Page 13 - ISC-12

10Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal
x √
Z
−x
50. Let f be a real-valued function defined on the interval (−1, 1) such that e f(x) = 2+ t + 1 dt,
4
0
for all x ∈ (−1, 1), and let f −1 be the inverse function of f. Then (f −1 )(2) is equal to
1 1 1
(A) 1. (B) . (C) . (D) .
3 2 e
[JEE 2010]

51. If the distance of the point P(1, −2, 1) from the plane x + 2y − 2z = α, where α > 0, is 5, then the
foot of the perpendicular from P to the plane is

8 4 7 4 4 1
(A) , , − . (B) , − , .
3 3 3 3 3 3

1 2 10 2 1 5
(C) , , . (D) , − , .
3 3 3 3 3 2
[JEE 2010]

52. Two adjacent sides of a parallelogram ABCD are given by
−→ −−→
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
AB = 2i + 10j + 11k and AD = −i + 2j + 2k.
The side AD is rotated by an acute angle α in the plane of the parallelogram so that AD becomes
0
0
AD . If AD makes a right angle with the side AB, then the cosine of the angle α is given by
√ √
8 17 1 4 5
(A) . (B) . (C) . (D) .
9 9 9 9
[JEE 2010]
4 1
53. A signal which can be green or red with probability and , respectively, is received by station A
5 5
3
and then transmitted to station B. The probability of each station receiving the signal correctly is .
4
If the signal received at station B is green, then the probability that the original signal was green is
3 6
(A) . (B) .
5 7
20 9
(C) . (D) .
23 20

[JEE 2010]

54. Let P(3, 2, 6) be a point in space and Q be a point on the line
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
~r = (i − j + 2k) + µ(−3i + j + 5k)
−→
Then the value of µ for which the vector PQ is parallel to the plane x − 4y + 3z = 1 is
1 1
(A) . (B) − .
4 4
1 1
(C) . (D) − .
8 8
[JEE 2009]