 and a > 0 then

Choose an answer

a > b

a < b

a = b

None

Choose an answer

n!

0!

1

None of these

Choose an answer

0

2

4/3

5/3

Domain of cosθis

Choose an answer

Set of odd numbers

Set of integers

Set of real numbers

Set of complex numbers

Choose an answer

1

3

2-i

-1

Choose an answer

Derivative of sin x w.r.t. sin x is

Choose an answer

0

1

sin x

cos x

Choose an answer

A finite non-empty set

Null set

Both a and b

None of these

The perpendicular bisector of any chord of a circle

Choose an answer

Passes through the centre of the circle

Does not pass through the centre of the circle

May or may not pass through the centre of the circle

None of these

The value of sin-1 24/25 is equal to

Choose an answer

csc^-1 25/24

sec^-1 24/25

2 tan^-1 24/25

2cos^-14/5

If (2, 3) is the mid point of (a, 3) and (5, b) then

Choose an answer

a = 1 , b = -3

a = -1 , b = 3

a = 1 , b =3

a = -1 , b = -3

The only function which is both even and odd is

Choose an answer

f(x) = α

f(x) = x

f(x) =0

Both A & B

(1,0) is in the solution of the inequality

Choose an answer

3x + 2y > 8

2x - 3y < 4

2x + 3y > 3

x - 2y < -5

Choose an answer

The numbers of G₁, G₂, G₃...... G_nare called n geometric means between a and b is a, G₁, G_2,G₃, ... G_n, b are in

Choose an answer

H.P.

A.P.

G.P.

None of these

If the matrices A and B are conformable for multiplication then (AB)^t= ______

Choose an answer

AB

A^tB^t

B^tA^t

A^tB

The seventh term of (x3+1/x)⁸is

Choose an answer

71

-22

27

28

The sides of a right angled triangle are in A.P The ratio of sides is

Choose an answer

1:2:3

3:4:5

2:3:4

5:8:3

Choose an answer

The set of real roots of the equation log_{(5x + 4)}(2x +3)³- log_{(2x + 3)}(10x²+ 23x + 12) = 1 is

Choose an answer

{-1}

{-3/5}

Empty set

{-1/3}

Which is in the solution set of 4x - 3y < 2

Choose an answer

(3, 0)

(4, 1)

(1, 3)

None

A vector with magnitude one is called

Choose an answer

constant vector

unit vector

zero vector

null vector

The complement of set A relative to universal set U is the set

Choose an answer

The probability to get an odd number in a dice thrown once is

Choose an answer

1/2

1/6

1/3

2

√2 +√3 +√5) = (√2 +√3 +√5: this property is called

Choose an answer

associative property w.r.t addition

commutative property

Closure property w.r.t addition

Additive identity

Choose an answer

In(x²- x + 1)⁴+ c

Choose an answer

1

2

3

4

For the parabola the line through focus and perpendicular to the directrix is called

Choose an answer

Tangent

Vertex

Axis

None

Which of the following is factor of x11+a11, where n is an odd integer

Choose an answer

x-a

x+a

2x-a

2x+a

Choose an answer

None of these

PQ is a post of given height a, and AB is a tower at some distance;αandβare the angles of elevation of B, the top of the tower, at P and Q respectively. The height of the tower and its distance from the post are

Choose an answer

0

-1

1

-2

Choose an answer

a sec(ax + b) + c

- a sec(ax + b) + c

The property used in -3 <-2 ⇒0 <1

Choose an answer

Commutative property

Additive property of inequality

Additive inverse

Additive identity

If y = 2^x , then

Choose an answer

y₁ -ln2y = 0

y₂ -(ln2)² y = 0

y₂ -(ln2)y₁ = 0

All are correct

The value of x, and y, when (x + iy)²= 5 + 4i

Choose an answer

X = 2, y = 1

X = -2, y = 1

X = 2, y = -1

X = 2, y = 2

Decimal part of irrational number is

Choose an answer

Terminating

Repeating only

Neither repeating nor terminating

Repeating and terminating

Choose an answer

images

pre-images

constants

none of these

3x + 4 < 0 is

Choose an answer

inequality

equation

identity

not inequality

sin 2 α=

Choose an answer

Every real number is

Choose an answer

A complex number

A rational number

A natural number

A prime number

Sine rule for a triangle states that

Choose an answer

a/sin A = b/sin B = c/sin C

sin A/a = sin B/b = sin C/c

a/sin A + b/sin B + c/sin C

2a/sin A = 2b/sin B = 2c/sin C

The roots of the equation ax²+ bx + c = 0 are complex/imaginary if

Choose an answer

b²- 4ac < 0

b²- 4ac = 0

b²- 4ac > 0

None of these

The graph of the linear equation of the form ax =by = c is a line which divided the plane into:

Choose an answer

Two similar regions

Two disjoint regions

Four equal parts

One region

Choose an answer

sec x tan x

-cosec x cot x

sec²x

-sin x

a.a^-1 = a^-1.a = 1 is a

Choose an answer

Commutative law of multiplication

Multiplicative identity

Associative law of multiplication

Multiplicative inverse

The first three terms in the expansion of (1 - x)^-2are

Choose an answer

1 - 2x + 3x²

1 - 2x - 3x²

1 + 2x + 3x²

-2 - 2x +3x²

Ifθ= 60° then

Choose an answer

sinθ= 1/2

tanθ= cot 30°

θ=π/4

secθ= 4

cos (180° -θ)=

Choose an answer

sinθ

- cosθ

- sinθ

None of above

Choose an answer

A complex number

A rational number

A natural number

An irrational number

Choose an answer

For any set B, BUB' is

Choose an answer

Is set B

Set B'

Universal set

None of these

If ∀a,b ε R,then a +b ε R is a property

Choose an answer

Closure law of addition

Associative law of addition

Additive inverse

Additive identity

The line y = 2 x + c is a tangent to the parabola y²= 16 x if c equals

Choose an answer

-2

-1

0

2

If y is an image of x under the function f, then we write

Choose an answer

y = f(x)

x = f(y)

y = x

none of these

The equations of the line thro' the point (2, 3, -5) and equally inclined to the axis are

Choose an answer

The nth term of a G.P. is

Choose an answer

a₁rⁿ

a₁rⁿ⁺¹

a₁r^n-1

a₁r^-n

Cos 0° = ______

Choose an answer

-1

0

1

Undefined

A,G,H are in

Choose an answer

A.P

G.P

H.P

None of these

A matrix with a single row is called a

Choose an answer

Column matrix

Row matrix

Null matrix

Identity matrix

sin(a + β)+sin(a - β) =_____;

Choose an answer

2cosa cosβ

2sina cosβ

2cosa sinβ

-2sina sinβ

Choose an answer

cosec x + c

-cosec x + c

-sec x + c

sec x + c

In any triangle ABC,with usual notation αsinβ =____;

Choose an answer

b sinα

bsinβ

αsinα

None of these

How many arrangements of the letters of the word ADDING can be made

Choose an answer

Z is the set of integers, (z, *) is a group with a * b = a + b + 1, a, b∈G. then inverse of a is

Choose an answer

-a

a + 1

-2 -a

None of these

The equation |x + 4| = x has solution

Choose an answer

x = -2

x = 2

x = -4

x = 4

Choose an answer

The positive value of k for which the equation x² + kx + 64 = 0 has one of the roots 0

Choose an answer

4

64

8

All values of k

The point which divides the line joining the points (2, 4, 5) and (3, 5, -4) in the ratio -2 : 3 lines on

Choose an answer

ZOX plane

XOY plane

YOZ plane

None of these

For all points (x,y) on y-axis

Choose an answer

x is positive

x = 0

x is negative

y = 0

6! = ______

Choose an answer

360

720

6.5.4

None of these

A quadrilateral whose diagonals are perpendicular bisector of each other is

Choose an answer

Square

Rectangle

Rhombus

Parallelogram

Trapezium

tan^-1(1/4) + tan^-1(2/9) is equal to

Choose an answer

1/2 cos^-1(3/5)

1/2 sin^-1(3/5)

1/2 tan^-1(3/5)

tan^-11/2

Choose an answer

cosec x + c

-cosec x + c

-sec x + c

sec x + c

cos^-1(cos x) =

Choose an answer

x

cos x

x = 1/x

cos^-2 x

The vector k = [0,0,1] is called unit vector along:

Choose an answer

x -axis

y - axis

z- axis

None of these

The domain of the principle cos function is

Choose an answer

Period of Sine and Cosine function is

Choose an answer

π

2π

-π

-2π

w^-12= ______

Choose an answer

0

1

w

w²

If u = xi + yj, then|u|

Choose an answer

x² + y²

(x² +y²)²

x²-y²

√(x²+y²)

The physical quantity which possesses both magnitude and direction is called a

Choose an answer

scalar

vector

constant

none of these

If P, Q, R be the A.M., G.M., H.M. respectively between any two rational numbers a and b, then P - Q is

Choose an answer

If u v = Proj_uv then

Choose an answer

U and v are parallel

v is a unit vector

U is a unit vector

Both b and c

Choose an answer

The matrix A = [aij]mxn with m ≠ n is always

Choose an answer

Symmetric

Hermition

Skew-symmetric

None

Choose an answer

56

7

8

8/7

Choose an answer

The multiplicative inverse of (a,b) is

Choose an answer

A

A'

U

None of these

One degree is denoted by

Choose an answer

1⁰

1'

1"

1 rad

Choose an answer

If A⊆ B, and B is a finite set, then

Choose an answer

n (a) < n(B)

n(B)<(A)

n(A)≤ n (B)

n(A)≥ n(B)

A sequence whose reciprocal is an A.P is called

Choose an answer

Oscillator

H.P

G.P

None of these

Choose an answer

One-to-one and onto

One-to-one but not on to

Onto but not one-to-one

Neither one-to-one nor onto

99th term of the series 2 + 7 + 14 + 23 + 34 + ..... is

Choose an answer

9998

9999

10000

None of these

e-radii are denoted by

Choose an answer

η

r₂

r₃

All of these

Choose an answer

(2.02)4 s equal to

Choose an answer

16

16.6496

17

18

The line y =mx +1 is tangent to the parabola y² =4x if

Choose an answer

m=1

m=2

m=3

m=4

In a school there are 150 students Out of these 80 students enrolled for mathematics class.50 enrolled for English class and 60 enrolled for Physics class The student enrolled for English cannot attend any other class but the students of mathematics and Physics can take two courses at a time find the number of students who have taken both physics and mathematics.

