A paper is dipped in a dil. $$\text{H}_2\text{SO}_4$$ solution of  'X' upon treatment with $$\text{SO}_2$$ gas turns into green.The compound  'X' is :

The given test is a standard qualitative test for the detection of sulphur dioxide ((SO_2)) gas.

Paper dipped in an acidified solution of potassium dichromate acts as an oxidizing agent. When (SO_2) is passed over the paper, a redox reaction takes place in which the orange dichromate ion ((Cr_2O_7^{2-})) is reduced to the green chromium(III) ion ((Cr^{3+})), while (SO_2) is oxidized to sulphate.

The reaction can be represented as

$$K_2Cr_2O_7 + H_2SO_4 + 3SO_2 \rightarrow K_2SO_4 + Cr_2(SO_4)_3 + H_2O.$$

The formation of chromium(III) sulphate, (Cr_2(SO_4)_3), is responsible for the characteristic green colour observed on the paper.

Therefore, the compound represented by (X) is potassium dichromate ((K_2Cr_2O_7)).

Hence, the correct answer is Option D.