JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Critical Thinking

  • question_answer
    The least remainder when \[{{17}^{30}}\] is divided by 5 is [Karnataka CET  2003]

    A) 1

    B) 2

    C) 3

    D) 4

    Correct Answer: D

    Solution :

    17 = 2 (mod 5)         \[{{(17)}^{5}}={{(2)}^{5}}\,(\text{mod 5)}\] = 2 (mod 5) Þ  \[{{({{17}^{5}})}^{6}}={{(2)}^{6}}\](mod 5) Þ  \[{{(17)}^{30}}=4\] (mod 5) Hence required remainder = 4.


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