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  3. CET Karnataka Engineering

CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2001

  • question_answer
    If    the    lines \[x+2ay+a=0,\]\[x+3by+b=0\]and\[x+4cy+c=0\]are  concurrent, then a, b and c are in:

    A)  A.P.                                      

    B)  G.P.

    C)  H.P.      

    D)  none of these

    Correct Answer: C

    Solution :

    Given lines will be concurrent if \[\left| \begin{matrix}    1 & 2a & a  \\    1 & 3b & b  \\    1 & 4c & c  \\ \end{matrix} \right|=0\Rightarrow -bc+2ca-ab=0\]\[\Rightarrow \]\[b=\frac{2ca}{c+a}\]\[\Rightarrow \]\[a,b,c\]are in H.P.                                


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