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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2011

  • question_answer
    If lines represented by \[x+3y-6=0,\]\[2x+y-4=0\]and \[kx-3y+1=0\]are concurrent, then the value of \[k\]is

    A) \[\frac{6}{19}\]                                

    B) \[\frac{19}{6}\]

    C)  \[-\frac{19}{6}\]                              

    D)  \[-\frac{6}{19}\]

    Correct Answer: B

    Solution :

    Given lines are, \[x+3y-6=0\] \[2x+y-4=0\] \[kx-3y+1=0\] these given lines will concurrent when \[\left| \begin{matrix}    1 & 3 & -\,6  \\    2 & 1 & -\,4  \\    k & -\,3 & 1  \\ \end{matrix} \right|=0\] Expand with respect to \[{{R}_{1}}:\] \[1(1-12)-3(2+4k)-6\,(-6-k)=0\] \[\Rightarrow \]               \[-11-6-12k+36+6k=0\] \[\Rightarrow \]               \[=-6k-17+36=0\] \[\Rightarrow \]                               \[6k=19\] \[\Rightarrow \]                               \[k=\frac{19}{6}\]


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