We know when x is divided by 12 , the remainder is 5 , we get $\(\mathrm{x}=12 \mathrm{k}+5\)$, where k is any positive integer (\(Using Dividend = Divisor \times Quotient + Remainder \))

Now the square of integer x is $\(\mathrm{x}^2=(12 \mathrm{k}+5)^2=144 \mathrm{k}^2+120 \mathrm{k}+25=8\left(18 \mathrm{k}^2+15 \mathrm{k}\right)+25\)$ which has its first part (bracket term) a multiple of 8 , so the remainder when $\(x^2\)$ is divided by 8 is same as the remainder obtained when 25 is divided by 8 i.e. 1

Hence the answer is (A).