Number of Hydroxyl Groups in Hydrogenated and Hydroxylated Major Product

To find the total number of hydroxyl groups present in a molecule of the major product $\mathbf{P}$, we analyze the two steps of the reaction sequence:

1. Step 1: Selective Hydrogenation using Lindlar's Catalyst $\text{Reagents: } \text{H}_2, \, \text{Pd-BaSO}_4, \, \text{quinoline}$ Lindlar's catalyst selectively reduces alkynes to $(Z)$-alkenes (cis-alkenes) without reducing the existing carbon-carbon double bonds ($\text{C}=\text{C}$) in the molecule.

   • The reactant has one internal alkyne group ($-\text{C}\equiv\text{C}-$) and two alkene double bonds (one in the cyclopentenyl ring and one in the cyclohexenyl ring).
   • Therefore, the alkyne is stereoselectively reduced to a cis-alkene: $-\text{C}\equiv\text{C}- \xrightarrow{\text{H}_2, \, \text{Pd-BaSO}_4, \, \text{quinoline}} -\text{CH}=\text{CH}-$
   • After this step, the intermediate contains a total of $3$ carbon-carbon double bonds:
     • $1$ in the 5-membered ring
     • $1$ in the acyclic chain (formed from the alkyne)
     • $1$ in the 6-membered ring

2. Step 2: Dihydroxylation using Baeyer's Reagent $\text{Reagents: } \text{dil. } \text{KMnO}_4 \text{ (excess)}, \, 273\text{ K}$ Cold, dilute alkaline $\text{KMnO}_4$ (Baeyer's reagent) carries out syn-dihydroxylation across carbon-carbon double bonds, converting each $\text{C}=\text{C}$ bond into a vicinal diol (adding $2$ hydroxyl groups per double bond): $-\text{CH}=\text{CH}- \xrightarrow{\text{dil. } \text{KMnO}_4, \, 273\text{ K}} -\text{CH(OH)}-\text{CH(OH)}-$ Since $\text{KMnO}_4$ is present in excess, all $3$ double bonds undergo dihydroxylation: $\text{Total number of hydroxyl } (-\text{OH}) \text{ groups} = 3 \times 2 = 6$

Therefore, the total number of hydroxyl groups present in a molecule of the major product $\mathbf{P}$ is 6.