JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Alcohols Phenols and Ethers

Phosphoric acid protonates the hydroxyl group of cyclohexylmethanol and water leaves, which would give a primary carbocation on the exocyclic carbon. A $1,2$-hydride shift from the ring carbon next to it moves the charge into the ring and produces the tertiary $1$-methylcyclohexyl cation. Loss of a $\beta$-hydrogen from this cation gives the more substituted alkene, so A is $1$-methylcyclohexene.
Diborane then adds across the double bond with boron going to the less substituted carbon and hydrogen to the more substituted one, and alkaline hydrogen peroxide replaces the boron by a hydroxyl group with retention of configuration at that carbon. The hydroxyl therefore sits on the ring carbon adjacent to the methyl-bearing carbon.
P is $2$-methylcyclohexan-$1$-ol.