Page 36 - ISC-12

Multiple Correct Choices Type Jai Baba Ki13
x − 1 y + 1 z x + 1 y + 1 z
57. If the straight lines = = and = = are coplanar, then the plane(s)
2 k 2 5 2 k
containing these two lines is(are)

(A) y + 2z = −1. (B) y + z = −1. (C) y − z = −1. (D) y − 2z = −1.

[JEE 2012]

1 1 1
58. Let X and Y be two events such that P(X|Y ) = , P(Y |X) = and P(X ∩ Y ) = . Which of the
2 3 6
following is (are) correct?
2
(A) P(X ∪ Y ) = . (B) X and Y are independent.
3
1
c
(C) X and Y are not independent. (D) P(X ∩ Y ) = .
3
[JEE 2012]

 
1 4 4
59. If the adjoint of a 3 × 3 matrix P is 2 1 7, then the possible value(s) of the determinant of P


1 1 3
is(are)

(A) −2. (B) −1. (C) 1. (D) 2.

[JEE 2012]

ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
60. The vector(s) which is/are coplanar with vectors i + j + 2k and i + 2j + k, and perpendicular to the
ˆ
ˆ
ˆ
vector i + j + k is/are
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
(A) j − k. (B) −i + j. (C) i − j. (D) −j + k.
[JEE 2011]
61. If
 π π
 −x − if x ≤ −
2 2




 π

 − cos x if − < x ≤ 0

f(x) = 2

 x − 1 if 0 < x ≤ 1






ln x if x > 1

then
π
(A) f(x) is continuous at x = . (B) f(x) is not differentiable at x = 0.
2
3
(C) f(x) is differentiable at x = 1. (D) f(x) is differentiable at x = − .
2
[JEE 2011]