Page 19 - ISC-12

16Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for
Statement-1.
(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.
[JEE 2008]

75. Let f(x) be differentiable on the interval (0, ∞) such that f(1) = 1 and
2
2
t f(x) − x f(t)
lim = 1
t→x t − x
for each x > 0. Then f(x) is
1 2x 2 1 4x 2 1 2 1
(A) + . (B) − + . (C) − + . (D) .
3x 3 3x 3 x x 2 x

[JEE 2007]

76. One Indian and four American men and their wives are to be seated randomly around a circular table.
Then the conditional probability that the Indian man is seated adjacent to his wife given that each
American man is seated adjacent to his wife, is
1 1 2 1
(A) . (B) . (C) . (D) .
2 3 5 5

[JEE 2007]

x
c
77. The tangent to the curve y = e drawn at the point (c, e ) intersects the line joining the points
(c − 1, e c−1 ) and (c + 1, e c+1 )
(A) on the left of x = c. (B) on the right of x = c.

(C) at no point. (D) at all points.

[JEE 2007]

 
sec x
Z 2
 f(t) dt 
2
  equals

78. lim  2
π
2
x→ π  x − 
4 16

8 2 2 1
(A) f(2). (B) f(2). (C) f . (D) 4f(2).
π π π 2
[JEE 2007]
ˆ
2ˆ
2ˆ ˆ
ˆ ˆ
2ˆ
ˆ ˆ
79. The number of distinct real values of λ, for which the vectors −λ i+j +k, i−λ j +k and i+j −λ k
are coplanar, is
(A) zero (B) one (C) two (D) three
[JEE 2007]