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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 45

  • question_answer
    If a, b, c, d are such unequal real numbers that \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}}){{p}^{2}}-2(ab+bc+cd)p+({{b}^{2}}+{{c}^{2}}+{{d}^{2}})\le 0,\]  then a, b, c, d are in-

    A) A.P.              

    B)        G.P.

    C) H.P.              

    D)        None of these

    Correct Answer: B

    Solution :

    [b] \[{{(ap-b)}^{2}}+{{(bp-c)}^{2}}+{{(cp-d)}^{2}}\le 0\] \[{{(ap-b)}^{2}}+{{(bp-c)}^{2}}+{{(cp-d)}^{2}}=0\] \[\Rightarrow p=\frac{b}{a}=\frac{c}{b}=\frac{d}{c}\] \[\Rightarrow \] a, b, c, d are in G.P.


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