Page 50 - ISC-12

Comprehension Type Jai Baba Ki3

Paragraph for Question Nos. 10 and 11

Let n 1 and n 2 be the number of red and black balls, respectively, in box I. Let n 3 and n 4 be the number of

red and black balls, respectively, in box II.

10. One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly out of
1
this box. The ball was found to be red. If the probability that this red ball was drawn from box II is ,
3
then the correct option(s) with the possible values of n 1 , n 2 , n 3 and n 4 is(are)

(A) n 1 = 3, n 2 = 3, n 3 = 5, n 4 = 15. (B) n 1 = 3, n 2 = 6, n 3 = 10, n 4 = 50.
(C) n 1 = 8, n 2 = 6, n 3 = 5, n 4 = 20. (D) n 1 = 6, n 2 = 12, n 3 = 5, n 4 = 20.

11. A ball is drawn at random from box I and transferred to box II. If the probability of drawing a red ball
1
from box I, after this transfer, is , then the correct option(s) with possible values of n 1 and n 2 is(are)
3
(A) n 1 = 4 and n 2 = 6. (B) n 1 = 2 and n 2 = 3.

(C) n 1 = 10 and n 2 = 20. (D) n 1 = 3 and n 2 = 6.

[JEE 2015]

Paragraph for Question Nos. 12 and 13

0
Let F : R → R be a thrice differentiable function. Suppose that F(1) = 0, F(3) = −4 and F (x) < 0 for

1
all x ∈ , 3 . Let f(x) = x F(x) for all x ∈ R.
2
12. The correct statement(s) is(are)

0
(A) f (1) < 0. (B) f(2) < 0.
0
0
(C) f (x) 6= 0 for any x ∈ (1, 3). (D) f (x) = 0 for some x ∈ (1, 3).
Z 3 Z 3
00
3
0
2
13. If x F (x) dx = −12 and x F (x) dx = 40, then the correct expression(s) is(are)
1 1
Z 3
0
0
(A) 9f (3) + f (1) − 32 = 0. (B) f(x) dx = 12.
1
Z 3
0
0
(C) 9f (3) − f (1) + 32 = 0. (D) f(x) dx = −12.
1
[JEE 2015]
Paragraph for Question Nos. 14 and 15

Given that for each a ∈ (0, 1),
Z 1−h
−a
lim t (1 − t) a−1 dt
h→0+
h
exists. Let this limit be g(a). In addition, it is given that the function g(a) is differentiable on (0, 1).