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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 26

  • question_answer
    If \[f(x)\] is a differentiable function such that \[f(1)=\sin 1,\] \[f(2)=\sin 4\]and \[f(3)=\sin 9,\] then the minimum number of distinct solutions of equation \[f'(x)=2x\cos {{x}^{2}}\] in \[(1,3)\] is

    A) \[1\]                      

    B)        \[2\]                    

    C) \[3\]                    

    D)        4

    Correct Answer: B

    Solution :

    [b] Let \[g(x)=f(x)-\sin {{x}^{2}}\] According to the question, we have \[g(1)=g(2)=g(3)=0\] \[\Rightarrow \,\,\,\,\,g'(x)=0\] at least twice \[\Rightarrow \,\,\,\,\,\,\,f'(x)=2x\,\,\cos x\] at least twice. 


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