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J & K CET Engineering J and K - CET Engineering Solved Paper-2013

  • question_answer
    The lines \[3x+y-14=0\] \[\lambda x-2y=0\] \[3x-8y+4=0\] are concurrent. Then, the value of \[\lambda \] is

    A)  \[1\]                     

    B)  \[2\]

    C)  \[3\]                   

    D)  \[4\]

    Correct Answer: A

    Solution :

    Given lines are \[3x+y-14=0\] ?.(i) \[\lambda x-2y=0\] ?..(ii) \[3x-8y+4=0\] ?..(iii) If these lines are concurrent, then \[\left| \begin{matrix}    3 & 1 & -14  \\    \lambda  & -2 & 0  \\    3 & -8 & 4  \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[3(-8)-1(4\lambda )-14(-8\lambda +6)=0\] \[\Rightarrow \] \[-24-4\lambda +112\lambda -84=0\] \[\Rightarrow \] \[108\lambda =108\] \[\therefore \] \[\lambda =1\]


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