If 17200 is divided by 18, the remainder is -

Answer: Option C

$$\begin{array}{rl}& =17^{200}÷18\\ & ={\left(18-1\right)}^{200}÷18\end{array}$$
Apply Binomial theorem
$$={\left(18\right)}^{200}{\left(-1\right)}^0+{\left(18\right)}^{199}{\left(-1\right)}^1+$$       $$.....+{\left(18\right)}^1{\left(-1\right)}^{199}$$   $$+{\left(18\right)}^0{\left(-1\right)}^{200}$$

$$\Rightarrow$$ Remainder always comes from last term is (18)⁰ (- 1)²⁰⁰
$$\begin{array}{rl}& =\frac{{\left(18\right)}^0{\left(-1\right)}^{200}}{18}\\ & =1\times 1^{200}\\ & =1\\ & \text{So, remainder}=1\end{array}$$