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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 17

  • question_answer
    Let \[f(x)=x({{x}^{2}}+mx+n)+2,\] for all \[x\in R\] and m, \[n\in R\] . If Rollers Theorem holds for \[f(x)\] at \[x=4/3\]in \[x\in [1,\,\,2],\] then \[(m+n)\] equals

    A) 1                      

    B)        2                       

    C) 3             

    D)        4

    Correct Answer: C

    Solution :

       [c] \[f(1)=f(2)\] \[\Rightarrow \,\,3m+n+7=0\]     ?.(1) and \[f'(x)\,\,(at\,\,x=4/3)=0\] gives \[8m+3n+16=0\]           ?..(2) \[\Rightarrow \,\,\,\,m=-5,\,\,n=8\]     


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