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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2001

  • question_answer
    kIf the lines\[x-y-1=0,4x+3y=k\]and \[2x-3y+1=0\]are concurrent, then k is:

    A)  1                                            

    B)  \[-1\]                   

    C)  25                         

    D)         5

    E)  \[-20\]

    Correct Answer: C

    Solution :

    \[\because \]The given lines are concurrent, then \[\left| \begin{matrix}    1 & -1 & -1  \\    4 & 3 & -k  \\    2 & -3 & 1  \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[1\left| \begin{matrix}    3 & -k  \\    -3 & 1  \\ \end{matrix} \right|+1\left| \begin{matrix}    4 & -k  \\    2 & 1  \\ \end{matrix} \right|-1\left| \begin{matrix}    4 & 3  \\    2 & -3  \\ \end{matrix} \right|=0\]              \[\Rightarrow \]\[1(3-3k)+1(4+2k)-1(12-6)=0\] \[\Rightarrow \]               \[k=25\]


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