Question # 1

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

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1/18

1/12

1/36

None of these

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

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Diagonal matrix

Rectangular matrix

Square matrix

Scalar matrix

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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

If P is a proposition then its negative is denoted by

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

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-2

-3

2

3

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The solution set of sin x + cos x = 0 is

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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

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H.P.

A.P.

G.P.

None of these

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

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trigonometric function

algebraic function

exponential function

logarithmic function

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

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√7

√41

√19

√(2&7)

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

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a

b

a + b

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

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commutative property of multiplication

distributive property of multiplication

associative property of multiplication

multiplicative inverse

What is the period of 6 sin x=?

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π

-π

π/2

2π

The general solution of tan 3x = 1 is

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

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10 / 3

5 / 3

3 / 5

3 / 10

1 radian = ______

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180°

90°

57.296°

60°

Which of the following integrals can be evaluated

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

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the secant of the circle

the arc of the circle

the chord of the circle

the circumference of the circle

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6

360

120

24

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

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General term

Common ratio

Common difference

None of these

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Range of cosec x is ______

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{-1, 1}

R

Negative real numbers

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

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0

1

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110

220

1320

None of these

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

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A

A'

-A

A

In (x + iy) x is the known as

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Imaginary part of complex number

Real part of complex number

Complex number

None of above

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x^-2+ c

not possible

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0

1

undefined

The identity element with respect to subtraction is

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0

-1

0 and 1

None of thes

(a^-1)^-1=

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a^-1

a

-a

None of above

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

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m x m

m x n

n x n

n x m

cos (α+β) + cos (α-β) =

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4 cosαcosβ

2 cosαcosβ

2 sinαsinβ

2 sinαcosβ

If f (x) = 2x+1 then fof (x) = _______;

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4x+3

2x +3

4x +1

None of these

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quadratic function

constant function

trigonometric function

linear function

The magnitude of vector a 2i-7j is

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√23

√43

3

√53

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if the value of the sphere, v =4/3πr²^, then the which of the following statement is true?

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r is the function of v

v is the function ofπ

π is independent variable

None of these

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Inverse of the function y-10x is

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y=logx

y=lnx

x=10y

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

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-2

2

3

1

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If f(x) = x²then f(2) is

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-2

2

4

-4

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

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a⁴cos (ax + b)

a⁴sin (ax + b)

-a⁴sin (ax + b)

a⁴tan (ax + b)

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A natural number

A rational number

An irrational number

A whole number

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

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graph

Continuity

Discontinuity

Periods

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

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2x + 3y = 0

2x - 3y = 0

3x + 2y = 0

3x - 2y = 0

Tan^-11/x = ______

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sin x

sec^-1X

cot^-1X

None of these

Cos 0° = ______

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-1

0

1

Undefined

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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

(1,0) is in the solution of the inequality

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3x + 2y > 8

2x - 3y < 4

2x + 3y > 3

x - 2y < -5

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

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

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8

12

10

14

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

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xyz

0

1

None of these

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

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10

5

2

Fifteen girls compete in a race. The first three places can be taken by them in

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3! ways

12! ways

15 x 14 x 13 ways

42 ways

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

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1:2

3:2

2:3

2:1

Cosec 60° = ______

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The period of tan [x/3] is ______

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2π

4π

3π

5π

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Cos 2x = sin 4y

Cos 4y = cos 2x

Cos 3y = sin 4x

None of these

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3

6

0

None of these

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

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Addition

Multiplication

Division

Subtraction

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

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If A∩B=B, then n(A∩B) is equal to

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n(a)

n(a)+n(c)

n(c)

None of these

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

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n - 1

n + 1

n + 2

n + 3

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 expansion of (1 - 3x)^-1is valid if

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| x | < 1

| x | < 3

| x | < 1/3

None of these

2/9,5/7∈ R,(2│9)(5│7)=10/63∈R this property is called

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Associative property

Identity property

Commutative property

Closure property w.r.t multiplication

For a square matrix A, if A = A^t, then A is called

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matrix

Transpose

Symmetric

Non-symmetric

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

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

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Addition

Multiplication

Subtraction

None

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The range of y = cot x = ______

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-∞> y > +∞

-∞> x > +∞

-∞ <y < +∞

None of above

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

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2ⁿ

2²ⁿ

2 . n

n²

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x³- x²+ x + c

6x - 2 + c

x³- 2x + c

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

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3

1

2

4

The two parts into which 57 should be divided so that their product is 782 are

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43,14

34,23

33,24

44,13

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A parabola

An ellipse

A hyperbola

A circle

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In f(x) + c

f(x) - c

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

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1 x 1

1 x 10

10 x 10

10 x 1

If x³- x²+ 5x+ 4 is divided by x - 2, then the reminder is

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0

2

18

14

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

2x + y = 2 is:

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(2,6)

(6,2)

(-2,2)

(2,-2)

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

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0≤ y < 1

0 < y < 1

0≤ y≤ 1

0 < y≤1

x = ________ is in the solution of 2x + 3 > 0

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1

-2

-3

-4

Period of 3 sin x is ______

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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

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4/63

5/9

45/49

None of these

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

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[0 ,∞ )

(0 ,∞)

(-∞ ,3]

[0,∞)

s > t then

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(s - t)²> (t - s)²

(s - t)²< (t - s)²

(s - t)²= (t - s)²

None