A dipeptide, "x" on complete hydrolysis gives "y" and "z". "y" on treatment with aq. HNO$$_2$$ produces lactic acid. On the other hand "z" on heating gives a cyclic molecule.

Based on the information given, the dipeptide X is:

To determine the correct dipeptide X, we first identify the amino acids Y and Z obtained on hydrolysis.

The first clue states that amino acid Y produces lactic acid on treatment with aqueous $$\mathrm{HNO_2}$$.

Nitrous acid converts the primary amino group $$\left(-NH_2\right)$$ of an aliphatic amino acid into a hydroxyl group $$\left(-OH\right)$$.

Since the product formed is lactic acid,

$$\mathrm{CH_3-CH(OH)-COOH},$$

the original amino acid must have been

$$\mathrm{CH_3-CH(NH_2)-COOH},$$

which is alanine.

Hence,

• $$Y =$$ Alanine.

The second clue states that amino acid Z forms the given cyclic compound on heating.

When $$\alpha$$-amino acids are heated, two molecules condense to form a six-membered cyclic diamide known as a diketopiperazine.

From the structure of the cyclic product, the carbon atoms between the nitrogen and carbonyl groups are simple $$CH_2$$ units with no alkyl substituents.

This is possible only if the amino acid is glycine,

$$\mathrm{H_2N-CH_2-COOH}.$$

Therefore,

• $$Z =$$ Glycine.

The required dipeptide X is obtained by condensation of alanine and glycine.

Hence,

• $$Y =$$ Alanine
• $$Z =$$ Glycine
• $$X =$$ Alanine-Glycine

Therefore, the correct answer is Alanine-Glycine.