Find the average of cubes of first 49 positive integers.

Answer: Option A

Sum of cubes of first n positive consecutive numbers is $$=\frac{{\left(n\left(n+1\right)\right)}^2}{4}$$
Average
$$=\frac{{\left(n\left(n+1\right)\right)}^2}{4}$$
$$\begin{array}{rl}& \Rightarrow n=49\\ & \Rightarrow \frac{49{\left(50\right)}^2}{4}\\ & \Rightarrow 30625\end{array}$$