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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Self Evaluation Test - Determinats

  • question_answer
    For all values of A, B, C and P, Q, R the value of the determinant\[{{(x+a)}^{3}}\left| \begin{matrix}    \cos (A-P) & \cos (A-Q) & \cos (A-R)  \\    \cos (B-P) & \cos (B-Q) & \cos (B-R)  \\    \cos (C-P) & \cos (C-Q) & \cos (C-R)  \\ \end{matrix} \right|\] is

    A) \[1\]

    B) \[0\]

    C) \[2\]

    D) None of these

    Correct Answer: B

    Solution :

    [b] We have, \[\left| \begin{matrix}    \cos (A-P) & \cos (A-Q) & \cos (A-R)  \\    \cos (B-P) & \cos (B-Q) & \cos (B-R)  \\    \cos (C-P) & \cos (C-Q) & \cos (C-R)  \\ \end{matrix} \right|\] \[\left| \begin{matrix}    \cos A & \sin A & 0  \\    \cos B & \sin B & 0  \\    \cos C & \sin C & 0  \\ \end{matrix} \right|\times \left| \begin{matrix}    \cos P & \sin P & 0  \\    \cos Q & \operatorname{sinQ} & 0  \\    \cos R & \sin R & 0  \\ \end{matrix} \right|=0.0=0\]


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