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KVPY Sample Paper KVPY Stream-SX Model Paper-27

  • question_answer
    The set of integer values of x satisfying \[\frac{\left( {{2}^{\frac{\pi }{{{\tan }^{-1}}x}}}-4 \right)(x-4)(x-10)}{x!-(x-1)!}<0\] is-

    A) {2, 3}

    B) {5, 6, 7, 8, 9}

    C) \[\phi \]

    D) None of these

    Correct Answer: B

    Solution :

    \[\because \,\,x!-(x-1)!\ne 0\Rightarrow x\in {{I}^{+}}-\{1\}\]
    \[{{2}^{\pi /{{\tan }^{-1}}x}}-4>0\,\,as\,\,{{\tan }^{-1}}x<\pi /2\]
    \[\therefore \,\,\,\,\frac{(x-4)(x-10)}{(x-1)!(x-1)}<0\]
    \[\therefore \,\,\,\,x\in \{5,\,\,6,\,\,7,\,\,8,\,\,9\}\]


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