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.