A hydrocarbon X ($\mathrm{C}{}_5\mathrm{H}{}_8$) liberates hydrogen with sodium, gives a ketone on Hg(II)-catalysed hydration and gives 2-methylbutane on complete hydrogenation. X is

Hydrogen evolution with sodium means a terminal alkyne, and hydration to a ketone fits $\mathrm{R}-\mathrm{C}\equiv \mathrm{CH}$. Hydrogenation to 2-methylbutane fixes the branched skeleton, so X is $(\mathrm{CH}{}_3){}_2\mathrm{CH}-\mathrm{C}\equiv \mathrm{CH}$, which hydrates to 3-methylbutan-2-one. Pent-1-yne would give pentane, pent-2-yne is not terminal, and isoprene has no acidic hydrogen and gives no ketone.