Step 1: Understanding the Concept:
The diploid chromosome number (\( 2n \)) is a fundamental cytogenetic characteristic of plant species.
Understanding these numbers is essential for plant breeding, cytogenetics, and hybridization studies.
Step 2: Detailed Explanation:
- (A) Carrot (Daucus carota): A biennial root crop belonging to the family Apiaceae.
Its diploid chromosome number is \( 2n = 18 \). Thus, (A) matches (III).
- (B) French bean (Phaseolus vulgaris): A leguminous vegetable crop belonging to the family Fabaceae.
Its diploid chromosome number is \( 2n = 22 \). Thus, (B) matches (IV).
- (C) Chilli (Capsicum annuum): A solanaceous crop valued for its fruits.
Its diploid chromosome number is \( 2n = 24 \). Thus, (C) matches (I).
- (D) Sponge gourd (Luffa aegyptiaca): A popular cucurbitaceous vegetable.
Its diploid chromosome number is \( 2n = 26 \). Thus, (D) matches (II).
This pairing results in the sequence: (A) - (III), (B) - (IV), (C) - (I), (D) - (II).
Step 3: Final Answer:
The correct matching sequence corresponds to option (A).