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).