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JEE Main & Advanced Sample Paper JEE Main Sample Paper-37

  • question_answer
    Let\['a'\]denote the roots of equation\[\cos ({{\cos }^{-1}}x)+{{\sin }^{-1}}\sin \left( \frac{1+{{x}^{2}}}{2} \right)=2{{\sec }^{-1}}(\sec x)\]then possible values of\[[|10a|]\]where\[[\,\,.\,\,]\] denotes the greatest integer function will be

    A) \[1\]                                         

    B) \[5\]

    C) \[10\]                           

    D)  Both [a] and [c]

    Correct Answer: D

    Solution :

    \[x\in [-1,\,\,0]\] \[x+\frac{1+{{x}^{2}}}{2}=-2x\] \[{{x}^{2}}+6x+1=0\] \[x=2\sqrt{2}-3\Rightarrow |10a|=[|20\sqrt{2}-30|]=30-20\sqrt{2}\]      \[x\in [0,\,\,1]\] \[x+\frac{1+{{x}^{2}}}{2}=2x\] \[1+{{x}^{2}}=2x\Rightarrow x=1\Rightarrow |10a|=10\]     \[|10a|=10,\,\,|20\sqrt{2}-30|\] \[\Rightarrow \]            \[[|10a|]=1,\,\,10\]


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