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JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer
    If \[a,\,\,\,b,\,\,\,c,\,\,\,d\] and \[p\] are distinct non zero real numbers such 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) \[GP\].

    C) \[H.P.\]           

    D)  satisfy\[ab=cd\]

    Correct Answer: B

    Solution :

    \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}}){{p}^{2}}-2(ab+bc+cd)p\]\[+{{b}^{2}}+{{c}^{2}}+{{d}^{2}}\le 0\] \[\Rightarrow \]\[({{a}^{2}}{{p}^{2}}-abp+{{b}^{2}})+({{b}^{2}}{{p}^{2}}-2bcp+{{c}^{2}})\] \[\Rightarrow \]\[ap-b=0,\,\,bp-c=0\And cp-d=0\] \[\Rightarrow \]\[\frac{b}{a}=\frac{c}{b}=\frac{d}{c}\Rightarrow a,\,\,b,\,\,c\]and\[d\]in\[GP\] Also\[ad=be\]


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