Choose an answer

40

30

50

60

If A is such that a,A,B are in A.P then A is called

Choose an answer

A.M

Common ratio

Common difference

None of these

Choose an answer

direction ratios

direction cosines

direction angles

none of these

A point of a solution region where two of its boundary lines intersect, is called

Choose an answer

Boundary

Inequality

Half plane

Vertex

A = B if

Choose an answer

A is equivalent to B

Choose an answer

A rational number

An irrational number

An odd number

A prime number

tan(cot^-1x) is equal to

Choose an answer

cot(tan^-1x)

tan x

secon x

None of these

Choose an answer

E-radius corresponding to < C is

Choose an answer

The A.M. of two numbers is 34 and G.M. is 16, the numbers are

Choose an answer

2 and 64

64 and 3

64 and 4

None of these

The fifth term of (a+2x3)¹⁷ is

Choose an answer

4013 x³a¹³

2208a¹³ x¹²

223x⁷a¹⁸

38080a¹³ x¹²

Choose an answer

The law of cosines reduces to a² +c² =b²for

Choose an answer

α = 90°

β = 90°

γ = 90°

α +β +γ =180°

x = 0 is in the solution of the inequality

Choose an answer

x > 0

3x + 4 < 0

x + 3 < 0

x - 2 < 0

The multiplicative inverse of 0 is

Choose an answer

1

-1

0

Does not exist

Through how many radians does the hour hand of a clock turn in one hour

Choose an answer

The set of complex numbers forms

Choose an answer

Commutative group w.r.t addition

Commutative group w.r.t multiplication

Commutative group w.r.t division

Non commutative group w.r.t addition

Cos (α+β) - cos (α-β) =

Choose an answer

-2 sinα sinβ

2 sinαcosβ

-2 sinαcosα

4 sinα cosβ

Φ set is the _______ of all sets

Choose an answer

Subset

Union

Universal

Intersection

What is the circular measure of the angles between the hands of which at 4 o clock

Choose an answer

π/6

3π/2

π/4

2π/3

sn (2sin-10.8)

Choose an answer

0.56

0.69

-0.16

0.96

1,1/3,1/5,1/7,1/9..... is a

Choose an answer

geometric sequence

finite sequence

infinite sequence

arithmetic series

2.333....is a

Choose an answer

Irrational no

Complex no

Rational no

None of these

Tan 3x tan 2x-tan x is equal to

Choose an answer

Tan x tan 2x tan 3x

-tan x tan 2x tan 3x

Tan x tan 2x - tan - tan x tan 3x - tan 2x tan 3x

None of these

The angle of depression of a point A on the ground from the top of the tower is 30^𝜊,then the anglel of elevation of the top of the tower at the point A is

Choose an answer

60^𝜊

40^𝜊

41^𝜊

30^𝜊

Each complex cube root of unity is square of

Choose an answer

itself

1

-1

the other

Choose an answer

2

-1

8

not defined

In (x + iy), y is called as

Choose an answer

Imaginary part

Complex number

Real part

None of above

The sum of first twenty odd integers in A.P is

Choose an answer

400

397

404

408

The additive identity of real number is

Choose an answer

1

2

1/2

0

cos(π/2-θ) = ________;

Choose an answer

cosθ

sinθ

-cosθ

-sinθ

The trigonometric function are continuous whenever

Choose an answer

They are defined

their limit exist

Their period is given

All are incorrect

Choose an answer

0

1

undefined

The differential equation of all st. lines which are at a constant distance to form the origin is

Choose an answer

The points (5, -4, 2),(4, -3, 1),(7, -6, 4),(8, -7, 5) are vertices of a

Choose an answer

Square

Parallelogram

Rectangle

Rhombus

If #n = (n-5)²+ 5, then find #3 x #4.

Choose an answer

54

12

4

9

The equation of the tangent at vertex to the parabola is y² = -8(x -3)

Choose an answer

y=0

x=3

x=1

x=5

The value of x which is unchanged by the mapping in the function defined by f ; x⟶ x² + 5x -5 for x> 0 is

Choose an answer

1

5

-5

-1

The zero vector is regarded to be parallel to

Choose an answer

Every vector

Is some cases

Both a,b

None

If the roots of ax²- bx - c = 0 change by the same quantity, then the expression in a, b, c that does not change is

Choose an answer

To each element of a group there corresponds ______ inverse element

Choose an answer

Two

One

No

Three

a >b ⇒a +c >b +c is known as

Choose an answer

Trichotomy property

Additive property of inequality

Transitive property

Multiplicative property

The greatest integer which divides the number 101¹⁰⁰- 1 is

Choose an answer

100

1000

10000

100000

For each natural number n, n (n+1) is

Choose an answer

an even

an odd

multiple of 3

Irrational

Choose an answer

The slope of the tangent of the circle x³ + y³ =25 at (4,3) is:

Choose an answer

-4/5

4/3

-25/4

25/3

The vertex of the graph of the quadratic function f(x) =-x2+6x+1,is

Choose an answer

(-3,10)

(-3,-10)

(3,10)

(3,-10)

Tan 30° = _____

Choose an answer

The transpose of a column matrix is a

Choose an answer

Column matrix

Row matrix

Scalar matrix

Null matrix

Choose an answer

Parametric equation of circle : x²+y²+r², are

Choose an answer

r1 = x cos𝜽 r² = y sin𝜽

x = r cos𝜽 y = r sin𝜽

x = r sin𝜽1 y = r sin𝜽2

x = r₁ cos𝜽 y = r_{2 sin𝜽}

The tangent to the parabola y² =4ax and perpendicular line from the focus on it meet

Choose an answer

x =0

y =0

x =-9

y = -a

A circle is a limiting case of an ellipse whose eccentricity

Choose an answer

Tends to a

Tends to b

Tends to 0

Tends to a + b

Choose an answer

a₁+ a₂

a²₁+ a²₂

∫Sec² (ax + b) dx is equal to:

Choose an answer

tan² (ax + b)

1/a tan² (ax + b)

1/atan (ax +b)

tan (ax + b)

The system of measurement in which the angle is measured in radians is called the

Choose an answer

circular system

CGS system

sexagesimal system

none of these

Choose an answer

A

B

U

None of these

The set {1, -1, 1, -1}, form a group under

Choose an answer

Addition

Multiplication

Subtraction

None

The distance between the points (1, 2) and (2, 1) is

Choose an answer

3

6

The series obtained by adding the terms of an arithmetic sequence is called the

Choose an answer

Infinite series

Harmonic series

Geometric series

Arithmetic series

A and B throw a dice. The probability that A's throw is not greater then B's is

Choose an answer

5 / 12

7 / 12

1 / 6

1 / 2

Choose an answer

16

256

64

1024

Arithmetic mean between a and b is

Choose an answer

a-b=ab

ab=a

a+b=ab

There is no integer n for which 3ⁿ is

Choose an answer

Even

Prime

Odd

Real

The distance of the point (-2 , -3) from x-axis is

Choose an answer

2

-3

3

5

Choose an answer

8

4

64

Choose an answer

perpendicular vectors

parallel vectors

concurrent vectors

none of these

Choose an answer

The distance of the point (-2 , 3) from y-axis is

Choose an answer

2

-2

3

1

Choose an answer

The solution set of sin x + cos x = 0 is

Choose an answer

The sum of all odd numbers between 100 and 200 is

Choose an answer

6200

7500

6500

3750

Tan 180° = ______

Choose an answer

-1

0

1

Undefined

Choose an answer

I₃

rI₃

r

none

Choose an answer

The domain of the principle sine function is

Choose an answer

Two circle s₁: x²+ y² +2x- 2y- 7= 0: s₂: x²+ y²- 6x+ 4y+ 9= 0

Choose an answer

Touch externally

Touch internally

Intersects each other

Do not intersects

Choose an answer

A

A'

U

A A'

Some of two real numbers is also a real number , this property is called:

Choose an answer

Commutative property w.r.t addition

Closure property w.r.t. addition

Associative property w.r.t. addition

Distributive property w.r.t addition

Choose an answer

In set builder notation the set {0, 1, 2, ............, 100} can be written as

Choose an answer

P(A) + P(B)

P(A) - P(B)

P(A) . P(B)

P(A) / P(B)

cos 2α=

Choose an answer

1 - 2 sin²α

sin ²α+ cos²β

sin²α- cos²β

None of these

The sum of coefficients in the binomial expansion equals to

Choose an answer

2

2ⁿ⁺¹

2^n-1

2ⁿ

In R the number of identity elements w.r.t.'.' is

Choose an answer

One

Two

Three

Four

Choose an answer

The equation of the circle with centre origin and radius r is

Choose an answer

x²+ y²= 1

x²+ y²= r²

x²+ y²= 0

x²- y²= r²

The largest possible domain of the function:

y=√(x ) is:

Choose an answer

(0 ,∞)

12

(3 , 12)

( 3 ,∞)

{x|x∈R∧x≠x} is a

Choose an answer

Infinite set

Null set

Finite set

None of these

Choose an answer

(n + 2) (n + 1) n= ______

Choose an answer

The sum of an infinite geometric series exist if

Choose an answer

| r | < 1

| r | > 1

r = 1

r = -1

If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is:

Choose an answer

an ellipse

a circle

a parabols

a hyperbola

Choose an answer

x = secθ,y = tanθ are the parametric equations of

Choose an answer

Circle

Hyperbola

Ellipse

parabola

If cos^-1p + cos^-1q + cos^-1r =πthen p²+ q²+ r²+ 2pqr is equal to

Choose an answer

3

1

2

-1

The value of x for which the polynomials x² - 1 and x² -2x + 1 vanish simultaneously is

Choose an answer

2

1

-1

-2

a >b, b >c ⇒a >c is a

Choose an answer

Multiplicative property

Additive property

Trichotomy property

Transitive property of inequality

An integral of 1/x dx is:

Choose an answer

1/x²

1/-x²

1/lnx

lnx

If f (x)=a₀ +a₁x+a₂x²+a₃x³-----+0_n-1x^n-1+a_nxⁿ then f⁽ⁿ⁾ (x) is equal to

Choose an answer

n!

a_nn!

