JEE (Advanced) 2007 Paper-2

Instructions

If a continuous function f defined on the real line R, assumespositive 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.
Consider $$f(x) = ke^x - x$$ for all real x where kis a real constant.

Question 62

The positive value of k for which $$ke^x - x = 0$$ has only one root is


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