Page 9 - ISC-12

6Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal

(
2
x cos if x 6= 0

π
28. Let f(x) = x , x ∈ R, then f is
0 if x = 0
(A) differentiable both at x = 0 and at x = 2.
(B) differentiable at x = 0 but not differentiable at x = 2.
(C) not differentiable at x = 0 but differentiable at x = 2.
(D) differentiable neither at x = 0 nor at x = 2.
[JEE 2012]

3
2
29. The function f : [0, 3] → [1, 29], defined by f(x) = 2x − 15x + 36x + 1, is
(A) one-one and onto. (B) onto but not one-one.
(C) one-one but not onto. (D) neither one-one nor onto.
[JEE 2012]

30. Let P = [a ij ] be a 3 × 3 matrix and let Q = [b ij ], where b ij = 2 i+j a ij for 1 ≤ i, j ≤ 3. If the
determinant of P is 2, then the determinant of the matrix Q is

10
12
13
11
(A) 2 . (B) 2 . (C) 2 . (D) 2 .
[JEE 2012]
Z 2
sec x
31. The integral dx equals (for some arbitrary constant K)
(sec x + tan x) 9/2

1 1 1
(A) − − (sec x + tan x) 2 + K.
(sec x + tan x) 11/2 11 7

1 1 1
(B) − (sec x + tan x) 2 + K.
(sec x + tan x) 11/2 11 7

1 1 1
(C) − + (sec x + tan x) 2 + K.
(sec x + tan x) 11/2 11 7

1 1 1
(D) + (sec x + tan x) 2 + K.
(sec x + tan x) 11/2 11 7
[JEE 2012]

32. The point P is the intersection of the straight line joining the points Q(2, 3, 5) and R(1, −1, 4) with
the plane 5x−4y −z = 1. If S is the foot of the perpendicular drawn from the point T(2, 1, 4) to QR,
then the length of the line segment PS is
1 √ √
(A) √ . (B) 2. (C) 2. (D) 2 2.
2
[JEE 2012]

33. The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2 and
2
x − y + z = 3 and at a distance √ from the point (3, 1, −1) is
3
√ √
(A) 5x − 11y + z = 17. (B) 2 x + y = 3 2 − 1.
√ √ √
(C) x + y + z = 3. (D) x − 2 y = 1 − 2.

[JEE 2012]