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KVPY Sample Paper KVPY Stream-SX Model Paper-15

  • question_answer
    If \[f(x)=2{{e}^{x}}-c\] ln x monotonically increases for every \[x\in (0,\infty ),\] then the true set of values of c is-

    A) \[\left( -\infty ,\frac{1}{e} \right)\]

    B) \[\left( -\infty ,\frac{2}{e} \right)\]

    C) \[[0,\infty )\]

    D) \[(-\infty ,0]\]

    Correct Answer: D

    Solution :

    \[f(x)=2{{e}^{x}}-c\ell nx\] \[f'(x)=2{{e}^{x}}-\frac{c}{x}\ge 0\] \[\Rightarrow \frac{2x{{e}^{x}}-c}{x}\ge 0\] \[\Rightarrow c\le 2x{{e}^{x}}\] \[\Rightarrow c\le 0\]


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