Answer: Option A
:
A
The question is asking for the remainder when ${21}^{643}$ is divided by 25.
We can use the last two digits technique to get the answer, since the remainder when a number is divided by 25, depends only on the last two digits.
For numbers ending in 1, the last two digits of a power expression $a^b$ can be determined as -
The last digit is always 1.
The $2^{nd}$ last digit = product of tens digit of base * unit digit of the power i.e. ${21}^{643}=......61(6=2\times 3)$
When 61 is divided by 25, the remainder is 11.