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JEE Main & Advanced JEE Main Paper (Held On 8 April 2017)

  • question_answer
    The number of real values of \[\lambda \]for which the system of linear equations \[2x+4y-\lambda z=0\] \[4x+\lambda y+2z=0\] \[\lambda x+2y+2z=0\] has infinitely many solutions, is : [JEE Online 08-04-2017]

    A)  3                                            

    B)  1

    C)  2                                            

    D)  0

    Correct Answer: B

    Solution :

                    \[\Delta =0\]                 \[\left| \begin{matrix}    2 & 4 & -\lambda   \\    4 & \lambda  & z  \\    \lambda  & z & 2  \\ \end{matrix} \right|\begin{matrix}    2 & 4  \\    4 & \lambda =0  \\    \lambda  & z  \\ \end{matrix}\]                 \[=-(32+8-{{\lambda }^{3}})=0\]                 \[=\lambda 3+4\lambda -40=0\]


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