The remainder when (1213 + 2313) is divided by 11.

Answer: Option C

$$\begin{array}{rl}& \frac{{12}^{13}}{11}\text{gives}\text{Remainder}1\\ & \text{It}\text{can}\text{be}\text{written}\text{as}\\ & \frac{\left(12\times 12\times 12\times 12........13\text{times}\right)}{11}\\ & \text{On}\text{dividing}\text{it}\text{gives}\text{remainder}\text{1,}\text{each}\text{time}.\\ & 1\times 1\times 1\times 1.........13\text{times}\\ & \text{So,}\text{final}\text{remainder}\text{will}\text{be}1\\ & \frac{{23}^{13}}{11}\Rightarrow \text{Remainder}1\\ & \text{Thus},\\ & \text{The}\text{remainder}\text{of}\frac{\left({12}^{13}+{23}^{13}\right)}{11}\\ & =\left(1+1\right)\\ & =2\end{array}$$