Page 55 - ISC-12

8Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal

Paragraph for Question Nos. 35 to 37

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.

35. The probability that X = 3 equals
25 25 5 125
(A) . (B) . (C) . (D) .
216 36 36 216

36. The probability that X ≥ 3 equals
125 25 5 25
(A) . (B) . (C) . (D) .
216 36 36 216

37. The conditional probability that X ≥ 6 given X > 3 equals
125 25 5 25
(A) . (B) . (C) . (D) .
216 216 36 36
[JEE 2009]

Paragraph for Question Nos. 38 to 40

3
Consider the functions defined implicitly by the equation y − 3y + x = 0 on various intervals in the
real line. If x ∈ (−∞, −2) ∪ (2, ∞), the equation implicitly defines a unique real-valued differentiable
function y = f(x).
If x ∈ (−2, 2), the equation implicitly defines a unique real-valued differentiable function y = g(x)
satisfying g(0) = 0.

√ √ √
00
38. If f(−10 2) = 2 2, then f (−10 2) =
√ √ √ √
4 2 4 2 4 2 4 2
(A) . (B) − . (C) . (D) − .
3
3
3 2
3 2
7 3 7 3 7 3 7 3
39. The area of the region bounded by the curve y = f(x), the x-axis, and the lines x = a and x = b,
where −∞ < a < b < −2, is
b x
Z
(A) 2 dx + bf(b) − af(a).
a 3[(f(x)) − 1]
b x
Z
(B) − dx + bf(b) − af(a).
2
a 3[(f(x)) − 1]
x
Z b
(C) 2 dx − bf(b) + af(a).
a 3[(f(x)) − 1]
Z b x
(D) − dx − bf(b) + af(a).
2
3[(f(x)) − 1]
a
1
Z
0
40. g (x) dx =
−1
(A) 2 g(−1). (B) 0. (C) −2 g(1). (D) 2 g(1).

[JEE 2008]