Page 53 - ISC-12

6Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal
3
25. Let ω be a solution of x − 1 = 0 with Im (ω) > 0. If a = 2 with b and c satisfying (E), then the value
3 1 3
of + + is equal to
ω a ω b ω c
(A) −2. (B) 2.

(C) 3. (D) −3.

2
26. Let b = 6, with a and c satisfying (E). If α and β are the roots of the quadratic equation ax +bx+c = 0,
then
∞ n
1 1
X
+
α β
n=0
is
(A) 6. (B) 7.
6
(C) . (D) ∞.
7

[JEE 2011]

Paragraph for Question Nos. 27 and 28

Let U 1 and U 2 be two urns such that U 1 contains 3 white and 2 red balls, and U 2 contains only 1 white ball.
A fair coin is tossed. If head appears then 1 ball is drawn at random from U 1 and put into U 2 . However,
if tail appears then 2 balls are drawn at random from U 1 and put into U 2 . Now 1 ball is drawn at random

from U 2 .

27. The probability of the drawn ball from U 2 being white is
13 23
(A) . (B) .
30 30
19 11
(C) . (D) .
30 30

28. Given that the drawn ball from U 2 is white, the probability that head appeared on the coin is
17 11
(A) . (B) .
23 23
15 12
(C) . (D) .
23 23

[JEE 2011]

Paragraph for Question Nos. 29 to 31

Let p be an odd prime number and T p be the following set of 2 × 2 matrices:
( " # )
a b
T p = A = : a, b, c ∈ {0, 1, 2, . . . , p − 1}
c a

29. The number of A in T p such that A is either symmetric or skew symmetric or both. and det (A)

divisible by p is