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KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • question_answer
    The function \[f:R\to R\] is defined by \[f\,(x)=-{{x}^{3}}+2a{{x}^{2}}-3bx+c,\] where a, b, \[c\in R,\] is a bijective function. If \[4{{a}^{2}}\le kb,\] then value of k may be

    A) 11

    B) 13

    C) 17

    D) All of these

    Correct Answer: D

    Solution :

    \[f\,(x)=-{{x}^{3}}+2a{{x}^{2}}-3bx+c\]
    \[f'\,(x)=-\,3{{x}^{2}}+4a{{x}^{2}}-3b\le 0\]  \[\forall \,\,x\] if
                \[16{{a}^{2}}-36b\le 0\]
                \[4{{a}^{2}}\le 9b\]     \[\therefore \]      \[k\ge 9\]


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