Page 17 - ISC-12

14Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal
(x − 1) n
68. Let g(x) = ; 0 < x < 2, m and n are integers, m 6= 0, n > 0, and let p be the left
m
log cos (x − 1)
hand derivative of |x − 1| at x = 1. If lim g(x) = p, then
x→1+
(A) n = 1, m = 1. (B) n = 1, m = −1.

(C) n = 2, m = 2. (D) n > 2, m = n.
[JEE 2008]

69. The total number of local maxima and local minima of the function
(
(2 + x) 3 if − 3 < x ≤ −1
f(x) =
x 2/3 if − 1 < x < 2

is
(A) 0. (B) 1. (C) 2. (D) 3.

[JEE 2008]

00
70. Let f and g be real-valued functions defined on the interval (−1, 1) such that g (x) is continuous,
00
0
g(0) 6= 0, g (0) = 0, g (0) 6= 0, and f(x) = g(x) sin x.
00
STATEMENT-1: lim [g(x) cot x − g(0) cosec x] = f (0).
x→0
and
0
STATEMENT-2: f (0) = g(0).
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(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]

71. Consider three planes
P 1 : x − y + z = 1
P 2 : x + y − z = −1
P 3 : x − 3y + 3z = 2

Let L 1 , L 2 , L 3 be the lines of intersection of the planes P 2 and P 3 , P 3 and P 1 and P 1 and P 2
respectively.
STATEMENT-1: At least two of the lines L 1 , L 2 and L 3 are non-parallel.
and
STATEMENT-2: The three planes do not have a common point.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(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]