Step 1: Identifying allylic secondary alcohol.
An allylic alcohol is one in which the hydroxyl group (-OH) is attached to a carbon atom adjacent to a double bond. A secondary alcohol has the hydroxyl group attached to a carbon atom that is bonded to two other carbon atoms.
Step 2: Analyzing the options.
(A) But-2-en-1-ol: This is a primary alcohol, not secondary.
(B) But-3-en-2-ol: This is an allylic secondary alcohol, but it doesn't fit the structure we are looking for.
(C) 2-Methyl but-3-en-2-ol: Correct — This is an allylic secondary alcohol. The -OH group is attached to a secondary carbon, and the alcohol is adjacent to a double bond.
(D) Prop-2-en-1-ol: This is a primary alcohol, not secondary.
Step 3: Conclusion.
The correct answer is (C) 2-Methyl but-3-en-2-ol.