Find the remainder when 10 + 102 + 103 + 104 + ........ + 1099 is divided by 6.

Answer: Option A

The remainder when 10 is divided by 6 is 4.
The remainder when 10² is divided by 6 is 4.
The remainder when 10³ is divided by 6 is 4.
The remainder when 10⁴ is divided by 6 is 4.
Thus, remainder is always 4.
So, the required remainder,
$$\begin{array}{rl}& =\frac{4+4+4+4+.....99\text{ times}}{6}\\ & =\frac{396}{6}\end{array}$$
Thus, Required remainder is 0.