JEE Main & Advanced Sample Paper JEE Main Sample Paper-5

  • question_answer
    The unit digit of \[{{17}^{1983}}+{{11}^{1983}}-{{7}^{1983}}\] is equal to

    A)  2                            

    B)  3                      

    C)  5                                            

    D)  1

    Correct Answer: D

    Solution :

     Consider the given expression \[{{17}^{1983}}+{{11}^{1983}}-{{7}^{1983}}=({{17}^{1983}}-{{7}^{1983}})+{{11}^{1983}}\] \[=(17\cdot 7)({{17}^{1982}}+{{17}^{1981}}\cdot {{7}^{1}}+...+{{7}^{1982}})+{{11}^{1983}}\] Clearly, last digit of\[{{17}^{1983}}-{{7}^{1983}}\]is 0. Also last digit is\[{{11}^{1983}}\]is 1. Thus, last digit of \[{{17}^{1983}}+{{11}^{1983}}-{{7}^{1983}}\]is 0+1=1

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