Step 1: Understanding the Concept:
The basic chromosome number (\(x\)) represents the number of chromosomes in a single complete set. Horticultural crops vary widely in their \(x\) values.
Step 2: Detailed Explanation:
A. Carnation (Dianthus caryophyllus): The basic chromosome number is \(x = 15\). Cultivated carnations are generally diploid (\(2n = 30\)). (Match with III).
B. Marigold (Tagetes spp.): For the most common marigolds, specifically Tagetes erecta and Tagetes patula, the basic chromosome number is \(x = 12\). (Match with IV).
C. Tuberose (Polianthes tuberosa): Tuberose belongs to the Agavoideae family. Its basic chromosome number is \(x = 30\). (Match with II).
D. Chrysanthemum: Chrysanthemum species are based on a basic chromosome number of \(x = 9\). Cultivars can be diploid, tetraploid, or hexaploid (e.g., \(2n = 18, 36, 54\)). (Match with I).
Matching these results in: A-III, B-IV, C-II, D-I.
Step 3: Final Answer:
The correct matching sequence is A-III, B-IV, C-II, D-I.