0

a_n

Choose an answer

direction ratios

direction cosines

direction angles

none of these

In R, the additive inverse of a is

Choose an answer

0

1

-a

1/a

Choose an answer

The slope of the normal at (4,3) to the circle x²+y²=25 is

Choose an answer

3/4

-3/4

4/3

-4/3

x⁴- 3x³+ 3x + 1 = 0 is called ______

Choose an answer

Reciprocal equation

Exponential equation

Radical equation

None of these

The number of proper subset of A ={a.b.c.d} is

Choose an answer

3

6

8

16

Choose an answer

A = C

A = B

B = C

None of these

The position vector of any point in space is

Choose an answer

If A = {x/x is a positive integer and 4x<23}, then A=

Choose an answer

{1,2,3,4,5,6,7}

{4,5,6...........22}

{1,2,3,.........23}

{1,2,3,4,5}

The set { 1 , -1} is closed w.r.t.

Choose an answer

Addition

Multiplications

Subtraction

None of these

Domain of tangent function is

Choose an answer

sin(a-90°)=______;

Choose an answer

sina

cosa

-sinθ

-cosa

If A(x₁, y₁) , B(x₂, y₂) and C(x₃, y₃) are the vertices of a triangle then its centroid is

Choose an answer

1

0

-1

2

Choose an answer

all are correct

1.4142135... is ______

Choose an answer

A natural number

A rational number

A prime number

An irrational number

A person standing on the bank of a river observes that the angle subtended by a tree of the opposite bank is 60°, when he retreats 40 m from the bank, he finds the angle to be 30°. The height of the tree and the breadth of the river are

Choose an answer

Reflexive property

Symmetric property

Transitive property

Additive property

If T = {2,4,6,8,10,12}, then

Choose an answer

T = (First six natural numbers)

T = (First six odd numbers)

T = (First six real numbers)

T = ( First six even numbers)

The equation of the circle with centre (-h, -k) and radius r is

Choose an answer

(x +h)²+ (y+k)²= r²

(x +h)²+ (y-k)²= r²

(x -h)²+ (y+k)²= r²

(x -h)²+ (y-k)²= r²

The function whose range consists of just one element is called

Choose an answer

One-One Function

Identity Function

Onto Function

Constant Function

∀x, y ∈ R, either x = y or x > y or x < y is

Choose an answer

Transitive property

Reflexive property

Trichotomy property

None of these

An improper rational fraction can be reduced by division to a

Choose an answer

Proper fraction

Polynomial

mixed form

The coefficient of x¹⁰in the expansion (x³+3/x²)¹⁰is

Choose an answer

1700

17023

17027

17010

The line 3x - 4y = 0

Choose an answer

Is a tangent to the circle x²+ y²= 25

Is a normal to the circle x²+ y²=25

Does not meet the circle x²+ y²= 25

Does not pass thro' the origin

If 2x^1/3+ 2x^-1/3= 5, then x is equal to

Choose an answer

1 or -1

2 or 1/2

8 or 1/8

4 or 1/4

a_n - a_n-1 will be common difference in an A.P if

Choose an answer

n = 1 ∀n∈ N

n>1∧n∈N

n∈Z

None of the above

If n is any positive integer then n²> n + 3 for

Choose an answer

The value of k (k > 0) for which the equation x²+ kx + 64 = 0 and x²- 8x + k = 0 both will have real roots is

Choose an answer

8

-16

-64

16

An unbiased die is thrown. Then the probability of getting a prime is

Choose an answer

1/2

2/3

3/4

None of these

Choose an answer

None of these

∫x sin xdx is equal to:

Choose an answer

sin x/x + cos x

sin x - cos x/x

x cos x + sin x

- x cos x + sin x

Choose an answer

30°

45°

60°

120°

The mid point of the line segment joining the points A(-8,3) and B(2,-1) is

Choose an answer

(-3,1)

(-6,2)

(5,2)

(-5,2)

By expressing cos 113° in terms of trigonometrical ratios, answer will be

Choose an answer

− cos 76° = -0.7093

− cos 65° = -0.4258

− cos 67° = -0.3907

− cos 62° = -0.8520

The graph of a linear function is

Choose an answer

a circle

triangle

a straight line

none of these

If a₁and r are the first term and the common ratio respectively then (n + 1)th term of the G.P. is

Choose an answer

0

a₁r^n-1

a₁rⁿ⁺¹

a₁rⁿ

The distance between the points (0 , 0) and (2, 1) is

Choose an answer

5

0

3

Choose an answer

The physical quantity which can be specified by a number alongwith unit is called a

Choose an answer

scalar

vector

constant

none of these

the largest degree of the terms in the polynomials is called

Choose an answer

terms of the polynomial

degree of a polynomial

co-efficient

monomial

If the lines 2x-3y-1=0,3x-y-5=0 and 3x+py+8=0 meet at a unique point then

Choose an answer

p = -14

p = -1

p =0

p=12

a_n -a_n-1,∀n∈N∧n>1 in an A.P is called

Choose an answer

Common difference

nth term

Common ratio

None of these

The graph of a quadratic function is

Choose an answer

Circle

Straight line

Parabola

Triangle

The three noncollinear points through which a circle passe are known, then we can find the:

Choose an answer

Variables x and y

Value of x and c

three constants f,g and c

inverse of the circle

If n is any positive integer then n! > 2^n-1for

Choose an answer

The set of rational number is represented by

Choose an answer

W

R

Q'

Q

Choose an answer

0

1

2

3

Choose an answer

Parallel to the plane

At right angles to the plane

Lies in the plane

Meet the plane obliquely

The set of ordered pairs (x,y) such that ax+ by < c, and (x,y) such that ax + by>0, are called

Choose an answer

Linear Inequalities

Feasible regions

Half planes

Boundary

For every positive integers n 1+5+9+....+ (4n - 3) is

Choose an answer

n(2n - 1)

(2n - 1)

n - 1

n

i³ =

Choose an answer

-1

i

-i

1

If G is the centroid of the triangle, then GA +GB+GC=

Choose an answer

0

1

-1

3

i =

Choose an answer

√1

√2

√-2

√-1

Choose an answer

y : x

x : y

-y : x

-x : y

The number of permutations of n objects of which there are n₁like of one kind, n₂like of the second kind and n₃like objects of third kind are

Choose an answer

Which term of the A.P 5,8,11,24.............is 320

Choose an answer

104^th

106^th

105^th

64^th

Choose an answer

Proper fraction

Improper fraction

Rational fraction

None of these

0.25 is ______

Choose an answer

An irrational number

A natural number

A prime number

A rational number

Choose an answer

2s²

2s³

s³

3s³

A number A is said to be the A.M between the two numbers a and b if a, A, b are in

Choose an answer

A.M

A.P

G.P

G.M

The two parts into which 57 should be divided so that their product is 782 are

Choose an answer

43,14

34,23

33,24

44,13

A polynomial of arbitrary degree

Choose an answer

f(x) = o

f(x) = x

f(x) = a

f(x) = ax + b,a ≠ 0

Choose an answer

The radian measure of the central angle of an arc 50 m long on a circle of radius 25 m is

Choose an answer

3

2

1

Choose an answer

An equation which holds good for all values of variables is called

Choose an answer

Equation

Conditional equation

Constant

None

If a = 2i +2j, b= 3i -j and c=4i +5j, the 3b -a-2c =

Choose an answer

-i -15j

i-15j

i-3j

None of these

Choose an answer

Principle of equality of fractions

Rule for product of fractions

Golden rule for fractions

Rule for quotient of fractions

If a cone is cut by a plane perpendicular to the axis of the cone, then the section is a

Choose an answer

parabola

circle

hyperbola

ellipse

The number of divisors of 1029, 1547 and 122 are in

Choose an answer

A.P.

G.P.

H.P.

