Page 52 - ISC-12

Comprehension Type Jai Baba Ki5

20. Which of the following is true for 0 < x < 1?
1 1 1
(A) 0 < f(x) < ∞. (B) − < f(x) < . (C) − < f(x) < 1. (D) −∞ < f(x) < 0.
2 2 4

1
−x
21. If the function e f(x) assumes its minimum in the interval [0, 1] at x = , which of the following is
4
true?
1 3 1
0
0
(A) f (x) < f(x), < x < . (B) f (x) > f(x), 0 < x < .
4 4 4
1 3
0
0
(C) f (x) < f(x), 0 < x < . (D) f (x) < f(x), < x < 1.
4 4
[JEE 2013]
Paragraph for Question Nos. 22 and 23

2
2
2
Let f(x) = (1 − x) sin x + x for all x ∈ R, and let
Z x 2(t − 1)
g(x) = − ln t f(t) dt, for all x ∈ (1, ∞).
t + 1
1
22. Which of the following is true?

(A) g is increasing on (1, ∞).
(B) g is decreasing on (1, ∞).
(C) g is increasing on (1, 2) and decreasing on (2, ∞).

(D) g is decreasing on (1, 2) and increasing on (2, ∞).

23. Consider the statements:
2
P : There exists some x ∈ R such that f(x) + 2x = 2(1 + x )
Q : There exists some x ∈ R such that 2f(x) + 1 = 2x(1 + x)
Then

(A) both P and Q are true. (B) P is true and Q is false.
(C) P is false and Q is true. (D) both P and Q are false.

[JEE 2012]

Paragraph for Question Nos. 24 to 26

Let a, b and c be three real numbers satisfying
 
1 9 7
h i h i
a b c 8 2 7 = 0 0 0 . ...(E)


7 3 7
24. If point P(a, b, c), with reference to (E), lies on the plane 2x + y + z = 1, then value of 7a + b + c is

(A) 0. (B) 12. (C) 7. (D) 6.