Page 10 - ISC-12

Single Correct Choice Type Jai Baba Ki7
√
ˆ
ˆ
~
~
ˆ
~
ˆ
ˆ
ˆ
34. If ~a and b are vectors such that |~a + b| = 29 and ~a × (2i + 3j + 4k) = (2i + 3j + 4k) × b, then a
ˆ
ˆ
ˆ
~
possible value of (~a + b) · (−7i + 2j + 3k) is
(A) 0. (B) 3. (C) 4. (D) 8.
[JEE 2012]
35. If P is a 3 × 3 matrix such that P T = 2P + I, where P T is the transpose of P and I is the 3 × 3
   
x 0
identity matrix, then there exists a column matrix X = y 6= 0 such that
 
 
z 0
 
0
(A) PX = 0. (B) PX = X. (C) PX = 2X. (D) PX = −X.
 
0
[JEE 2012]

36. Four fair dice D 1 , D 2 , D 3 and D 4 each having six faces numbered 1, 2, 3, 4, 5 and 6, are rolled
simultaneously. The probability that D 4 shows a number appearing on one of D 1 , D 2 and D 3 is
91 108
(A) . (B) .
216 216
125 127
(C) . (D) .
216 216

[JEE 2012]

37. The value of the integral
π/2 π + x
Z
2
x + ln dx
−π/2 π − x
is
π 2
(A) 0. (B) − 4.
2

π 2 π 2
(C) + 4. (D) .
2 2
[JEE 2012]

38. The value of √
Z ln 3 2
x sin x
dx
√ sin x + sin (ln 6 − x )
2
2
ln 2
is
1 3 1 3
(A) ln . (B) ln .
4 2 2 2
3 1 3
(C) ln . (D) ln .
2 6 2

[JEE 2011]