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JEE Main & Advanced Sample Paper JEE Main Sample Paper-12

  • 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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