Page 21 - ISC-12

18Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal
Z
Then x n−2 g(x) dx equals

n 1−
(1 + nx ) 1 n
(A) + K.
n(n − 1)
n 1−
(1 + nx ) 1 n
(B) + K.
n − 1
n 1+
(1 + nx ) 1 n
(C) + K.
n(n + 1)
n 1+
(1 + nx ) 1 n
(D) + K.
n + 1
[JEE 2007]

86. Let H 1 , H 2 , . . . , H n be mutually exclusive and exhaustive events with P(H i ) > 0, i = 1, 2, . . . , n. Let
E be any other event with 0 < P(E) < 1.
STATEMENT-1: P(H i |E) > P(E|H i ) · P(H i ) for i = 1, 2, . . . , n.
because
n
P
STATEMENT-2: P(H i ) = 1.
i=1
(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 2007]

−→ −→ −→ −→ −→ −→
87. Let the vectors PQ, QR, RS, ST, TU and UP represent the sides of a regular hexagon.
−→ −→ −→
~
STATEMENT-1: PQ × RS + ST 6= 0.
because
−→ −→ −→ −→
~
~
STATEMENT-2: PQ × RS = 0 and PQ × ST 6= 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 2007]

2
88. Let F(x) be an indefinite integral of sin x.
STATEMENT-1: The function F(x) satisfies F(x + π) = F(x) for all real x.

because
2
2
STATEMENT-2: sin (x + π) = sin x for all real x.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.