Page 51 - ISC-12

4Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal

1
14. The value of g is
2
(A) π. (B) 2π.
π π
(C) . (D) .
2 4

1
15. The value of g 0 is
2
π π
(A) . (B) π. (C) − . (D) 0.
2 2
[JEE 2014]

Paragraph for Question Nos. 16 and 17

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3, 4, 5;
and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes.
th
Let x i be the number on the card drawn from the i box, i = 1, 2, 3.

16. The probability that x 1 + x 2 + x 3 is odd, is
29 53 57 1
(A) . (B) . (C) . (D) .
105 105 105 2

17. The probability that x 1 , x 2 , x 3 are in an arithmetic progression, is
9 10 11 7
(A) . (B) . (C) . (D) .
105 105 105 105

[JEE 2014]

Paragraph for Question Nos. 18 and 19

A box B 1 contains 1 white ball, 3 red balls and 2 black balls. Another box B 2 contains 2 white balls, 3 red
balls and 4 black balls. A third box B 3 contains 3 white balls, 4 red balls and 5 black balls.

18. If 1 ball is drawn from each of the boxes B 1 , B 2 and B 3 the probability that all 3 drawn balls are of

the same colour is
82 90 558 566
(A) . (B) . (C) . (D) .
648 648 648 648

19. If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white
and the other ball is red, the probability that these 2 balls are drawn from box B 1 is
116 126 65 55
(A) . (B) . (C) . (D) .
181 181 181 181
[JEE 2013]

Paragraph for Question Nos. 20 and 21

Let f : [0, 1] → R (the set of all real numbers) be a function. Suppose the function f is twice differentiable,
00
0
x
f(0) = f(1) = 0 and satisfies f (x) − 2f (x) + f(x) ≥ e , x ∈ [0, 1].