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KVPY Sample Paper KVPY Stream-SX Model Paper-19

  • 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 the eight solutions of \[f(x)=0\] is -

    A) 12

    B) 32   

    C) 16

    D) 15

    Correct Answer: B

    Solution :

    Symmetric about \[x=4\] \[2\left\{ \left[ \frac{{{x}_{1}}+{{x}_{2}}}{2} \right]+\left[ \frac{{{x}_{3}}+{{x}_{4}}}{2} \right]+\left[ \frac{{{x}_{5}}+{{x}_{6}}}{2} \right]+\left[ \frac{{{x}_{7}}+{{x}_{8}}}{2} \right] \right\}\]\[=2\,\{4+4+4+4\}=16\times 2=32\]


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