JEE Main & Advanced AIEEE Solved Paper-2009

  • question_answer
    The remainder left out when\[{{8}^{2n}}{{(62)}^{2n+1}}\] is divided by 9 is     AIEEE  Solved  Paper-2009

    A) 0             

    B)                        2                             

    C) 7                             

    D)        8

    Correct Answer: B

    Solution :

    \[{{8}^{2n}}{{(62)}^{2n+1}}\] \[\Rightarrow \]\[{{(91)}^{2n}}{{(631)}^{2n+1}}\] \[\Rightarrow \]\[{{(}^{2n}}{{C}_{0}}{{9}^{2n}}{{}^{2n}}{{C}_{1}}{{9}^{2n1}}+\ldots ..{{+}^{2n}}{{C}_{2n}})\] \[-{{(}^{2n+1}}{{C}_{0}}{{63}^{2n+1}}{{}^{2n+1}}{{C}_{1}}{{63}^{2n}}+\ldots .\] \[{{-}^{2n+1}}{{C}_{2n+1}}\] Clearly remainder is ?2?.


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