A hydrocarbon of formula C5H8 gives a white precipitate with ammoniacal silver nitrate. On vigorous oxidative cleavage with hot alkaline KMnO4…

The white precipitate with $[\mathrm{Ag(NH_3)_2}]^+$ shows a terminal alkyne $\mathrm{R-C\equiv CH}$ (acidic $\equiv$C–H). Strong oxidation breaks the triple bond to give $\mathrm{RCOOH}$ and $\mathrm{CO_2}$. For the product acid to have a tertiary carbon, $\mathrm{R}$ must be isopropyl: $(\mathrm{CH_3})_2\mathrm{CH-C\equiv CH}\to(\mathrm{CH_3})_2\mathrm{CHCOOH}+\mathrm{CO_2}$. This is 3-methylbut-1-yne. Pent-1-yne would give straight-chain butanoic acid, pent-2-yne is internal (no Tollens-type precipitate), and the diene is not an alkyne.