• # question_answer The unit digit of ${{17}^{1983}}+{{11}^{1983}}-{{7}^{1983}}$ is equal to A)  2                             B)  3                       C)  5                                             D)  1

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