Calculate the number of secondary  hydroxyl groups in [Q]

To answer the question, let's analyze the reaction stepwise:

1. First Step (acid, heat):
   • The starting compound is a cyclic terpene-like structure with a tertiary alcohol and two isopropyl groups.
   • Upon acid-catalyzed dehydration (heat), an alkene is formed by elimination of water (E1 or E2 mechanism).
2. Second Step (aqueous dilute KMnO₄, cold, excess):
   • Cold, dilute, alkaline or neutral potassium permanganate causes syn-dihydroxylation (Baeyer’s test condition).
   • This means both ends of the double bond are converted to vicinal (neighbouring) diols (two –OH groups add across the alkene).
   • Each carbon of the original double bond now gets a hydroxyl group.
3. Type of Hydroxyl Groups:
   • A secondary hydroxyl group is one where the OH is attached to a secondary carbon (carbon bonded to two other carbons).
   • In this structure, both newly added –OH groups (from the syn addition to a disubstituted double bond in a ring) will be on secondary carbons.

Final Answer:

Number of secondary hydroxyl groups in [Q]: 2

Both –OH groups that are introduced in the oxidative dihydroxylation step end up as secondary alcohols (on secondary carbons of the ring).