Page 7 - ISC-12

4Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal
Z π/2
17
17. The following integral (2 cosec x) dx is equal to
π/4
√
Z log (1+ 2)
u
)
(A) 2(e + e −u 16 du.
0
√
Z log (1+ 2)
u
(B) (e + e −u 17 du.
)
0
√
log (1+ 2)
Z
u
)
(C) (e − e −u 17 du.
0
√
log (1+ 2)
Z
u
(D) 2(e − e −u 16 du.
)
0
[JEE 2014]
18. Let f : [0, 2] → R be a function which is continuous on [0, 2] and is differentiable on (0, 2) with
f(0) = 1. Let
x √
Z 2
F(x) = f( t) dt
0
0
0
for x ∈ [0, 2]. If F (x) = f (x) for all x ∈ (0, 2), then F(2) equals
4
2
(A) e − 1. (B) e − 1.
4
(C) e − 1. (D) e .
[JEE 2014]
19. Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so

that each envelope contains exactly one card and no card is placed in the envelope bearing the same
number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number
of ways it can be done is

(A) 264. (B) 265.
(C) 53. (D) 67.

[JEE 2014]

20. Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every
girl is at least one more than the number of girls ahead of her, is
1 1 2 3
(A) . (B) . (C) . (D) .
2 3 3 4

[JEE 2014]
1 3 1 1
21. Four persons independently solve a certain problem correctly with probabilities , , , . Then the
2 4 4 8
probability that the problem is solved correctly by at least one of them is
235 21 3 253
(A) . (B) . (C) . (D) .
256 256 256 256

[JEE 2013]