Page 8 - ISC-12

Single Correct Choice Type Jai Baba Ki5

1
22. Let f : , 1 → R (the set of all real numbers) be a positive, non-constant and differentiable function
2

1
0
such that f (x) < 2 f(x) and f = 1. Then the value of
2
1
Z
f(x) dx
1/2
lies in the interval

e − 1 e − 1
(A) (2e − 1, 2e). (B) (e − 1, 2e − 1). (C) , e − 1 . (D) 0, .
2 2
[JEE 2013]

π
h i
23. The area enclosed by the curves y = sin x + cos x and y = | cos x − sin x| over the interval 0, is
2
√ √ √ √ √ √
(A) 4( 2 − 1). (B) 2 2( 2 − 1). (C) 2( 2 + 1). (D) 2 2( 2 + 1).
[JEE 2013]
π y y

24. A curve passes through the point 1, . Let the slope of the curve at each point (x, y) be +sec ,
6 x x
x > 0. Then the equation of the curve is
y 1 y

(A) sin = log x + . (B) cosec = log x + 2.
x 2 x

2y 2y 1
(C) sec = log x + 2. (D) cos = log x + .
x x 2
[JEE 2013]

23 n
P −1 P
25. The value of cot cot 1 + 2k is
n=1 k=1
23 25 23 24
(A) . (B) . (C) . (D) .
25 23 24 23
[JEE 2013]
x + 2 y + 1 z
26. Perpendiculars are drawn from points on the line = = to the plane x + y + z = 3. The
2 −1 3
feet of perpendiculars lie on the line
x y − 1 z − 2 x y − 1 z − 2
(A) = = . (B) = = .
5 8 −13 2 3 −5
x y − 1 z − 2 x y − 1 z − 2
(C) = = . (D) = = .
4 3 −7 2 −7 5

[JEE 2013]
−→ −→
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
27. Let PR = 3i + j − 2k and SQ = i − 3j − 4k determine diagonals of a parallelogram PQRS and
−→
ˆ
ˆ
ˆ
PT = i + 2j + 3k be another vector. Then the volume of the parallelepiped determined by the vectors
−→ −→ −→
PR, PQ and PS is
(A) 5. (B) 20. (C) 10. (D) 30.
[JEE 2013]