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KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    If \[f\,(x)\] is a differentiable function satisfying \[f'\,(x)<2\] for all \[x\in R\] and \[f\,(1)=2,\] then greatest possible integral value of \[f\,(3)\]is

    A) 5

    B) 6

    C) 7

    D) 8

    Correct Answer: A

    Solution :

    \[\frac{f\,(3)-f\,(1)}{3-1}=f'\,(c),\] for some c such that \[1<c<3\]
    \[f'\,(c)=\frac{f\,(3)-2}{2}<2\]
    \[\therefore \]      \[f\,(3)<6\]


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