Correct Option: C

(17)²⁰⁰ = (18 – 1)²⁰⁰
With the help of binomial theorem we solve this question ,

(x + a)n =  xn + nxn–1.a +	n (n − 1)	xn − 2a2	+	n (n − 1) (n − 2)	xn − 3a3 + .....+ an
	1 × 2			1 × 2 × 3

We see that all the terms on the R.H.S. except aⁿ has x as one of its factor and hence are divisible by x. So, (x + a)ⁿ is divisible by x or not will be decided by aⁿ.
Let x = 18, a = – 1 and n = 200
∴  (18 – 1)²⁰⁰ is divisible by 18 or not will depend on (–1)²⁰⁰ as all other terms in its expansion will be divisible by 18 because each of them will have 18 as one of their factors.
(–1)²⁰⁰ = 1 (∵ 200 is even)
1 is not divisible by 18 and is also less than 18.
∴ 1 is the remainder.