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KVPY Sample Paper KVPY Stream-SX Model Paper-1

  • question_answer
    The function \[f\,(x)=0\] has eight distinct real solutions and f also satisfy \[f\,(4+x)=f\,(4-x).\] The sum of all eight solution of \[f\,(x)=0\] is

    A) 12                                

    B) 32      

    C) 16                                

    D) 15

    Correct Answer: B

    Solution :

    [b]
    We have,
    \[f(4+x)=f(4-x)\]
    \[\therefore \]\[f\,(x)\]is symmetric about \[x=4.\]
    Sum of its solution
    \[2\left[ \left( \frac{{{x}_{i}}+{{x}_{2}}}{2} \right)+\left( \frac{{{x}_{3}}+{{x}_{4}}}{2} \right)+\left( \frac{{{x}_{5}}+{{x}_{6}}}{2} \right)\left( \frac{{{x}_{7}}+{{x}_{8}}}{2} \right) \right]\]
    \[=2\,[4+4+4+4]\]
    \[=2\times 16=32\]


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