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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2005

  • question_answer
    If\[{{\left| \begin{matrix}    4 & 1  \\    2 & 1  \\ \end{matrix} \right|}^{2}}=\left| \begin{matrix}    3 & 2  \\    1 & x  \\ \end{matrix} \right|-\left| \begin{matrix}    x & 3  \\    -2 & 1  \\ \end{matrix} \right|,\]then the value of\[x\]is

    A)  6               

    B)  7

    C)  8               

    D)  11

    Correct Answer: A

    Solution :

     Given, \[{{\left| \begin{matrix}    4 & 1  \\    2 & 1  \\ \end{matrix} \right|}^{2}}=\left| \begin{matrix}    3 & 2  \\    1 & x  \\ \end{matrix} \right|-\left| \begin{matrix}    x & 3  \\    -2 & 1  \\ \end{matrix} \right|\] \[\Rightarrow \] \[{{(4-2)}^{2}}=(3x-2)-(x+6)\] \[\Rightarrow \] \[4=2x-8\] \[\Rightarrow \] \[2x=12\] \[\Rightarrow \] \[x=6\]


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