Page 57 - ISC-12

10Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal

46. The distance of the point (1, 1, 1) from the plane passing through the point (−1, −2, −1) and whose
normal is perpendicular to both the lines L 1 and L 2 is
2 7 13 23
(A) √ . (B) √ . (C) √ . (D) √ .
75 75 75 75

[JEE 2008]

Paragraph for Question Nos. 47 to 49

If a continuous function f defined on the real line R, assumes positive and negative values in R, then the
equation f(x) = 0 has a root in R. For example, if it is known that a continuous function f on R is positive

at some point and its minimum value is negative then the equation f(x) = 0 has a root in R.
x
Consider f(x) = ke − x for all real x where k is a real constant.
x
47. The line y = x meets y = ke for k ≤ 0 at
(A) no point. (B) one point.

(C) two points. (D) more than two points.

x
48. The positive value of k for which ke − x = 0 has only one root is
1
(A) . (B) 1.
e
(C) e. (D) log 2.
e
x
49. For k > 0, the set of all values of k for which ke − x = 0 has two distinct roots is

1 1
(A) 0, . (B) , 1 .
e e

1
(C) , ∞ . (D) (0, 1).
e
[JEE 2007]