Question

The digit in the unit's place of ${123}^{11}$ will be

• A. $9$
• B. $7$
• C. $1$
• D. $3$

Answer 1

The correct option is D $3$

Consider the expansion ${(125-2)}^{11}={125}^{11}-\left(\begin{array}{c}11\\ 1\end{array}\right){125}^{10}{2}^1+\left(\begin{array}{c}11\\ 2\end{array}\right){125}^9{2}^2-...+2^{11}$,

All the terms in the above expansion except the first and the last the units digit is $0$ because units digit of ${125}^p$ is $5$,when multiplied with an even number the corresponding unit digit is $0$,

$\therefore$ the unit's digit in ${123}^{11}$ is $5+8=13$ is $3$.