The last digit of (1001)2008 + (1002) = ?

Answer: Option B

$$\begin{array}{rl}& (1001{)}^{2008}+(1002)\\ & \downarrow \\ & \text{unit digit}\to {\text{1}}^{2008}+1002\end{array}$$
Unit digit will be 1 in case of 1 respective of power
⇒ 1 + 1002 = 1003
⇒ 3 unit digit (last digit)