Step 1: Understanding the Question:
The question asks to identify the specific polymer generated when the cyclic monomer $\varepsilon$-caprolactam undergoes polymerization.
Step 2: Detailed Explanation:
Let's trace the polymer products associated with each option:
Polyacrylonitrile (PAN) is an addition polymer synthesized from acrylonitrile ($\mathrm{CH}_2\mathrm{=CH-CN}$).
Neoprene is a synthetic rubber derived from the addition polymerization of chloroprene (2-chloro-1,3-butadiene).
Terylene (Dacron) is a polyester copolymer produced via the condensation reaction of ethylene glycol and terephthalic acid.
Nylon-6 is prepared by heating the single cyclic monomer $\varepsilon$-caprolactam with water at elevated temperatures ($533 - 543\text{ K}$). The ring structure undergoes a ring-opening polymerization process to form a continuous polyamide chain containing exactly six carbon atoms in its repeating structural unit:
$$\text{n } (\varepsilon\text{-caprolactam}) \xrightarrow{\mathrm{H}_2\mathrm{O},\ \Delta} \mathrm{\left[ -NH-(CH_2)_5-CO- \right]_n}\ \text{(Nylon-6)}$$
Step 3: Final Answer:
Nylon-6 is the polymer obtained from $\varepsilon$-caprolactam, matching option (D).