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KVPY Sample Paper KVPY Stream-SX Model Paper-8

  • question_answer
    If positive numbers \[{{a}^{-1}},{{b}^{-1}},{{c}^{-1}}(a\ne b\ne c)\] Are in A.P., then product of roots of equation \[{{x}^{2}}-kx+2{{b}^{101}}-{{a}^{101}}-{{c}^{101}}=0(k\in R)-\]

    A) has \[+ve\]sign              

    B) has \[-ve\]sign

    C) equal to zero                 

    D) not definite

    Correct Answer: B

    Solution :

    \[A.M.>G.M.\] \[\frac{{{a}^{101}}+{{c}^{101}}}{2}>{{(\sqrt{ac})}^{101}}>{{b}^{101}}\] \[2{{b}^{101}}-{{a}^{101}}-{{c}^{101}}<0\]


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