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JEE Main & Advanced Sample Paper JEE Main Sample Paper-24

  • question_answer
    Let \[A={{[{{a}_{ij}}]}_{3\times 3}},B={{[{{b}_{ij}}]}_{3\times 3}}\] where \[{{b}_{i\,j}}={{3}^{i-j}}{{a}_{i\,j}}\] and \[C={{[{{c}_{i\,j}}]}_{3\times 3}},\] where \[{{c}_{i\,j}}={{4}^{i-j}}{{b}_{i\,j}}\] be any three matrices. If det. \[A=2\], then det. B \[+\] del. C is equal to

    A)  4                                

    B)  3

    C)  2                                

    D)  1

    Correct Answer: D

    Solution :

    We have \[\det B=\det .\,C=\det .\,A=2,\] because \[\det .B=\left| \begin{matrix}    {{a}_{11}} & \frac{{{a}_{12}}}{3} & \frac{{{a}_{13}}}{{{3}^{2}}}  \\    3{{a}_{21}} & {{a}_{22}} & \frac{1}{3}{{a}_{23}}  \\    9{{a}_{31}} & 3{{a}_{32}} & {{a}_{33}}  \\ \end{matrix} \right|\,=|A|=2\] Similarly, \[\det .C=\det .B=|A|=2\] Hence \[\det .B+\det .C=2+2=4\].


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