When $$11^{121}$$ is divided by 13, what would be the remainder?

Seeing that 11, when divided by 13, leaves neither a remainder of 1 nor -1, we can look for a possible power of 11, which would leave a remainder of 1 or -1 when divided by 13. 
This method might be lengthy and not feasible without a calculator. 

Another property we can use here is Fermat little theorem, which states that $$\left[\frac{a^{p-1}}{p}\right]_R=1$$, where $$p$$ is a prime number. 

Hence, $$\left[\frac{\left(11^{10}\right)^{12}}{13}\right]_R=1$$

This would give the expression $$\left[\frac{11^{121}}{13}\right]_R=\left[\frac{\left(11^{10}\right)^{12}}{13}\right]_R\times\ \left[\frac{11}{13}\right]_R=1\times\ 11$$

Therefore, Option C is the correct answer.