None of these

Choose an answer

0

-1

1

not defined

A function whose domain is a subset of natural numbers is called ______

Choose an answer

Identity function

Sequence

Onto function

Series

If you are looking a high point from the ground, then the angle formed is

Choose an answer

Angle of elevation

Angle of depression

Right angle

Horizon

f(x) = x is

Choose an answer

trigonometric function

exponential function

quadratic function

identify function

If p and q are two statements then their conjunction is denoted by

Choose an answer

Write the first four terms of the arithmetic sequence 5, 2, -1, ... is

Choose an answer

3

-3

7

1

Three points whose position vector a,b,c are collinear

Choose an answer

a x b +b x c+ c x a = 0

a,b +b,c +c,a =0

a,|a x c| =0

a+b+c =0

The area bounded by y = x (x² - 4) and below x - axis is

Choose an answer

4

0

-4

8

The solution of the equation 3 tan²x = 1 is ____________

Choose an answer

none of these

Choose an answer

5th term of a G.P. is 2, then the product of first 9 terms is

Choose an answer

256

128

512

None of these

The set {x +iy / x, y ∈ Q} forms a group under the binary operation of

Choose an answer

Addition

Multiplication

Division

Both addition and multiplication

The number of triplets (x, y, z) satisfying sin^-1x +cos^-1y + sin^-1z = 2π is

Choose an answer

0

2

1

Infinite

Choose an answer

z is purely imaginary

a is any complex number

z is real

None of these

Choose an answer

Orthogonal

Involutary

Idempotent

Nilpotent

Choose an answer

sec 3x + c

- cosec 3x + c

Choose an answer

Biconditional

Implication

Antecedent

Hypothesis

General solution of tan 5θ= cot 2θis

Choose an answer

The order of the matrix A is 3 x 5 and that of B is 2 x 3.The order of the matrix BA is

Choose an answer

2 x 3

3 x 2

2 x 5

5 x 2

If a > 0 they parabola y² =-4ax lies in

Choose an answer

I and iv quadrant

I quadrant

II and III quadrant

All are incorrect

If the trace of matrix A is 5, then the trace of the matrix 3A is

Choose an answer

3/5

5/3

8

15

Choose an answer

The set of all positive even integers is

Choose an answer

Not a group

A group w.r.t. subtraction

A group w.r.t. division

A group w.r.t. multiplication

Choose an answer

A

-A

A^t

A^-

The mid point of the line segment joining the points (a,b) and (b,a) is

Choose an answer

The area enclosed between the graph y = x²-4x and the x- axis is:

Choose an answer

20/3

41/3

32/3

25/3

n² - 1 divisible by 8 when n is

Choose an answer

an odd integer

an even integer

Irrational

Prime Number

A joint equation of the lines through the origin and perpendicular to the lines ax² +2hxy +by² =0 is indentical is ax² +2hxy +by² =0 if

Choose an answer

h² = ab

a + b =0

a = b

a ≠ b

a = b = 0

If|a| =|b| = |a+b|=1, then|a-b| is equal to:

Choose an answer

1

√3

√2

7

If for the matrix A, A⁵= I, then A^-1=

Choose an answer

A²

A³

A

None of above

The sum of the coefficient in the expansion of (a + x)⁵is

Choose an answer

32

16

8

5

If f (x) = 2x+1 then fof (x) = _______;

Choose an answer

4x+3

2x +3

4x +1

None of these

Choose an answer

The graph of linear equation 2x + 3y = 10

Choose an answer

Parabola

Circle

Hyperbola

Straight line

If f(x) = x²then f(0) is

Choose an answer

0

1

2

none of these

If the distance of any point on the curve from any of the two lines approaches zero then if is called

Choose an answer

Axis

Directrices

Asymptotes

None

cos (α+β) + cos (α-β) =

Choose an answer

4 cosαcosβ

2 cosαcosβ

2 sinαsinβ

2 sinαcosβ

Choose an answer

A

A'

U

U'

Choose an answer

The probability that a slip of numbers divisible by 4 is picked from the slips of number 1,2,3,4,......10 is

Choose an answer

1/5

2/5

1/10

3/10

Choose an answer

(x³- 3x²)⁸+ c

3x²- 6x + c

Geometric mean between a and b is

Choose an answer

A box contains 10 red 30 white and 20 black marbles When a marble is drawn at random the probability that it is either red or white is

Choose an answer

1/6

1/3

1/2

2/3

The discriminant of the quadratic equation ax²+ bx + c = 0 is

Choose an answer

b²+ 4ac

b²- 4ac

4ac - b²

a²- 4ac

If f(x)= x³ then f(-2) is

Choose an answer

-2

-4

-8

8

The order of the matrix A is 3 x 5 and that of B is 2 x 3. The order of the matrix BA is

Choose an answer

2 x 3

3 x 2

2 x 5

5 x 2

The set of natural no. is closed under

Choose an answer

multiplication

subtraction

difference

division

Choose an answer

1

0

-2

3

Choose an answer

4A - 3I

3A - 4I

A - I

None of these

Ifα,βare the roots of ax²+ bx + c = 0 andα+ h,β+ h are the roots of px²+ qx + r=0, then h =

Choose an answer

Domain of cot x is ______

Choose an answer

If the circumference of a circle is divided into 360 congruent parts, the angle subtended by one part at the centre of the circle is

Choose an answer

1⁰

1'

1"

1 rad

The equation of a line parallel to the tangent to the circle x²+ y²= 16 at the point (2, 3) and passing thro' the origin is

Choose an answer

2x + 3y = 0

2x - 3y = 0

3x + 2y = 0

3x - 2y = 0

The value of the expression sinθ+ cosθlies between

Choose an answer

1

0

Every term of a G.P. is positive and also every term is the sum of two preceding terms. Then the common ratio of the G.P. is

Choose an answer

3

1

2

4

Choose an answer

(a + b)c = a . c + bc

a + b = b + a

(a + b) + c = a + (b + c)

a(b+ c) = ab + ac

The transport of a rectangular matrix is a

Choose an answer

Square matrix

Rectangular matrix

Row matrix

Column matrix

Range of cos x is ______

Choose an answer

[-1, 1]

R

Negative real numbers

R - { x | - 1 < x < 1}

Choose an answer

none of these

Choose an answer

The position vector of the point P(a, b, c) is

Choose an answer

G.P

H.P.

A.P.

No particular sequence

Choose an answer

0

1

-A

-1

Choose an answer

-3 -2i

3 +2i

1 + 2i

1 - 2i

Choose an answer

-10

10/7

-10/7

-7/10

If for two events A and B , P(A∪B)=1,then events A and B are

Choose an answer

Certain events

Mutually exclusive

Complementary events

Independent

Choose an answer

If a polynomial P(x) is divided by x - a, then the remainder is

Choose an answer

P(o)

P(-a)

P(a)

None of these

Choose an answer

Polynomial

Equation

Improper rational fraction

Proper rational fraction

Choose an answer

120° degrees are equal to how many radians?

Choose an answer

1 degree = _______

Choose an answer

0.00175 rad

0.175 rad

0.0175 rad

1.75 rad

The mid point of the line segment joining the points (4,0) and (0,4) is

Choose an answer

(4,4)

(2,2)

(-4,-4)

(-2,-2)

The common ration of a geometric sequence cannot be

Choose an answer

0

1

2

3

Choose an answer

If p, q, r and in A.P., a is G.M. between p and q and b is G.M. between q and r, then a², q², b²are in

Choose an answer

A.P.

G.P.

H.P.

None of these

Choose an answer

1

2

3/2

5/2

Choose an answer

xa^x-1

a^x

x in a

a^xIn a

Fifteen girls compete in a race. The first three places can be taken by them in

Choose an answer

3! ways

12! ways

15 x 14 x 13 ways

42 ways

Choose an answer

The area of circle of unit radius =

Choose an answer

0

1

4

π

If the pth, qth, and rth terms of an A.P. are in G.P:., then the common ratio of the G.P. is

Choose an answer

A relation in which the equality is true only for some values of the unknown is called

Choose an answer

An identity

An equation

A polynomial

None

If A=B, then

Choose an answer

A⊂B and B⊂A

A⊆B and B⊈A

A⊆B and B⊆A

None of these

Any recurring decimal represents a

Choose an answer

Irrational no

Integer

Rational no

None of these

Choose an answer

3x²+ 2

3x²+ 2x + 3

x³+ x²

none of these

Choose an answer

The two different parts of the hyperbola are called its

Choose an answer

Vertices

Directrices

Nappes

Branches

Domain of sec x is ______

Choose an answer

Ifᵨ> 1 , then the conic, is:

Choose an answer

Ellipse

Parabola

Hyperbola

None of these

Two tangents drawn from (2,3) to the circle x²+y² =9 are

Choose an answer

Real and distinct

Imaginary

Real and coincident

None of these

The sum of first n even number is

Choose an answer

n²

n(n+1)

n+1

n+2

A square matrix A for which A^t= -A is called a

Choose an answer

Column matrix

Symmetric matrix

Skew-symmetric matrix

Row matrix

Every identity matrix is

Choose an answer

Row-vector

Scalar

Column-vector

All

A subset of set of complex number whose elements are of the form (a,0) is called

Choose an answer

Real number

Complex number

Rational number

Irrational number

Choose an answer

an A.P.

a G.P.

A H.P.

