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JEE Main & Advanced Sample Paper JEE Main Sample Paper-14

  • question_answer
    Let \[a={{({{\sin }^{-1}}x)}^{{{\sin }^{-1}}x}},\] \[b=\,{{({{\sin }^{-1}}x)}^{{{\cos }^{-1}}x}},\] \[c={{({{\cos }^{-1}})}^{{{\sin }^{-1}}x}},\] \[d={{({{\cos }^{-1}}x)}^{{{\cos }^{-1}}x}}\] and if \[x\,\in \,\,(0,\,1)\] then

    A)  a > b > d > c                      

    B)  d > c > a > b

    C)  b > a > d > c                      

    D)  a < b < d < c

    Correct Answer: B

    Solution :

     When \[x\,\in \,(0,1)\] \[\Rightarrow \]               \[{{\cos }^{-1}}\,x>{{\sin }^{-1}}\,x\] Also,      \[{{\cos }^{-1}}x>1\] and        \[{{\sin }^{-1}}\,x<1\] \[\therefore \] \[{{({{\cos }^{-1}}x)}^{{{\cos }^{-1}}x}}\] is greatest and \[({{\sin }^{-1}}x)\] least. \[\Rightarrow \] \[{{({{\sin }^{-1}})}^{{{\sin }^{-1}}x}}<\,{{({{\cos }^{-1}}x)}^{{{\sin }^{-1}}x}}\] \[\Rightarrow \]               \[d>c>a>b\]


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