Write the smallest equivalence relation from the set
cos x
A to A, where A = {1, 2, 3}. (i) Evaluate: ∫ dx
3cos x - 5
 0 1 -2 
 OR

2] 5 10 2  2 x +1 3x 
Statement 1: If ‘A’ is an invertible matrix, then (A2)-1
of the differential equation (1 + x2) dy + (1 + y2)
= (A-1)2
dx = 0
Statement 2: If ‘A’ is an invertible matrix, then |A-1|

(a) Statement 1 is true and Statement 2 is false. In subparts (i) to (xi) choose the correct options and (b) Statement 2 is true and Statement 1 is false. in subparts (xii) to (xv), answer the questions as (c) Both the statements are true. instructed. (d) Both the statements are false. 0 a  16 1x -1
Which of the following is a homogenous differential -2
equation? (c) (d) 0
(a) (4x2 + 6y + 5) dy - (3y2 + 2x + 4) dx = 0

For what value of x, is A =  -1 0 3  a skew

Evaluate: ∫ ( log x ) dx
 x -3 0 
symmetric matrix? Question 9

(a) Statement 1 is true and Statement 2 is false. In subparts (i) to (xi) choose the correct options and (b) Statement 2 is true and Statement 1 is false. in subparts (xii) to (xv), answer the questions as (c) Both the statements are true. instructed. (d) Both the statements are false. 0 a  16 1x -1
If A =   , then A is: (iv) ∫ 2 dx is equal to:
0 0  0 x +1

(a) Statement 1 is true and Statement 2 is false. In subparts (i) to (xi) choose the correct options and (b) Statement 2 is true and Statement 1 is false. in subparts (xii) to (xv), answer the questions as (c) Both the statements are true. instructed. (d) Both the statements are false. 0 a  16 1x -1
Assertion: Consider the two events A and B such
(b) (xy) dx - (x3 + y3) dy = 0
A B
(c) (x3 + 2y2) dx + 2xy dy = 0 that n(A) = n(B) and P   = P   .
B A
(d) y2 dx + (x2 - xy - y2) dy = 0
Reason: The events A and B are mutually exclusive.