Once you attempt the question then PrepInsta explanation will be displayed.

This again is a question that we need to solve by trial and error. Clearly, N is an odd number. So, the remainder when we divide N by 24 has to be odd.

If the remainder when we divide N by 24 = 1, then N2 also has a remainder of 1. we can also see that if the remainder when we divide N by 24 is -1, then N2 a remainder of 1.

When remainder when we divide N by 24 is ±3, thenN^{2} has a remainder of 9.

When remainder when we divide N by 24 is ±5, thenN^{2} has a remainder of 1.

When remainder when we divide N by 24 is ±7, then N^{2} has a remainder of 1.

When remainder when we divide N by 24 is ±9, then N^{2} has a remainder of 9.

When remainder when we divide N by 24 is ±11, thenN^{2}has a remainder of 1.

So, the remainder when we divide N by 24 could be ±1, ±5, ±7 or ±11.

Or, the possible remainders when we divide N by 24 are 1, 5, 7, 11, 13, 17, 19, 23.

Or, the possible remainders when we divide N by 12 are 1, 5, 7, 11.

The question is "What are the possible remainders we can get if we divide N by 12?"

Hence the answer is "1, 5, 7, 11".