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KVPY Sample Paper KVPY Stream-SX Model Paper-18

  • question_answer
    let \[f\left( x \right)=\left[ r+p\sin x \right],x\in \left( 0,\pi  \right),r\in I\,and\,p\] is prime number ([.] denotes integer function).the number of points at which \[f\left( x \right)\] is non-differentiable is

    A) \[p\]

    B) \[p-1\]

    C) \[2p+1\]

    D) \[2p-1\]

    Correct Answer: D

    Solution :

    \[f\left( x \right)\] is non-differentiable at only those points where \[P\]sin \[x\]acquires integral value. Now \[\sin x=\frac{r}{P}\]will have two solution in \[\left( 0,\pi  \right)\]for and \[\sin x=1\]will have only one solution. \[\Rightarrow \]Total number of points of non-differentiability \[=\left( p-1 \right)+1=2p-1.\]


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