Page 34 - ISC-12

Multiple Correct Choices Type Jai Baba Ki11
0
47. Let f(x) = x sin πx, x > 0. Then for all natural numbers n, f (x) vanishes at

1
(A) a unique point in the interval n, n + .
2

1
(B) a unique point in the interval n + , n + 1 .
2
(C) a unique point in the interval (n, n + 1).
(D) two points in the interval (n, n + 1).

[JEE 2013]

48. A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted
into an open rectangular box by folding after removing squares of equal area from all four corners. If
the total area of removed squares is 100, the resulting box has maximum volume. Then the lengths of
the sides of the rectangular sheet are

(A) 24. (B) 32. (C) 45. (D) 60.

[JEE 2013]

49. A line l passing through the origin is perpendicular to the lines
ˆ
ˆ
ˆ
l 1 : (3 + t)i + (−1 + 2t)j + (4 + 2t)k, −∞ < t < ∞
ˆ
ˆ
ˆ
l 2 : (3 + 2s)i + (3 + 2s)j + (2 + s)k, −∞ < s < ∞
√
Then, the coordinate(s) of the point(s) on l 2 at a distance of 17 from the point of intersection of l
and l 1 is (are)

7 7 5
(A) , , . (B) (−1, −1, 0).
3 3 3

7 7 8
(C) (1, 1, 1). (D) , , .
9 9 9
[JEE 2013]

50. The function f(x) = 2|x| + |x + 2| − |x + 2| − 2|x| has a local minimum or a local maximum at

x =
2
(A) −2. (B) − .
3
2
(C) 2. (D) .
3
[JEE 2013]
y z y z
51. Two lines L 1 : x = 5, = and L 2 : x = α, = are coplanar. Then α can take
3 − α −2 −1 2 − α
value(s)

(A) 1. (B) 2.
(C) 3. (D) 4.

[JEE 2013]