Question number

Question

Answer Key

1

A relation R in a set A is called Reflexive relation if

(a) (a, a) ∈ R for all a ∈ A

2

The principal value of sin -1 (1/√2) is

(c) π/4

3

Match List - I with List - II.

List-I

(A) Domain of sin -1 x

(B) Range of tan -1 x

(C) Range of cos -1 x

List - II

(i) ((- π/2, π/2)

(ii) [0, π]

(iii) [-1,1]

Choose the correct answer from the options given below :

(d) A-iii, B-i, C-ii

4

For a 2 x 2 matrix A=[a ij ] whose elements are given by an overline a ij = 2i - j then A is equal to

(b) [ 1 0 ]

[ 3 2 ]

5

Let A be a nonsingular matrix of order 3 x 3 then |adj A| is equal to

(b) 3|A|

6

If f(x) = 2cosx, then f'(π/4) is

(a) 2

7

For the given figure consider the following statements 1 and 2:

Statement 1: Left hand derivative of y = f(x) at x = 1 is -1.

Statement 2: The function y = f(x) is differentiable at x = 1 Then which of the following are true?

(a) Statement 1 is true, Statement 2 is false

8

The absolute maximum value of the function f given by f(x) = x 3 , x ∈ [- 2, 2] is

(d) 8

9

∫ e x (sinx - cosx) dx is

(c) e x sinx

10

The degree of the differential equation is d 3 y/dx 3 + d 2 y/dx 2 + e dy/dx = 0 is

(d) Not defined

11

The direction cosines of the vector vec a = i - j + 2k are

(b) 1/√6, -1/√6, 2/√6

12

The angle between two vectors a and b with |a| = √3, |b| = 2 and a . b = √6 is

(c) π/4

13

The equation of y-axis in space is

(b) x = 0 z = 0

14

If P(A) = 1/2, P(B|A)= 2/3 then P( A ∩ B) is

(c) 1

15

Assertion [A]: For two events E and F if P(E) = 1/5, P(F) = 1/2, P(E|F)= 1/5, then E and F are independent events. and

Reason [R]: If E and Fare two independent events then P(F|E)= P(F)

Then which of the following are true?

(c) Both [A] and [R] are true

Q.No.

Question

Answer Key

16

The value of cos(sec -1 (2) - sin -1 (√3/2) is

1

17

If y = sin -1 (cos x) then dy/dx =

-1

18

The value of 7 ∫ 13 1 dx =

6

19

The projection of vector i + j along the vector i - j is

0

20

If P(A ∩ B)= 4/13 and P(B) = 9/13 then P(A'|B) =

5/9