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JEE Advanced 2007Paper 2
Exam
JEE Advanced
Year
2007
Paper
Paper 2
Subject
Mathematics
Chapter
Functions

JEE Advanced 2007 · Paper 2 · Mathematics · Functions

Paragraph: If a continuous f defined on the real line R , assume...

Paragraph: If a continuous ff defined on the real line RR, assume positive and negative values in RR, then the equation f(x)=0f(x)=0 has a root in RR. For example, if it is known that a continuous function ff on RR is positive at some point and its minimum values is negative, then the equation f(x)=0f(x)=0 has a root in RR. Consider f(x)=kex−xf(x)=k e^x-x for all real xx, where kk is real constant.Question: For k>0k>0, the set of all values of kk for which kex−x=0k e^x-x=0 has two distinct roots, is

Options

  1. A(0,1e)\left(0, \frac{1}{e}\right)
  2. B(1e,1)\left(\frac{1}{e}, 1\right)
  3. C(1e,∞)\left(\frac{1}{e}, \infty\right)
  4. D(0,1)(0,1)

Correct answer

A. (0,1e)\left(0, \frac{1}{e}\right)

Step-by-step solution

For two distinct roots 1+ln⁡k<0(k>0)1+\ln k < 0(k>0) ln⁡k<−1k<1e\ln k < -1 \quad k < \frac{1}{e} Hence, $k \in\left(0, \frac{1}{e}\right)
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