This looks like a CAT question with only 4 answer choices.
Re-phrase the question as find remainder of 25^x/7.
Now check for periodicity of 25^x/7.
When x=1, remainder=4
When x=2, remainder=2
When x=3, remainder=1
When x=4, remainder=4
So periodicity of 25^x is 3. We need to reduce x (i.e. 26^27) to fall into this periodicity.
Find remainder of 26^27/3:
=> 104/3 = 2
Therefore, we need to find 25^2/7's remainder which is, by our periodicity map, 2. (C).