If r is a multiple of 3, which of the following could not be the remainder when r to the power of 2 is divided by 10?

Answer 1

I think you forgot to type the choices. But anyway, you just have to apply some exponential rules and division rules:
*When 2 is raised with an integer (greater than 1), the last digit of the number has a repeating pattern of 2, 4, 8, 6.
*A number is divisible by 10 if the last digit of that number is equal to zero.
*A number is divisible by 3 if the sum of the digits is divisible by 3 (for example, 51 is divisible by 3, because 5+1 = 6 and six is obviously divisible by 3).

By applying these rules, you should be able to get the answer. :3