None of these

f(x) = sin x is:

Choose an answer

an odd function

an even function

an implicit function

an exponential function

n(n-1)(2n-1), for all natural numbers n, is divisible by

Choose an answer

12

6

2

18

Choose an answer

all

Choose an answer

cos 3x + c

- cos 3x + c

Choose an answer

-2

-1

1

2

For a set A, A∪A^c= ---------------------

Choose an answer

A

∅

A^c

U

Choose an answer

3

2

8

0

Which of the following is not a unit vector

Choose an answer

[1, 1, 1]

[0, 1, 0]

[0, 0, 1]

[1, 0, 0]

The value of sin 28°cos 17°+cos 28°sin 17°is

Choose an answer

A and B be two square matrices and if their inverse exist, the (AB)^-1=

Choose an answer

A^-1B^-1

AB^-1

A^-1B

B^-1A^-1

24 can be written as a product of

Choose an answer

Odd factors

Even factors

Whole factors

Prime factors

Sin 270° = ______

Choose an answer

-1

0

1

Undefined

Choose an answer

I

14 I

0

None of these

The additive inverse of 1 is

Choose an answer

1

-1

0

Does not exist

For trival solution |A| is

Choose an answer

A

|A| = 0

A = 0

None of these

If a = [1,4,3] and B= [2,-1,5] athen the mid point M of AB is:

Choose an answer

[1,1,1.5]

[2,2,1.5]

[1.5,1.5,4]

None of these

Sand falls from a tube in such a way that it forms a cone whose height is always 4/3 times the radius of its base and radius of the base increases at the rate of 1/8 cm/sec. When this radius is 1 meter, the rate at which the amount of sand increases is

Choose an answer

cos⁴θ- sin⁴θ=

Choose an answer

cos4θ

cos2θ

-sinθ

sin2θ

if one root of the equation ix² - 2(i + 1) x +(2 - i)= 0 is 2 - i then the other root is

Choose an answer

-i

2 + i

i

2 - i

Choose an answer

[0,1[

[0, 1]

]0, 1[

None of these

Coordinates of the focus of the parabola x² - 4x -8y-4=0 are:

Choose an answer

(0,2)

(,0,1)

(2,0)

(1,2)

tan(3π/2 +θ)=______;

Choose an answer

tanθ

cotθ

-tanθ

-cotθ

2/9,5/7∈ R,(2│9)(5│7)=10/63∈R this property is called

Choose an answer

Associative property

Identity property

Commutative property

Closure property w.r.t multiplication

Choose an answer

Domain of secθis

Choose an answer

w^-1= ______

Choose an answer

0

1

w

w²

There is no element common in

Choose an answer

N and W

E and W

N and O

Q and Q'

Associative law of multiplication

Choose an answer

ab - ba

a(bc) - (ab) c

a(b + c) = ab +ac

(a +b)c = ac + bc

a + x is ______

Choose an answer

A trinomial

A binomial

A monomial

None of these

Choose an answer

4

3

2

1

The angle of elevation of the tops of two towers at the middle point of the line joining the foots of the tower are 60^οand 30^οrespectively. The the ratio of the heghts of the tower is

Choose an answer

2 : 1

3 : 1

1 : 2

1 : 3

Range of tanθis

Choose an answer

Set of complex numbers

Set of real numbers

Set of odd numbers

Set of positive integers only

Choose an answer

a sin(ax + b) + c

- a sin(ax + b) + c

Choose an answer

If a_n= 2n -3, write the first four terms

Choose an answer

-3, -1, 1, 3

1, 3, 5, 7

-1, 1, 3, 5

None of these

Any whole number can be written as a product of factors which are

Choose an answer

Even number

Odd numbers

Prime number

Rational number

Choose an answer

The centre fo the circle x²+ y²+ 12x -10 = 0 is

Choose an answer

(12, -10)

(6, -5)

(-12, 10)

(-6, 5)

If the angle of a triangle are in the ratio 2 : 3 : 7, the triangle is

Choose an answer

Obtuse

Acute

Right angle

Isosceles

The feasible region which can be enclosed within a circle is called

Choose an answer

Bounded region

Convex region

Unbounded region

None

Choose an answer

1, 2, 3

1, 5, 9

2, 5, 8

3, 6, 9

22.5°=______

Choose an answer

none of these

The roots of ax²+bx+c=0 are

Choose an answer

Rational ⇔ b² -4 ac ≥ 0

Irrational ⇔ b² -4 ac > 0

Real ⇔ b² -4 ac ≠ 0

Rational ⇔ b² -4 ac = 0

The parametric equation of a curve are x = t², y = t³then

Choose an answer

If cos 20°=K and cos x=2 k²-1, then the possible values of x between 0° and 360° are

Choose an answer

140°

50° and 140°

50° and 130°

40° and 320°

If 2 tan¹(cos x) = tan^-1(cosec²x), then x is equal to

Choose an answer

π/ 3

π/ 2

π/ 6

π

The angle of depression of a point situated at a distance of 70 meters from the base of a tower is 45°. The height of the tower is

Choose an answer

70 m

85 m

35 m

None of these

cos (α-β) = cosαcosβ+ sinαsinβis true for all

Choose an answer

α>β> 0

α>β

β>α

None of these

Choose an answer

none of these

Choose an answer

-2x³

2x^-3

-2x^-3

2x³

If A is singular then |A| = ______

Choose an answer

1

0

2

None of these

sin (sin^-1(1/2))=

Choose an answer

0

2

∞

1/2

If a parabola opens down, then its vertex is at the

Choose an answer

Right of the parabola

Left of parabola

Lowest point on the parabola

Highest point on the parabola

Choose an answer

π / 3

π / 4

π / 2

π

Choose an answer

0

1

Choose an answer

a cosec(ax + b) + c

- a cosec(ax + b) + c

The direction cosines of a line equally inclined with co-ordinate axes are

Choose an answer

Trichotomy property

Additive property of inequality

Transitive property

Multiplicative property

Choose an answer

none of these

a function from A to B is denoted by

Choose an answer

f: A→ B

f: B → A

f: → A :B

f → A→ B

If the radius of a circle is increased by 1 then area of circle will be

Choose an answer

π r²

π(r+1)²

π r² +1

2π (r+1)

If x³+ ax²- a²x - a³is divided by x + a, then the remainder is

Choose an answer

0

a³

2a³

-2a³

The general solution of the differential equation x dy / dx = 1 + y is:

Choose an answer

2

1

3

None

Choose an answer

A(α) - A(β)

A(α) + A(β)

A(α-β)

A(α+β)

Choose an answer

none of these

A circle which touches one side of a triangle extermally and the other two sides produced is called

Choose an answer

In-circle

Circumcircle

e-circle

Point circle

If a, b, c are in AP., a, b, c are in G.P. then A, m²b, c are in

Choose an answer

A.P.

G.P.

H.P.

None of these

If sin x + sin²x = 1, then the value of Cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x + 2 cos⁴x + cos²x-2 is equal to

Choose an answer

0

1

2

sin²x

Choose an answer

If one root of the equation x²- 3x + a = 0 is 2 then a = ______

Choose an answer

0

1

2

3

If f(x) = -x³then f(-2) is

Choose an answer

-2

-4

-8

8

The symbol of irrational is

Choose an answer

W

N

Q

Q'

The curve f(x,y) = 0 has a central symmetry if

Choose an answer

f(-x,-y)=f(x,y)

f(x,-y)=f(x,y)

f(-x,y)=f(x,y)

f(-x,-y)≠ f(x,y)

If A is a skew-symmetric matrix of order n and P, any square matrix of order n, prove that P' AP is

Choose an answer

Skew-symmetric

Symmetric

Null

Diagonal

Z is a group under

Choose an answer

Subtraction

Multiplication

Addition

None of these

If B ={x/x€ Z ^ - 3 < x < 6}, then n (B) =

Choose an answer

5

{-3,-2,-1,0,1,2,3,4,5,6}

8

9

Every recurring decimal represents

Choose an answer

A natural number

A rational number

An irrational number

A whole number

A conjunction of two statement p and q is true only if

Choose an answer

p is true

q is true

Both p and q are true

both p and q are false

The maximum value of Z = 3x+ 4y subjected to the constrains x+ y ≤ 40,x+ 2y ≤ 60, x ≥ 0 and y ≥ 0 is

Choose an answer

120

100

140

160

Choose an answer

c = 0

c = -1

c = -2

c = 1

Choose an answer

If the roots of 3x²kx + 12 = 0 are equal then k = ______

Choose an answer

If A is a skew-symmetric matrix then A^t= ______

Choose an answer

-A

A²

2A

A

Three dice are thrown together. The probability of getting a total of at least 6 is

Choose an answer

103 / 108

10 / 216

93 / 108

None of these

For non-trival solution |A| is

Choose an answer

A = 0

A^t= 0

|A| = 0

None of these

Geometrically the modulus of a complex number represents its distance from the

Choose an answer

Point (1,0)

Point (0,1)

Point (1,1)

Point (0,0)

(a+bi) - (c+di)=

Choose an answer

(a+b) = (c+d)

(a+c) + i(b+d)

(a - c) + (c- d)i

(a - c)+ (b - d)i

The solution of equation x² + 2 = 0 in the set of real number is

Choose an answer

^{Infinite set}

Singleton set

Null set

None of these

The roots of the equations will be equal if b²- 4ac is

Choose an answer

Positive

Negative

1

Zero

The end points of the major axis of the ellipse are called its

Choose an answer

Foci

Vertices

Co - vertices

None of these

Choose an answer

150°= ______

Choose an answer

5

-5

none

A bag contains 5 white, 7 red and 5 black balls. If four balls are drawn one by one with replacement, the probability that none is white is

Choose an answer

(11/16)²

(5/16)²

(11/16)⁴

(5/16)⁴

Choose an answer

-2x cos x²

-2x²sin x²

-x²sin x

-2x²sin x²

Choose an answer

0 is a symbol of

Choose an answer

singleton set

Empty set

Equivalent set

Infinite set

The 5^th and 13^thterms of an A.P are 5 and-3 respectively The first term of the A.P is

Choose an answer

1

-15

9

2

Sum of all the four forth roots of unity is

Choose an answer

₁

-1

i

=1

The multiplicative inverse of 4 is

Choose an answer

-4

-1/4

1/4

1

The familiar plane curves, namely circle, ellipse, parabola and hyperbola are called:

Choose an answer

cones

conics

nappes

apex

Choose an answer

0

1

-1

2

Choose an answer

Principle of equality of fractions

Rule for product of fraction

Rule for quotient of fraction

Choose an answer

none of these

x = ________ is in the solution of 2x + 3 > 0

Choose an answer

1

-2

-3

-4

In triangle ABC, in which b=95, c=34, a =52^𝜊then the value of a=

Choose an answer

18 cm

18.027 cm

20.7 cm

19 cm

Choose an answer

none of these

If f(x) = x²then f(2) is

Choose an answer

-2

2

4

-4

The arbitrary constants involving in the solution can be determined by the given conditions. Such conditions are called

Choose an answer

Boundaries

Variable separable

Initial values

None

The angle of elevation of the top of a tree from a point 17 meters from is foot is 42^𝜊The height of the tree is

Choose an answer

12m

21m

17m

15m

Choose an answer

The principal value of sin^-1(-1/2)

Choose an answer

π/3

π/4

π/6

-π/6

The range of inequality x + 2 > 4 is

Choose an answer

(-1, 2)

(-2, 2)

(1,∞)

None

Choose an answer

none of these

Two dice are rolled The number of possible out come in which at least one die shows 2 is?

