Let's analyze each term in List-I with the definitions presented in List-II:

• A. Two or more alternative forms of a gene: These are called alleles. Thus, A matches with III 'Allele'.
• B. Cross of F$_1$ progeny with homozygous recessive parent: This specific type of cross is known as a test cross, often used to determine the genotype of an individual having dominant phenotype. Therefore, B matches with IV 'Test cross'.
• C. Cross of F$_1$ progeny with any of the parents: This is defined as a back cross, which can be used for multiple purposes, including the testing of the parental genes in the offspring. So, C matches with I 'Back cross'.
• D. Number of chromosome sets in plant: This describes how many sets of chromosomes are present, i.e., the level of ploidy of the organism. Therefore, D matches with II 'Ploidy'.

From the analysis:

• A matches with III
• B matches with IV
• C matches with I
• D matches with II

Accordingly, the correct answer that matches all the descriptions is:

Option C: A-III, B-IV, C-I, D-II.