Page 26 - ISC-12

Multiple Correct Choices Type Jai Baba Ki3

8. Which of the following is(are) NOT the square of a 3 × 3 matrix with real entries?
       
1 0 0 1 0 0 1 0 0 −1 0 0
(B) 0 1 (C) 0 −1 (D)  0 −1
       
(A) 0 1 0 0  0  0 
0 0 1 0 0 −1 0 0 −1 0 0 −1
[JEE 2017]

1 1 2
9. Let x and y be two events such that P(X) = , P(X|Y ) = and P(Y |X) = . Then
3 2 5
4 1
(A) P(Y ) = . (B) P(X|Y ) = .
15 3
1 2
(C) P(X ∩ Y ) = . (D) P(X ∪ Y ) = .
5 5

[JEE 2017]

0
10. Let f : R → R is a differentiable function such that f (x) > 2f(x) for all x ∈ R, and f(0) = 1, then
(A) f(x) is increasing in (0, ∞). (B) f(x) is decreasing in (0, ∞).

0
(C) f(x) > e 2x in (0, ∞). (D) f (x) < e 2x in (0, ∞).
[JEE 2017]

1 − x (1 + |1 − x|) 1
11. Let f(x) = cos for x 6= 1. Then
|1 − x| 1 − x
(A) lim f(x) = 0. (B) lim f(x) does not exist.
x→1− x→1−
(C) lim f(x) = 0. (D) lim f(x) does not exist.
x→1+ x→1+
[JEE 2017]

cos 2x cos 2x sin 2x

12. If f(x) = − cos x cos x − sin x , then

sin x sin x cos x

0
(A) f (x) = 0 at exactly three points in (−π, π).
0
(B) f (x) = 0 at more than three points in (−π, π).
(C) f(x) attains its maximum at x = 0.
(D) f(x) attains its minimum at x = 0.

[JEE 2017]

3
2
13. If the line x = α divides the area of region R = {(x, y) ∈ R : x ≤ y ≤ x, 0 ≤ x ≤ 1} into two
equal parts, then
1 1
2
4
2
4
(A) 0 < α ≤ . (B) < α < 1. (C) 2α −4α +1 = 0. (D) α + 4α − 1 = 0.
2 2
[JEE 2017]