I fixed the OAs

See now sir. let me know if you need further explanations about the question itself

Thanks a lot! And B also my bad, I missed it the first time.

All those single digit numbers who have the same unit's digit as the number itself irrespective of the powers and those numbers whose 99th power can result in the same unit's digit as the number itself, can be the value of y. A number ending with 0 or I or 5 or 6 always ends with the same number i.e. 0/1/5/6 itself respectively, so the values of y can be 0 or 1 or 5 of 6, so the options (C), (D), (E) & (F) are correct.


The pattern for the unit's digit of 7 is of 4 steps

The repeating pattern of seven is a number ending in 7
9
3
7


we get the unit's digit of \(N = (897)^{99} = (897)^{96+3}\) as 3 which is not same as 7. So 7 is not possible.

(B) 9.

The pattern for the unit's digit of 9 is of two steps i.e.


for 9 raised to an odd integer ends with 9 & for 9 raised to an even integer with 1, so the unit's digit of \(N = (899)^{99} = (899)\) is 9 only.

So, the value of y can be 9.

Hence the answer is (B), (C), (D), (E) & (F).