KVPY Sample Paper KVPY Stream-SX Model Paper-19

  • question_answer
    For every \[x\in R\] the value of the expression \[y=\frac{{{x}^{2}}}{8}+x\cos x+\cos 2x\] is never less than ?

    A) \[-\,1\]

    B) 0   

    C) 1

    D) 2

    Correct Answer: A

    Solution :

    \[y=\frac{{{x}^{3}}}{8}+x\cos x+cos2x\]
    \[\frac{{{x}^{3}}}{8}+x\cos x+2{{\cos }^{2}}x-1\]
    \[=2{{\left( \cos x+\frac{x}{4} \right)}^{2}}=-1.\]

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