Page 16 - ISC-12

Single Correct Choice Type Jai Baba Ki13

64. Let g(x) = log f(x), where f(x) is a twice differentiable positive function defined on (0, ∞) such
that f(x + 1) = x f(x). Then, for N = 1, 2, 3, . . . ,

1 1
g 00 N + − g 00 =
2 2

1 1 1
(A) −4 1 + + + · · · + .
9 25 (2N − 1) 2

1 1 1
(B) 4 1 + + + · · · + .
9 25 (2N − 1) 2

1 1 1
(C) −4 1 + + + · · · + .
9 25 (2N + 1) 2

1 1 1
(D) 4 1 + + + · · · + .
9 25 (2N + 1) 2
[JEE 2008]

65. Consider the curves
2
C 1 : y = 4x
2
2
C 2 : x + y − 6x + 1 = 0
Then,

(A) C 1 and C 2 touch each other only at one point.

(B) C 1 and C 2 touch each other exactly at two points.
(C) C 1 and C 2 intersect (but do not touch) at exactly two points.
(D) C 1 and C 2 neither intersect nor touch each other.

[JEE 2008]

66. If 0 < x < 1, then
√
−1
2
−1
2
1 + x [{x cos (cot x) + sin (cot x)} − 1] 1/2 =
x √ √
2
2
(A) √ . (B) x. (C) x 1 + x . (D) 1 + x .
1 + x 2
[JEE 2008]

ˆ
67. The edges of a parallelepiped are of unit length and are parallel to non-coplanar unit vectors ˆa, b, ˆc
such that
1
ˆ
ˆ
ˆ a · b = b · ˆc = ˆc · ˆa =
2
Then, the volume of the parallelepiped is
√
1 1 3 1
(A) √ . (B) √ . (C) . (D) √ .
2 2 2 2 3

[JEE 2008]