Page 6 - ISC-12

Single Correct Choice Type Jai Baba Ki3
2
Z π/2 x cos x
11. The value of dx is equal to
1 + e x
−π/2
π 2 π 2
2
2
(A) − 2. (B) + 2. (C) π − e π/2 . (D) π + e π/2 .
4 4
[JEE 2016]

n o
p
2
12. Area of the region (x, y) ∈ R : y ≥ |x + 3|, 5y ≤ x + 9 ≤ 15 is equal to
1 4 3 5
(A) . (B) . (C) . (D) .
6 3 2 3
[JEE 2016]

13. Let P be the image of the point (3, 1, 7) with respect to the plane x − y + z = 3. Then the equation of
x y z
the plane passing through P and containing the straight line = = is
1 2 1
(A) x + y − 3z = 0. (B) 3x + z = 0. (C) x − 4y + 7z = 0. (D) 2x − y = 0.

[JEE 2016]

f(x)
0
14. Let f : (0, ∞) → R be a differentiable function such that f (x) = 2 − for all x ∈ (0, ∞) and
x
f(1) 6= 1. Then

1 1
(A) lim f 0 = 1. (B) lim x f = 2.
x → 0+ x x → 0+ x
0
2
(C) lim x f (x) = 0. (D) |f(x)| ≤ 2 for all x ∈ (0, 2).
x → 0+
[JEE 2016]

15. From a point P(λ, λ, λ), perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1
and y = −x, z = −1. If P is such that ∠QPR is a right angle, then the possible value(s) of λ is(are)
√ √
(A) 2. (B) 1. (C) −1. (D) − 2.

[JEE 2014]

16. The function y = f(x) is the solution of the differential equation
4
dy xy x + 2x
+ = √
2
dx x − 1 1 − x 2
√
Z 3/2
in (−1, 1) satisfying f(0) = 0. Then f(x) dx is
√
− 3/2
√ √
π 3 π 3
(A) − . (B) − .
3 2 3 4
√ √
π 3 π 3
(C) − . (D) − .
6 4 6 2
[JEE 2014]