Answer:
Prepare pent-2-yne as discussed in Q.
13 above and then convert in to pentan-2-one by hydration.
\[\underset{\text{Pent-2-yne}}{\mathop{C{{H}_{3}}-C\equiv
C-C{{H}_{2}}C{{H}_{3}}+{{H}_{2}}O}}\,\xrightarrow[333\,K]{60%\,\,{{H}_{2}}S{{O}_{4}},\,HgS{{O}_{4}}}\]\[\left[
C{{H}_{3}}-\overset{\begin{smallmatrix}
OH \\
|
\end{smallmatrix}}{\mathop{C}}\,=CHC{{H}_{2}}C{{H}_{3}}
\right]\xrightarrow{\text{Tautomerises}}\]
\[\underset{\text{Pentan}-2-one\,(major\,isomer)}{\mathop{C{{H}_{3}}-\overset{\begin{smallmatrix}
O \\
||
\end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}}}\,\]
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