Choose an answer

5

12

11

7

∫sec (ax + b) tan(ax + b) dx=_______

Choose an answer

sec(ax + b)/a

sec² (ax + b)/2

sec(ax + b)/x

1/2

The length of rectangle is twice as much as its breadth. If the perimeter is 120 cm, the length of the rectangle is

Choose an answer

Same as the original determinant

Additive inverse of the original determinant

Both A and B

Adj of the original matrix

Tan (π + Tan^-1 x) =?

Choose an answer

Tan x

X

-x

Cot^-1 x

d/dx (√x) =

Choose an answer

2√x

1/√x

1/2√x

None of these

The graph of a quadratic function is

Choose an answer

Circle

Ellipse

Parabola

Hexagon

Write the first four term of the arithmetic sequence if a₁ = 5 and other three consecutive terms are 23,26,29

Choose an answer

18 years

36 years

8 years

16 years

Cse π/3

Choose an answer

2

1

0

2/√3

If sinθ = 1 then θ =

Choose an answer

2nπ +π/2

2nπ

2π +n

Nπ +π/2

The direction cosines of y-axis are

Choose an answer

1,0,0

0,1,0

0,0,1

1,1,1

The number of real roots in cube roots of 8 is ?

Choose an answer

n x m

m x n

km x n

m x kn

If the sum of the roots of (a + 1)x² + (2a + 3)x + (3a + 4) = 0 is -1, then product of the roots is

Choose an answer

Commutative law w.r.t multiplication

Associative law w.r.t addition

Distributive law w.r.t addition

Multiplication of a scalar with the matrix

If α and β be irrational roots of a quadratic equation, then

Choose an answer

α = b/a and β = ca

α = a/b and β = -c/a

α² + β² = 1

α = -b/a and β= c/a

The value of x, and y, when (x+iy)²=5+4i

Choose an answer

X=2, y=-1

X=-2, y=1

X=2, y=-i

X=2, y=2

One of the roots of the equation 2x² + 3x + n = 0 is the reciprocal of the other, then n = --------------------

Choose an answer

Both A,B have the same number of columns

Both A,B do not have the same order

Number of col A is same as number of rows of B

Number of rows of A is same as number of col of B

3/2 is

Choose an answer

An irrational number

Whole number

A positive integer

A rational number

(x+2)² = x² +4x +4 is

Choose an answer

1

2

3

4

A fraction in which the degree of the numerator is less than the degree of the denominator is called

Choose an answer

1-i √-3 / 2

-1+i √-3 / 2i

-1+i √3 / 2

1+i √3 / 2

Cos 315° =

Choose an answer

0.707

0.5

1

0

Cos^-1 (-x) =_______.

Choose an answer

π +cos^-1 x

π -sin^-1 x

π +sin^-1 x

π -cos^-1 x

The area of circle of unit radius=

Choose an answer

0

1

4

π

The difference of two consecutive terms of an A.P is called

Choose an answer

Zero

One

Four

Infinite

The value of Cos (1/2 Cos^-1 1/2) is equal to

Choose an answer

√3/2

-3/4

1/16

1/4

The range of inequality x + 2 > 4 is

Choose an answer

(-1,2)

(-2,2)

(1,∞)

None

If Cosα = 3/5, Cosβ = 5/13, then

Choose an answer

Cos(α +β) =33/65

Sin(α +β) =56/65

sin²(α +β/2) =1/65

Cos(α +β) =63/65

d/dx a^x is

Choose an answer

xa^x-1

a^x

x in a

a^x in a

If i,m,n are the direction cosines of a vector O̅P̅ then

Choose an answer

I² + m² + n² =0

I² - m² + n² =1

I² + m² + n² =1

I² + m² - n² =0

The perpendicular bisector of any chord of a circle

Choose an answer

Passes through the center of the circle

Does not pass through the center of the circle

May or may not pass through the center of the circle

None of these

1+2+3+......+n=?

Choose an answer

n(n +1)/2

n +1/2

n(n +1)(2n +1)/6

n³

6 is

Choose an answer

A prime integer

An irrational number

A rational number

A odd integer

A standard deck of 52 cards shuffled what is the probability of choosing the queen of the diamonds

Choose an answer

1/5

1/13

5/52

1/52

If θ= 60° then

Choose an answer

sin θ = 1/2

tan θ = cot 30°

θ = π/4

Sec θ =4

F(x) = xx decreases in the interval

Choose an answer

(0,e)

(0.1)

(-∞.0)

None

Let A, B, and C be any sets such that A∪B=A∪C and A∩B=A∩C then

Choose an answer

A ≠ C

B = C

A = B

A ≠ B

Period of Sin 2x =

Choose an answer

π

4π

2nπ

2π

Sin^-1 (-x) =

Choose an answer

Cos^-1 1/x

-Sin^-1 X

1/sin-1x

Sin^-1 1/x

If f(x) = x³- 2x² +4x-1, then f(-2) =?

Choose an answer

0

-25

5

45

The equation of two polynomials P(x)/Q(x) where Q(x) ≠ 0 with no common factor is called

Choose an answer

12

1

10

-10

If Sin^-1 x + cos^-1 y = π, then x and y are

Choose an answer

Associative angles

Complementary angles

Reflex angles

Supplementary angles

The gradient of the line joining (1,4) and (-2,5) is

Choose an answer

3/8

-2 2/3

-1/3

2

If A and B are two events then P(A∪B) =? (when A and B are disjoint)

Choose an answer

P(A) - P(B)

P(A) x P(B)

P(A) + P(B)

P(A) + P(B) -P(A∩B)

8 > t then

Choose an answer

(s -t) ²>(t -8)²

(s -t) ²<(t -8)²

(s -t) ²=(t -8)²

None

If in isosceles right angled triangle one side is a then hypotenuse is

Choose an answer

a√2

a/2

a

Cannot be determined by given

The set of complex numbers forms a group under the binary operation of

Choose an answer

0

±1

1

{0,1}

If Z₁ = √-36, Z₂=√-25, Z₃= √-16, then what is the sum of Z₁, Z₂ and Z₃ ?

Choose an answer

√3 I

√7

-2-1

√5

Domain of Cosecθ is

Choose an answer

is R but θ= nπ

is R but θ ≠ nπ

is R but θ ≠ 2nπ

is R but θ ≠ nπ/2

The point (-5,3) is the center of a circle and P(7,-2) lies on the circle the radius of the circle is

Choose an answer

2

13

7

8

2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

Choose an answer

α = b/a and β = ca

α = a/b and β = -c/a

α² + β² = 1

α = -b/a and β= c/a

x² +2x -25 = 0 is

Choose an answer

1

2

3

4

0 (zero) is

Choose an answer

A irrational number

A rational number

A negative integer

A positive number

Two matrices A and B are conformable for multiplication (AB) if and only if

Choose an answer

Addition

Multiplication

Division

Subtraction

Which of the following is solution of Tan² x = 1/3

Choose an answer

7π/6

5π/6

π/6

All

1/x² -1 = ? (in case of making partial fraction)

Choose an answer

Ax +B/x² -1

A/x + B/ x- 1

A/ x+1 + B/x-1

None

The set { {a,b} } is

Choose an answer

{X/X∈ A∧x ∈ U}

{X/X∉ A∧x ∈ U}

{X/X∈ A and x ∉ U}

A-U

The line joining (1,3) to (a,b) has unit gradient then

Choose an answer

a-b =-2

a+b = 0

A-b =5

2a + 3b =1

The parametric equation of a curve are x = t², y = t²then

Choose an answer

dy/dx =3t/2

dy/dx =t⁵

dy/dx =5t⁴

None

If you looking a high point from the ground then the angle formed is

Choose an answer

Angle of elevation

Angle of depression

Right angle

Horizon

d/dx [cos x²] =________

Choose an answer

-2x cos x²

-2x² sin x²

x² sin x

-2x² sin x²

Which is not a half plane

Choose an answer

ax + by < c

ax + by > c

Both A and B

None

The two consecutive positive integers whose product is 56 are

Choose an answer

7, 8

14, 4

28, 2

56, 1

The nth term of A,P:1,5,9,15...........is given by

Choose an answer

4n - 3

4n + 1

3n -4

4n +3

An angle 0 is such that tan θ = 1 and cos θ is negative then

Choose an answer

Sin θ is positive

Cos θ = √2/4

cosθ = -1

sec θ is negative

The curves y =x², y= x interest at

Choose an answer

(0,0) ,(1,1)

(2,4)

(0,),(2,4)

(0,3),(-1,1)

If f (x) = x/x²- 4 then which is not included in the domain of f(x)

Choose an answer

0

-2

1

4

In general matrices do not satisfy

Choose an answer

Not a group

A group w.r.t. subtraction

A group w.r.t. division

A group w.r.t. multiplication

Which of the following is the solution of Cot²x = 1/√3

Choose an answer

π/5

π/3

π/7

π/9

Derivative of strictly increasing function is always

Choose an answer

Zero

Positive

Negative

Both A and B

A die is thrown what is the probability that there is a prime number on the top?

