Page 12 - ISC-12

Single Correct Choice Type Jai Baba Ki9
x y z
44. Equation of the plane containing the straight line = = and perpendicular to the plane
2 3 4
x y z x y z
containing the straight lines = = and = = is
3 4 2 4 2 3
(A) x + 2y − 2z = 0. (B) 3x + 2y − 2z = 0.
(C) x − 2y + z = 0. (D) 5x + 2y − 4z = 0.

[JEE 2010]

ˆ
ˆ
ˆ
ˆ
ˆ ˆ ˆ
45. Let P, Q, R and S be the points on the plane with position vectors −2i − j, 4i, 3i + 3j and −3i + 2j
respectively. The quadrilateral PQRS must be a
(A) parallelogram, which is neither a rhombus nor a rectangle.
(B) square.
(C) rectangle, but not a square.
(D) rhombus, but not a square.

[JEE 2010]

46. The number of 3 × 3 matrices A whose entries are either 0 or 1 and for which the system
   
x 1
   
A y = 0
z 0
has exactly two distinct solutions, is

9
(A) 0. (B) 2 − 1. (C) 168. (D) 2.
[JEE 2010]

1 Z x t ln (1 + t)
47. The value of lim dt is
x→0 x 3 t + 4
4
0
1 1 1
(A) 0. (B) . (C) . (D) .
12 24 64
[JEE 2010]

48. Let f, g and h be real-valued functions defined on the interval [0, 1] by
2 x
f(x) = e x 2 + e −x 2 , g(x) = xe x 2 + e −x 2 and h(x) = x e 2 + e −x 2 .
If a, b and c denote, respectively, the absolute maximum of f, g and h on [0, 1], then
(A) a = b and c 6= b. (B) a = c and a 6= b. (C) a 6= b and c 6= b. (D) a = b = c.

[JEE 2010]

4
Z 1 x (1 − x) 4
49. The value(s) of dx is(are)
1 + x 2
0
22 2 71 3π
(A) − π. (B) . (C) 0. (D) − .
7 105 15 2
[JEE 2010]