The alcohol shown is heated with alkaline $\mathrm{KMnO}{}_4$ and the mixture is then acidified. Which structure is the organic product?

The alcohol is cyclohexylmethanol, a primary alcohol. Hot alkaline permanganate oxidises it through the aldehyde to the carboxylate, which acidification converts into cyclohexanecarboxylic acid. The aldehyde is the PCC product, and the ring carbon is not cleaved.