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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2009

  • question_answer
    If\[n\]is a positive integer, then \[{{5}^{2n+2}}-24n-25\]is divisible by

    A)  574                                       

    B)  575

    C)  675                       

    D)         674

    E)  576

    Correct Answer: E

    Solution :

    Let \[P(n)={{5}^{2n+2}}-24n-25\] For \[n=1,\] \[p(1)={{5}^{2}}-24-25=576\] \[p(2)={{5}^{6}}-24(2)-25=15552\] \[=576\times 27\] Here, we see that\[p(n)\]is divisible by 576.


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