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JEE Main & Advanced Sample Paper JEE Main Sample Paper-23

  • question_answer
    If \[\Delta =\left| \begin{matrix}   1 & 3\cos \theta  & 1  \\    \sin \theta  & 1 & 3\cos \theta   \\    1 & \sin \theta  & 1  \\ \end{matrix} \right|,\theta \in R\]then the maximum value of A, is

    A)  3                                

    B)  9

    C)  10                               

    D)  13

    Correct Answer: C

    Solution :

    Apply \[{{R}_{3}}\to {{R}_{3}}-{{R}_{1}},\] We get \[\Delta =\left| \begin{matrix}    1 & 3\cos \theta  & 1  \\    \sin \theta  & 3\cos \theta  & 3\cos \theta   \\    0 & \sin \theta -3\cos \theta  & 0  \\ \end{matrix} \right|\,={{(3\cos \theta -\sin \theta )}^{2}}\] So, maximum value of \[\Delta \] equals 10.


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