Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (D)

$4$

Answer 2

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 ${{3}^{101}}+1$
$={{3}^{1}}+1=4$