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J & K CET Engineering J and K - CET Engineering Solved Paper-2005

  • question_answer
    The integer represented by the determinant \[\left| \begin{matrix}    215 & 342 & 511  \\    6 & 7 & 8  \\    36 & 49 & 54  \\ \end{matrix} \right|\] is exactly divisible by

    A)  \[146\]          

    B)  \[21\]

    C)  \[20\]           

    D)  \[335\]

    Correct Answer: C

    Solution :

    \[\left| \begin{matrix}    215 & 342 & 511  \\    6 & 7 & 8  \\    36 & 49 & 54  \\ \end{matrix} \right|\] \[=215(378-392)-342(324-288)\] \[+511(294-252)\] \[=-215\times 14-342\times 36+511\times 42\] \[=-3010-12312+21462\] \[=6140\] Which is exactly divisible by 20.


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