What will be the unit digit in the 7105 ?

Answer: Option B

$$\begin{array}{rl}& {\text{7}}^{105}\Rightarrow \\ & {\text{7}}^1\to 7\to 7\\ & {\text{7}}^2\to 49\to 9\\ & {\text{7}}^3\to 343\to 3\\ & {\text{7}}^4\to 2401\to 1\\ & \text{Divided power of 7 by 4}\\ & \frac{105}{4}\to \text{ remainder = 1}\\ & \Rightarrow {\text{7}}^1\text{is left unit digit = 1}\times 7=7\end{array}$$