IMO E

First determine the pattern 2 ^0=1, remainder when divided by 3=1
2^1=2, remainder when divided by 3=2
2^2=4, remainder=1
2^3=8 , remainder = 2
2^4=16 ,remainder =1
2^5=32 , remainder =2

Alternating pattern of 1 and 2. In all cases remainder is 1 when n=even.

I is not true. For n=0, remainder =1.
II For n=even, 3^n=(-3)^n. True
III √2 ^ n= integer(for n=0,2,4,..value is integer). True

Hence II and III must be true.

Agree answer should be D