Unit digit in ( 264 )^102 + ( 264 )^103 is :

Answer: Option A

$${\left(264\right)}^{102}+{\left(264\right)}^{103}$$
unit digit
$$\begin{array}{rl}& {\text{4}}^1\to 4\to 4\\ & 4^2\to 16\to 6\\ & 4^3\to 64\to 4\end{array}$$
Rule: When 4 has odd power, then unit digit is 4
When 4 has even power, then unit digit is 6

$$\begin{array}{rl}& \\ & {\left(264\right)}^{102}+{\left(264\right)}^{103}\\ & \downarrow \downarrow \\ & 4^{102}+4^{103}\end{array}$$
$$\text{unit digit}=6+4=10\to 0$$
    (even power)   (odd power)

$$\begin{array}{rl}& \mathbf{Alternate}\\ & \Rightarrow {\left(264\right)}^{102}+{\left(264\right)}^{103}\\ & \Rightarrow {\left(264\right)}^{102}+\left(1+264\right)\\ & \Rightarrow {\left(264\right)}^{102}+265\\ & \text{Multiple of }5\text{and }2\\ & \text{So},\text{unit digit is }0\end{array}$$