Question

The digit in the unit place of $7^{291}$ is

• A. $1$
• B. $3$
• C. $2$
• D. $7$

Answer 1

The correct option is B $3$

$a=7^{291}=7{(50-1)}^{145}$
$\Rightarrow a=7({50}^{145}-{145}_{C_1}{50}^{145}+{145}_{C_1}{50}^{145}-.....-{{145}_{C_{143}}{50}^2+145}_{C_{144}}50-{145}_{C_{145}})$
$\Rightarrow a=7(100\lambda +49)=700\lambda +343=700\lambda +340+3$
$\Rightarrow a=10k+3$
Therefore, digit in the unit place of $a$ is $3$.
Ans: B