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Q. The last digit in the integer $ {{3}^{101}}+1 $ is

J & K CETJ & K CET 2015Binomial Theorem

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 $