JEE Main & Advanced Sample Paper JEE Main - Mock Test - 21

  • question_answer
    If a, b, c are positive integers, then the determinant  is divisible by            

    A) \[{{x}^{3}}\]              

    B) \[{{x}^{2}}\]

    C) \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\]        

    D)  None of these

    Correct Answer: B

    Solution :

    [b]: Clearly, (Applying\[{{R}_{1}}\to {{R}_{1}}+{{R}_{2}}+{{R}_{3}}\]) \[={{x}^{2}}({{a}^{2}}+{{b}^{2}}+{{c}^{2}}+x)\] Hence \[\Delta \]is divisible by \[{{x}^{2}}\] as well as by x.

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