Choose an answer

1/2

1/3

1/6

2/3

The total cost of 2 apples and 3 oranges is $1.70,which of the following is true

Choose an answer

The cost of one apple

The cost of one orange

Both have equal cost per item

Cost of each single item can not be determined

The equation of the line with gradient 1 passing through the point (h,k) is

Choose an answer

Y = x+ k-h

Y = k/hx +1

Y = x + h -l

Ky = hx =1

In the triangle Δ ABC, where C is the right angle Tan A + Tan B=

Choose an answer

A +B

C² /AB

A²/BC

B²/AC

The circle (x -2)² + (y + 3)² =4 is not concentric with the circle

Choose an answer

(x -2)² + (y + 3)² =9

(x +2)² + (y - 3)² =4

(x -2)² + (y + 3)² =8

(x -2)² + (y + 3)² =5

The Domain of f(x) = log x is

Choose an answer

[0,∞]

(0, ∞)

[0,∞[

[∞ ,∞]

If -1 < x < 0, which of the following statement must be true?

Choose an answer

x < x² < x²

x < x³ < x²

x² < x³ < x

x²< x < x³

The value of the polynomial 3x³ + 4x² - 5x + 4 at x = -1 is

Choose an answer

A² + B²

A² + B²+ 2AB

A + B

A² + B² + AB+BA

The equation of the circle with center origin and radius 2√2 is

Choose an answer

x² + y² = 2√2

x² + y² = 8

x² - y² = 2√2

x² - y² = 8

If f(x) : A → B and g (x) : A → B then Dom [f(x) + g(x)] is

Choose an answer

Dom f(x) ∩ Dom g (x)

Dom f(x) ∪ Dom g(x)

[Domf(x)]² - [Dom g(x)]²

[Dom g(x)]²-[Domf(x)]²

Every prime number is also

Choose an answer

Rational number

even number

Irrational number

multiple of two numbers

Sin^-1 (-x) =?

Choose an answer

Sin^-1 x

-Sin^-1 x

Cos^-1 x

-Cos^-1 x

If f₁ (x) and f₂ (x) are any two anti derivatives of a function F (x) then the value of f₁ (x) = f₂ (x)

Choose an answer

A variable

A constant

Undefined

Infinity

If a line passes through origin then the equation of the line is

Choose an answer

y = m/x

y = mx

x = my

None

The number of ways in which we can courier 5 packets to 10 cities is

Choose an answer

2 x 5^o

5¹⁰

10⁵

2¹⁰

What is the domain of y = Cot^-1 x?

Choose an answer

Set of irrational numbers only

Set of all real numbers

Set of integers only

Set of complex numbers only

Sin x + Cos x=1 x=

Choose an answer

π

π/2

π/3

π/4

If 0 is not an integral multiple of π/2 then Cot⁴ θ+ Cot² θ=?

Choose an answer

Cosec⁴ θ -Cosec²θ

Tan θ - Tan² θ

Cosec² θ + Cosec θ

Sinθ Cosθ

If 2 Sin x Cos 2 x = Sin x then?

Choose an answer

X = nπ+ π/6

X = nπ +π/3

X = nπ +1

X = nπ + π/2

Which is in the solution set of 4x - 3y <2

Choose an answer

(3,0)

(4,1)

(1,3)

None

Which of the following is the subset of all sets ?

Choose an answer

A ≠ C

B = C

A = B

A ≠ B

If the angle between two vectors with magnitude 8 and 2 is 60° then their scalar product is

Choose an answer

12

8

16

1

If Sin θ =Cosθ then θ=

Choose an answer

30°

45°

60°

90°

Complex roots of real quadratic equation occur in

Choose an answer

Nilpotent matrix

Singular matrix

Non singular matrix

Diagonal matrix

Cos^-1 x =

Choose an answer

∏ = sin^-1 x

∏ + sin^-1 x

∏/2 - sin^-1 x

∏/2 +sin^-1 x

The sum of the series 1+5+9+13+17+21+25+29 is:

Choose an answer

10 cm

20 cm

30 cm

40 cm

If the 9^th tern of A.P is 8 and the 4^th term is 20. then the first term is

Choose an answer

1

2

-2

-1

If the vector 2i+4j-2k and 2i +6j+xk are perpendicular then x-7

Choose an answer

4

8

14

7

If P(E) is the probability that can event will occur then P(E)=

Choose an answer

1

0.5

2

0

r + 3 > 5 then which is true

Choose an answer

r + 2 > 4

r + 2 < 4

r + 2 + 4

None

A relation in which the equality is true only for some values of the unknown variable is called

Choose an answer

An identity

An equation

A polynomial

Inverse function

The multiplicative inverse of -1 in the set {1-,1} is

Choose an answer

40

30

50

20

∫1/ax +b dx =

Choose an answer

1/a log |ax + b| +c

Log |ax + b| +c

1/b log |ax +b| +c

1/x log |ax + b| +c

The statement that a group can have more than one identity elements is

Choose an answer

True

False

Fallacious

Some times true

If Z₁ = 1+i, Z₂ = 2+3i, then |Z₂-Z₁|=?

Choose an answer

√3 I

√7

-2-1

√5

Sec^-1 x=

Choose an answer

Cos^-1 1/x

Cosec^-1 1/x

Cos-1 (-x)

Tan^-1 x

A point of a solution region where two of its boundary lines intersect is called

Choose an answer

Boundary

Inequality

Half plane

Vertex

If A = [a_ij] and b = [b_ij] are the matrices of the order 3x3 then A-B=

Choose an answer

Circle

Ellipse

Parabola

Hexagon

d/dx (3y⁴) =

Choose an answer

12y³ dy/dx

8y³

8y³ dy/dx

12y³

The sum of the ages of Nazish and his son is 56 years. Eight years ago. Nazish was 3 time as old as his son. How old is the son now?

Choose an answer

m = n

m ≠ n

mn = 1

mn = 0

The conic is a parabola if

Choose an answer

e <1

e > 1

e = 1

e = 0

AreCot √3 =?

Choose an answer

π/2

π

2π

π/6

An angle of one radian is equivalent to

Choose an answer

90^o

60^o

67^o

57^o, 18^o

Sin^-1 x =?

Choose an answer

π/2- Sin^-1 x

π/2 -Cos^-1 x

-Sin^-1 x

-Cos^-1 x

In the function v = 4/3 π r³, V is a function of

Choose an answer

3/4

r

v

π

The end points of the major axis of the ellipse are called its

Choose an answer

foci

Vertices

Co-vertices

eccentricity

The set of the first elements of the ordered pairs forming a relation is called its

Choose an answer

-x

does not exist

1/x

0

Unit vector in the positive direction of x-axis is

Choose an answer

î

ĵ

k̂

All

The mid point of the line joining (=1,-3) to(3,-5) is

Choose an answer

(1, 1)

(1,-1)

(2, -8)

(1, -4)

If a and b are any two distinct negative real numbers and G-ab where A.G.H represent arithmetic geometric and harmonic means then

Choose an answer

1

ω²

ω

0

What is the domain of y= Sin^-1 x?

Choose an answer

-1 ≤ x ≤1

1 ≤ x ≤ 1

0 ≤ x ≤ π

-π/2 ≤ x ≤ π/2

If ab > 0 and a < 0, which of the following is negative?

Choose an answer

b

-b

-a

(a - b)²

Two natural numbers whose sum is 25 and difference is 5, are

Choose an answer

25, 20

20, 10

20, 5

15, 10

Which is not included in the domain of Cos^-1 x

Choose an answer

0

1

-1

2

The associative angle of 280^o is

Choose an answer

100^o

10^o

80^o

-80^o

The number of diagonals of a six sided figure are

Choose an answer

9

6

12

3

If y = (ax)^m + b^m, then dy/dx equals

Choose an answer

m (ax)^m x^m-1

ma^m x^m-1

m a^m x^m-1

m a^m x^m-2

For any set X, X∪X is

Choose an answer

15

15i

-15i

-15

The multiplicative inverse of x such that x = 0 is

Choose an answer

-x

does not exist

1/x

0

Second derivative of y = x⁹ + 10x² + 2x -1 at x = 0 is

Choose an answer

10

20

12

1

The line through the center and perpendicular to the transverse axis is called the

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Major axis

Minor axis

Focal axis

Conjugate axis

Given eight points in a plane no three of which are collinear how many lines do the points determine?

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16

64

28

36

The number of ways in which 5 distinct toys can be distributed among 3 children is

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3⁵

5³

C⁵₃

P⁵₃

The set (Q, .)

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Infinite set

Singleton set

Two points set

None

Which of the following is not defined?

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Arcsin 1/9

ArcCos (-4/3)

Arctan 11/12

Arccot (-4)

Sum of integers starting from to n is

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n(n+1)/4

n(n+1)/6

n(n+1)/2

n(n-1)/2

x-1/(x+2)(x-2) =

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4/3(x-4) -1/3(x-1)

3/4(x+2) + 1/4(x-2)

2/3(x-2) - 4/3(x+2)

3/x - 2/x+1

If A and B are matrices of same order than (A + B)(A + B)=

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addition

multiplication

subtraction

None

If Z= (1,2). tjem Z^-1 = ?

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(0.2, 0.4)

(-0.2, 0.4)

(0.2, -0.4)

(-0.2, -0.4)

Partial fraction of 1/x³-1 will be of the form

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Conjugate pair

ordered pair

reciprocal pair

quadratic function

The radius of the circle (x- 1)² + (y + 3)² =64 is

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8

2√2

4

64

If sin θ= 3/5 Cos θ=

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1/2

3/5

4/5

1

If A and B are matrices such that AB=BA=I then

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A and B are multiplicative inverse of each other

A and B are additive inverses of each other

A and B are singular matrices

A and B are equal

If x lies in {0, 2π} and Cosec x = 2 then x =

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π/ 6 and 5π/6

π +2nπ

nπ

2π/3 and π/3

How many elements are in the sample space of two rolling dies

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6

12

18

36

If A = (3,8) and B = (5,6) then the distance between A and B is

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2√2

2

1

6

Corola available in 5 models 8 colours and 3 sizes how many Corola must a local dealer have no hand in order to have one of each kind avialable?

