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JEE Main & Advanced Sample Paper JEE Main Sample Paper-29

  • question_answer
    If \[P=\left| \begin{matrix}    1 & c & 3  \\    1 & 3 & 3  \\    2 & 4 & 4  \\ \end{matrix} \right|\] is the adjoint of a \[3\times 3\] matrix Q and det. \[(Q)=4\], then c is equal to

    A) 0                                             

    B) 4

    C) 5                                             

    D) 11

    Correct Answer: D

    Solution :

    \[P=adj.Q\] \[\Rightarrow |P|=|adj.Q|=Q{{|}^{2}}\] \[\therefore \]\[|P|\,\,={{(4)}^{2}}\Rightarrow |P|\,\,=16\]      \[\Rightarrow \]\[\left| \begin{matrix}    1 & c & 3  \\    1 & 3 & 3  \\    2 & 4 & 4  \\ \end{matrix} \right|=16\] \[\Rightarrow 1(0)-c(-2)+3(-2)=16\Rightarrow 2c=22\Rightarrow c=11\]


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