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JEE Main & Advanced Sample Paper JEE Main Sample Paper-11

  • question_answer
    Let \[f:R\to R\] and\[{{f}_{n}}(x)=f\]\[({{f}_{n-1}}(x)\forall n\ge 2,\]\[n\in N,\]the roots of equation \[{{f}_{3}}(x){{f}_{2}}(x)f(x)\]\[-25{{f}_{2}}(x)+175f(x)\]= 375. Which also satisfy equation f(x) = x will be

    A)  5                                            

    B)  15

    C)  10                         

    D)  both [A] and [B]

    Correct Answer: D

    Solution :

     \[{{f}_{2}}(x)=f(f(x))=f(x)=x\] \[{{f}_{3}}(x)=f({{f}_{2}}(x))=f(x)=x\] \[\Rightarrow \]\[{{x}^{3}}-25{{x}^{2}}+175x-375=0\] \[(x-5)({{x}^{2}}-20x+75)\] \[{{(x-5)}^{2}}(x-15)=0\Rightarrow x=5,15\]


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