Step 1: Identify the alkene.
Among the alkenes with molecular formula
\[
\mathrm{C_5H_{10}},
\]
the compound showing cis/trans isomerism is
\[
\boxed{\mathrm{Pent\mbox{-}2\mbox{-}ene}.}
\]
Step 2: Bromination followed by dehydrohalogenation.
Pent-2-ene undergoes bromination to give
\[
\mathrm{2,3\mbox{-}dibromopentane.}
\]
Treatment with alcoholic KOH followed by
\[
\mathrm{NaNH_2}
\]
causes double dehydrohalogenation to form the alkyne
\[
\mathrm{CH_3CH_2C\equiv CCH_3}
\]
(pent-2-yne).
Step 3: Write the answer.
Hence,
\[
Y=\text{alc. }\mathrm{KOH,\ NaNH_2},
\]
and
\[
Z=\mathrm{CH_3CH_2C\equiv CCH_3}.
\]
Thus,
\[
\boxed{(C)}
\]
is the correct answer.