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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 32

  • question_answer
    If \[a\ne b\ne c\] and if \[ax+by+c=0;bx+cy+a=0,\]\[cx+ay+b=0\] are concurrent then \[{{2}^{{{a}^{2}}{{b}^{-1}}{{c}^{-1}}}}{{2}^{{{b}^{2}}{{c}^{-1}}{{a}^{-1}}}}{{2}^{{{c}^{2}}{{a}^{-1}}{{b}^{-1}}}}=\]

    A) 8              

    B)        0

    C) 2                     

    D)        None of these

    Correct Answer: A

    Solution :

    [a] \[\left| \begin{matrix}    a & b & c  \\    b & c & a  \\    c & a & b  \\ \end{matrix} \right|=0\] \[\Rightarrow 3acb-{{a}^{3}}-{{b}^{3}}-{{c}^{3}}=0\] \[\Rightarrow {{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc\] \[{{2}^{\frac{{{a}^{2}}}{bc}}}{{.2}^{\frac{{{b}^{2}}}{ca}}}{{.2}^{\frac{{{c}^{2}}}{ab}}}={{2}^{\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}}{abc}}}={{2}^{3}}=8\]           


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