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VIT Engineering VIT Engineering Solved Paper-2015

  • question_answer
    Find the value of k for which the simultaneous equations x + y + z = 3;  x + 2y + 3z = 4 and x + 4y + kz = 6 will not have a unique solution.

    A) 4                                             

    B) 1

    C) 3                                             

    D) 2

    Correct Answer: D

    Solution :

    The given system of equations will be consistent with unique solution, when              \[\left| \begin{matrix}    1 & 1 & 1  \\    1 & 2 & 3  \\    1 & 4 & k  \\ \end{matrix} \right|\ne 0\] \[\Rightarrow \]    \[1\left( 2k-12 \right)+1\left( 3-k \right)+1\left( 4-2 \right)\ne 0\] \[\Rightarrow \]                    \[k-12+3+2\ne 0\] \[\Rightarrow \]                        \[k-7\ne 0\] \[\Rightarrow \]                         \[k\ne 7\]


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