Step 1: Identify the first reaction.
Pyrrole reacts with CHCl$_3$/KOH through Ciamician-Dennstedt rearrangementThis reaction causes ring expansion of pyrrole to give chloropyridine
Step 2: Formation of product X.
In this rearrangement, pyrrole is converted mainly into 3-chloropyridine
\[
\text{Pyrrole} \xrightarrow{\text{CHCl}_3,\text{ KOH}} \text{3-chloropyridine}
\]
Step 3: Reaction of X with NaNH$_2$.
3-Chloropyridine reacts with NaNH$_2$ through elimination-addition mechanism involving pyridyne intermediate
Step 4: Formation of product Y.
Due to cine-substitution, the amino group enters adjacent to the position from where chlorine was removedTherefore, 3-chloropyridine gives 4-aminopyridine as the major product
\[
\text{3-chloropyridine} \xrightarrow{\text{NaNH}_2} \text{4-aminopyridine}
\]
Step 5: Conclusion.
Thus, X is 3-chloropyridine and Y is 4-aminopyridine
\[
\boxed{\text{C}}
\]