Choose an answer

24

120

16

39

Graph of the equation X² + y² = 4 is

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a circle

an ellipse

a parabola

A square

If Cⁿ_r, Pⁿ_r = 24:1 then r = ?

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1

2

3

4

The sum of the interior angles for a 16 sided polygon is

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0

ω

1

1 / ω

An m x n matrix is said to be rectangular if

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Forms a group w.r.t. addition

Non commutative group w.r.t. multiplication

Forms a group w.r.t. multiplication

Doesn't form a group

The equation of the normal to the circle x² + 2² = 25 at (4,3) is

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3x -4y =0

3x -4y= 5

4x + 3y=5

4x - 3y =25

The average of first 100 integers is=

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50 1/2

25 1/4

100

5050

Area of ΔABC=

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ab sin α

1/2 ab sin α

1/2 ac Sin γ

1/2 ac Sin β

120° degrees are equal to how many radians?

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π/3 radians

2π/3 radians

π/4 radians

π/2 radians

If k₁ : k₂ = 1:1 then the point P dividing the line is

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Mid point

Extreme left point

Extreme Right point

Plies out side k₁ and k₂

Sin 720° = ________

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1

0

2

1/2

In a school, there are 150 students. Out of these 80 students enrolled for mathematics class, 50 enrolled for English class, and 60 enrolled for Physics class. The student enrolled for English cannot attend any other class, but the students of mathematics and Physics can take two courses at a time. Find the number of students who have taken both physics and mathematics.

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40

30

50

20

∫cot (ax + b) dx =

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1/a log |sin (ax + b)| +c

1/a log |cos ax + b)

1/b |sin (ax + b)|

1/a log |sin (bx + a)|

In the figure angle A is =

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15

60

90

20

π/3 is

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A positive integer

A negative integer

A natural number

An irrational number

Find the geometric mean between 4 and 16

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7, 8

14, 4

28, 2

56, 1

In the figure PS is perpendicular to QR, if PQ = PR 26 and P8 = 24,then QR=

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10

20

40

26

A sequence of numbers whose reciprocals forms an arithmetic sequence is called

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Harmonic series

Arithmetic series

Harmonic sequence

Geometric sequence

For which of the following ordered pairs (s,t) is s + t> and s- t < -3?

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(3,2)

(2,3)

(1,8)

(0,3)

If 1 + Cos x = 0 then x =

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π +2n π

π + nπ

π - nπ

π/2

The angle a (0° < a< 180°) measured counterclockwise from positive x-axis to a non-horizontal straight line / is called the

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Rotation

Inclination

Radian

None

Sin-1 (√2/2)=?

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π/2

π/3

3π/4

2π

The common difference of the sequence 7,4,1......is

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1

-3

5

0

The cube roots of unity ω = -------------------------

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1-i √-3 / 2

-1+i √-3 / 2i

-1+i √3 / 2

1+i √3 / 2

How many different arrangements of the letters in the word QABABA are Possible?

Choose an answer

720

40

60

30

Which of the following is the equation of a line with slope 0 and passing through the point (4,3)

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X =4

X = -4

Y = 3

Y = -6

In 30,60,90 triangle if the smallest side is 6 than the side opposite to the angle of 60^o is

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12

3

6√3

6

ωⁿ = ?, when n = 3k

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0

ω

1

1 / ω

If y = sin(ax + b) then fourth derivative of y with respect to x=

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a⁴ cos (ax + b)

a⁴ sin (ax + b)

-a⁴ sin(ax +b)

a4 tan (ax + b)

x is a member of the set {-1,0,3,5} y is a member of the set {-2,1,2,4} which is possible?

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x- y =-6

x -y < -6

x -y > 6

None

If p and r are integers P = 0, and p ≠ -r, which of the following must be true?

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p < r

p > r

p + r < 0

p - r < -0

The nth term in G.P 3,-6,12,............ is

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25, 20

20, 10

20, 5

15, 10

Multiplicative inverse of "1" is

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4

3

2

1

If x < y, 2x = A and 2y = B then

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A =B

A < B

A< X

B < y

If a rectangle has an area 81x² and length of 27x. then what is its width?

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3x

9x

3x²

9x²

Which is an explicit function

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y = x² +2x -1

x² +xy +y² =2

xy² -y +9/xy =1

All are

Sin(a + b) + Sin(a- b) =

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Sin a Cos b

Sin a Sin b

Sin a + Cos b

Sin a - 2Cos b

Which is a proper rational fraction

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3x - 7/x² +4

2x² - 5/x² + 4

3x⁴/2x² - 15

All are proper rational fraction

In which quadrant is the solution of the equation sin x - 1 = 0

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II quadrants

II and III quadrants

III and Iv quadrants

I quadrant

If the order of A is n x m. Then order of kA is

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Forms a group

Does not form a group

Contains no additive identity

Contains no additive inverse

The principal value of sin^-1 [√3/2] is

Choose an answer

π/3

-π/3

2π/3

5π/3

The set of all positive even integers is

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Φ

{1,2,3}

{Φ}

{0}

If Cosθ =0, Then θ=

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nπ/2

(2n + 1)π/2

(2n - 1)π/2

(n ±1)π/2

What is the period of Cot x?

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2π

π

π/2

4π

If the diagonal of a square has coordinates (1,2) and(5,6) the length of a side is

Choose an answer

3

4

1

5

d/dx ∫x¹ dx =________.

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1/4 x⁴

X³

3x³

x⁴/4

The vertices of the ellipse x² + 4y² = 16 are

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(±,4,0)

(0,±,4)

(± 2,0)

(0,± 2)

The set {1, -1, i, -i}, form a group under

Choose an answer

addition

multiplication

subtraction

None

If x² +y² = 4, Then dy/dx =

Choose an answer

2x +2y

4 -x²

-x/y

y/x

If any two rows (or any two columns) of a square matrix are inter changed, the determinant of the resultant matrix is

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True

False

Fallacious

Some times true

√23 is

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A rational number

A irrational number

An even integer

A factor of 36

The magnitude of a vector can never be

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Zero

Negative

Positive

Absolute

ω⁸⁸ = ?

Choose an answer

A and B are multiplicative inverse of each other

A and B are additive inverses of each other

A and B are singular matrices

A and B are equal

The set (Z, +) forms a group

Choose an answer

Function on B

Range

Domain

A into B

Sin^-1 √3/2 =?

Choose an answer

2π/3

π/2

π/3

v/5

There are 30 Red balls and 25 Green balls in a bag of a ball is drawn from the bag randomly what is the probability that a Blue ball comes out?

Choose an answer

1

0.5

0

None

Any point where f is neither increasing nor decreasing and f(x) =0 at that point is called a

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Minimum

Maximum

Stationary point

Constant

Sin (2π -θ) =______.

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Cosθ

-Sinθ

-cosθ

What is the conjugate of -7 -2i ?

Choose an answer

-7 + 2i

7 + 2i

7-2i

√53

The complement of set A relative to universal set U is the set

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X

φ

Universal set

A function F(x) is called even if

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F(x) = F(-x)

F(x) = -F(x)

2F(x) = 0

If 4 - x > 5, then

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x > 1

x > -1

x < 1

x < -1

The fifth term of the sequence a_n = 3n - 2 is

Choose an answer

3

-3

13

-13

Sin-1 [-1/2] = ______.

Choose an answer

∏/3

-∏/6

-∏/3

∏/6

Given X, Y are any two sets such that number of elements in X=28, number of elements in set Y=28, and number of elements in set X∪Y=54, then number of elements in set X∩Y=

Choose an answer

-7 + 2i

7 + 2i

7-2i

√53

If a cone is cut by a plane perpendicular to the axis of the cone then the section is a

Choose an answer

Parabola

Circle

Hyperbola

Ellipse

Period is Tan x/5 is

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5π

4π

2π

π/5

If |A| ≠ 0 then A is called

Choose an answer

1

-1

±1

0

Domain of Y = csc x is

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R - nπ, n ε I

R

R -nπ/2,nεI

All negative Integers

Tan^-1 1/x =______

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Sin x

Sec^-1 X

Cot^-1 X

Sin Ix/cos- Ix

Ab > 0 and a > 0 then

Choose an answer

a > b

a < b

a = b

None

The two different parts of the hyperbola are called is

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Vertices

Directrices

Nappes

Branches

The center of a circle of radius 10 is on the origin which of the following points lies with in the circle

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(10,0)

(8,8)

(8,4)

(0,10)

The general solution of the differential equation dy/dx = log x is

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Y = -x log x- x +c

Y = x log x + x²

Y = x log x -x +c

Y= 2x log x + 2x +c

P(x) = 2x⁴ -3x³ +2x-1 is polynomial of degree

Choose an answer

1

2

3

4

The axis of the parabola y² = 4ax is

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x =0

Y =0

X = y

X = -y

The degree of the polynomial 2x⁴ + 3x² + 16x + 28 = x⁴ + 2x² is

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[a_{ij -}b_ji]

[a_{ij -}b_ij]

[a_{ij] - [}b_ij]

Cot 360° =______.

Choose an answer

Undefined

0.707

-0.5

0

There are 30 Red, 20 Green and some Blue bells in a bag if the probability of finding a Red ball is 1/3,how many are red balls in the bag

Choose an answer

120

20

40

90