$$\left( {{2^{71}} + {2^{72}} + {2^{73}} + {2^{74}}} \right)$$     is divided by :

A. 9

B. 10

C. 11

D. 13

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & \Leftrightarrow \left( {{2^{71}} + {2^{72}} + {2^{73}} + {2^{74}}} \right)\, \cr & = {2^{71}}\left( {{2^0} + {2^1} + {2^2} + {2^3}} \right)\, \cr & = {2^{71}}(1 + 2 + 4 + 8) \cr & = {2^{71}} \times 15 \cr & = {2^{70}} \times 30 \cr & {\text{It is divisible by 10}} \cr} $$