Step 1: Understand the clues.
In reaction I the monomer A reacts with NaOH (a base), and in reaction II the monomer C reacts with $NaHCO_3$ (which reacts with acidic groups). We must name the polymers X and Y.
Step 2: Read what NaOH tells us about A.
A monomer reacting cleanly with NaOH points to a precursor suited to basic conditions. This route leads to the melamine type polymer, so X is Melamine.
Step 3: Read what $NaHCO_3$ tells us about C.
$NaHCO_3$ reacts with carboxylic acid groups, releasing $CO_2$. So monomer C carries an acid group, such as a dicarboxylic acid used in polyester making.
Step 4: Identify the polyester polymer Y.
A polymer built from such an acid monomer and a glycol gives Glyptal, a glycerol and phthalic acid polyester. So Y is Glyptal.
Step 5: Cross check the other options.
Bakelite, Buna-S, Neoprene, Terylene and Novolac do not fit both the NaOH and $NaHCO_3$ monomer clues together, so they are ruled out.
Step 6: State the pair.
So X and Y are Melamine and Glyptal.
\[ \boxed{\text{Melamine; Glyptal}} \]