KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • question_answer
    \[\int{\sqrt{x-3}\,({{\sin }^{-1}}\ell nx+{{\cos }^{-1}}\ell n\,x)}\,\,dx\] is equal to

    A) \[\frac{\pi }{3}{{(x-3)}^{3/2}}+c\]

    B) 0

    C) does not exist    

    D) none of these

    Correct Answer: C

    Solution :

    \[\because \]       \[x>3\]
    So \[\ell n\,x>\ell n\,3>1\]
    So \[{{\sin }^{-1}}\,(\ell n\,x)\] & \[{{\cos }^{-1}}\ell n\,x\] are not define. Hence the given integral does not exist.

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