An unsaturated hydrocarbon X absorbs two hydrogen molecules on catalytic hydrogenation, and also gives following reaction:
X $$\xrightarrow[\frac{(ii) Zn}{H_2O}]{(i) O_3}$$ A $$\xrightarrow{[Ag(NH_3)_2]^+}$$ B (3-oxo-hexanedicarboxylic acid). X will be:

Step 1: Analyze Hydrogen Absorption

The problem states that X absorbs two moles of hydrogen ($$\text{H}_2$$) during catalytic hydrogenation. This directly tells us that X contains two carbon-carbon double bonds (a diene).

Step 2: Work Backwards from the Final Product B

Product B is given as 3-oxo-hexanedicarboxylic acid (commonly known as 3-oxohexanedioic acid). Its chemical structure is:

$$\text{HOOC--CH}_2\text{--CH}_2\text{--C}(=\text{O})\text{--CH}_2\text{--COOH}$$

Product B is obtained by treating intermediate A with Tollens' reagent ($$[\text{Ag}(\text{NH}_3)_2]^+$$). Tollens' reagent is a mild oxidizing agent that selectively oxidizes aldehyde groups ($$-\text{CHO}$$) into carboxylic acids ($$-\text{COOH}$$) without altering ketones.

Therefore, intermediate A must be a keto-dialdehyde with the following structure:

$$\text{OHC--CH}_2\text{--CH}_2\text{--C}(=\text{O})\text{--CH}_2\text{--CHO}$$

Step 3: Deduce the Structure of X via Ozonolysis Cleavage

Intermediate A is formed via the reductive ozonolysis ($$\text{O}_3\text{, then Zn/H}_2\text{O}$$) of hydrocarbon X. Ozonolysis cleaves double bonds and inserts oxygen atoms to form carbonyl compounds.

To reconstruct X, we connect the carbonyl carbons of A where the cleavage took place. Since one of the carbonyls is a ketone inside a continuous chain flanked by two aldehydes, X must be a cyclic system containing one endocyclic double bond and one exocyclic methylene ($$=\text{CH}_2$$) group:

• Connecting the aldehyde groups at positions 1 and 6 forms a 6-membered ring.
• The ketone at position 3 implies that an exocyclic double bond ($$=\text{CH}_2$$) was attached there before cleavage (yielding a side product of formaldehyde, $$\text{HCHO}$$).

This corresponds perfectly to 4-methylenecyclohex-1-ene.

Ozonolysis Mechanism Verification:

$$\text{4-methylenecyclohex-1-ene} \xrightarrow{\text{(i) } \text{O}_3 \text{ / (ii) } \text{Zn, H}_2\text{O}} \text{OHC--CH}_2\text{--CH}_2\text{--C}(=\text{O})\text{--CH}_2\text{--CHO} + \text{HCHO}$$

$$\text{OHC--CH}_2\text{--CH}_2\text{--C}(=\text{O})\text{--CH}_2\text{--CHO} \xrightarrow{[\text{Ag}(\text{NH}_3)_2]^+} \text{HOOC--CH}_2\text{--CH}_2\text{--C}(=\text{O})\text{--CH}_2\text{--COOH}$$

Conclusion:

The structural features match 4-methylenecyclohex-1-ene, which corresponds to the layout presented in Option C.

Answer: Option C