1. Identify Question Type:

This is a classification question from the domain of General Science (Chemistry), often included in General Intelligence and Reasoning sections. It requires knowledge of homologous series in organic chemistry.

2. Step-by-Step Logic and Solution:

The goal is to determine which homologous series the chemical formula C₃H₆ belongs to. We can do this by checking the general formula for each option.

• Let 'n' be the number of carbon atoms. In the given formula, C₃H₆, n = 3.
• Let 'm' be the number of hydrogen atoms. Here, m = 6.

Now, let's examine the general formulas for the homologous series given in the options:

1. Alkane: The general formula for an alkane is CₙH₂ₙ₊₂.
   • For n = 3, the formula would be C₃H₂(₃)₊₂ = C₃H₈.
   • This does not match C₃H₆.
2. Alkyne: The general formula for an alkyne is CₙH₂ₙ₋₂.
   • For n = 3, the formula would be C₃H₂(₃)₋₂ = C₃H₄.
   • This does not match C₃H₆.
3. Alkene: The general formula for an alkene is CₙH₂ₙ.
   • For n = 3, the formula would be C₃H₂(₃) = C₃H₆.
   • This matches the given formula perfectly. The compound is Propene.
4. Cycloalkane: The general formula for a cycloalkane is also CₙH₂ₙ.
   • For n = 3, the formula would be C₃H₂(₃) = C₃H₆.
   • This also matches the given formula (the compound would be Cyclopropane).

3. Core Logic/Pattern and Conclusion:

The formula C₃H₆ fits the general formula CₙH₂ₙ. Both the alkene and cycloalkane series share this general formula. However, alkenes are a fundamental homologous series characterized by a carbon-carbon double bond, while cycloalkanes are cyclic hydrocarbons. In the absence of further information (like "the compound is cyclic"), the formula CₙH₂ₙ is most commonly and primarily associated with the alkene series. Therefore, C₃H₆ (Propene) belongs to the alkene homologous series.

4. Elimination of Incorrect Options:

• Option 1 (alkane): Incorrect. The formula for a 3-carbon alkane is C₃H₈.
• Option 3 (cycloalkane): While technically correct as C₃H₆ can be cyclopropane, "alkene" is the more standard and expected classification for the general formula CₙH₂ₙ in competitive exams unless specified otherwise. Alkenes and cycloalkanes are functional isomers.
• Option 4 (alkyne): Incorrect. The formula for a 3-carbon alkyne is C₃H₄.

Thus, the most appropriate answer is alkene.