JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Self Evaluation Test - Principle of Mathematical Induction

  • question_answer
    The remainder when \[{{5}^{4n}}\] is divided by 13, is

    A) 1

    B) 8

    C) 9

    D) 10

    Correct Answer: A

    Solution :

    [a] For \[n=1;\,\,\,\,{{5}^{4}}=625=(624+1)=(48\times 13)+1,\] i.e., \[{{5}^{4}}\] leaves 1 as remainder when divided by 13.


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