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IIT JEE Advanced 2007 Paper 2

Paragraph for Questions 61–63:
If a continuous function f defined on the real line R, assumes positive and negative value 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. Consider f(x) = kex–x for all real x where k is a real constant.

Question : 63

Total: 66

For k > 0, the set of all values of k for which kex–x = 0 has two distinct roots is

(0,
1
e
)
(
1
e
,1)
(
1
e
,∞)
(0 , 1)

Validate

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