Step 1: Analyze each monomer combination and identify the corresponding polymer.
\begin{itemize}
\item A) Monomers: HO-(CH\(_2\))\(_2\)-OH (Ethylene glycol) and Benzene-1,2-dicarboxylic acid (Phthalic acid).
Ethylene glycol and phthalic acid (or phthalic anhydride) polymerize to form Glyptal. Glyptal is a type of polyester.
Therefore, A matches V (Glyptal).
\item B) Monomers: HO-(CH\(_2\))\(_4\)-OH (Butane-1,4-diol) and HOOC-Benzene-COOH (Terephthalic acid).
Butane-1,4-diol and terephthalic acid polymerize to form poly(butylene terephthalate), which is a type of polyester. Terylene (also known as Dacron or PET) is formed from ethylene glycol and terephthalic acid. Given the options and common polymer types, this combination is related to polyester formation.
Therefore, B matches III (Terylene).
\item C) Monomers: CH\(_2\)=CH-CH=CH\(_2\) (1,3-Butadiene) and CH\(_2\)=CH-CN (Acrylonitrile).
1,3-Butadiene and acrylonitrile copolymerize to form Buna-N (Nitrile rubber), which is a synthetic rubber.
Therefore, C matches II (Buna-N).
\item D) Monomer: Cl\(_2\)C=CH-CH=CH\(_2\) (Chloroprene).
Chloroprene (specifically 2-chloro-1,3-butadiene) polymerizes to form Neoprene, a synthetic rubber. The structure provided in D is 2-chlorobuta-1,3-diene, which is chloroprene.
Therefore, D matches IV (Neoprene).
\end{itemize}
Step 2: Combine the matches.
A - V (Glyptal)
B - III (Terylene)
C - II (Buna-N)
D - IV (Neoprene)
Step 3: Compare with the given options.
Let's check the options based on our derived matches:
% Option
(1) A-V, B-I, C-II, D-IV (Incorrect, B is not I)
% Option
(2) A-V, B-III, C-II, D-IV (Matches our findings)
% Option
(3) A-III, B-V, C-IV, D-II (Incorrect, A is not III)
% Option
(4) A-I, B-III, C-IV, D-II (Incorrect, A is not I)
The correct option is (2).