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J & K CET Engineering J and K - CET Engineering Solved Paper-2015

  • question_answer
    The last digit in the integer \[{{3}^{101}}+1\] is

    A)  \[1\]        

    B)  \[2\]     

    C)  \[3\]      

    D)  \[4\]

    Correct Answer: D

    Solution :

    The given integer is \[{{3}^{101}}+1.\] Unit digit in \[{{3}^{1}}=3\] in \[{{3}^{2}}=9\] in \[{{3}^{3}}=7\] in \[{{3}^{4}}=1\] in \[{{3}^{5}}=3\] [repeat] Now, on dividing 101 by 4 we get remainder =1 \[\therefore \]  Last digit in the integer \[{{3}^{101}}+1\] \[={{3}^{1}}+1=4\]


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