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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2003

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

    A)  2                                            

    B)  1

    C)  4                                            

    D)  2

    Correct Answer: C

    Solution :

    \[{{(17)}^{2}}=289\]                 \[\equiv -1\,(\bmod \,5)\]                 \[{{({{17}^{2}})}^{5}}\equiv {{(-1)}^{15}}(\bmod \,5)\]                 \[{{17}^{30}}\equiv -1\,\,(\bmod \,5)\] \[i.e.,\] \[{{17}^{30}}=4\,\,(\bmod \,5)\] \[\therefore \] The least remainder when \[{{17}^{30}}\] is divided by 5 is 4.


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