The remainder of 32^32^327:

Answer: Option D

$$\begin{array}{rl}& 32^{{32}^{32}}\text{means}32^{\left(\mathrm{32.32.32.32.......32}\text{times}\right)}\\ & \text{and}\text{the}\text{remainder}\text{of}\frac{32}{7}\text{is}4\\ & \text{So},\\ & \frac{4^{\left(\mathrm{32.32.32.32.......32}\text{times}\right)}}{7}\\ & \frac{4^{\left(\mathrm{2.2.2.2.2........32}\text{times}\right)}}{7}\\ & \text{Remainder}=4\\ & \text{Since},\frac{4}{7}\to \text{Remainder}4\\ & \frac{4^2}{7}\to \text{Remainder}2\\ & \frac{4^3}{7}\to \text{Remainder}1\\ & \frac{4^4}{7}\to \text{Remainder}4\end{array}$$