Step 1: Understanding the Concept:
Matching common vegetable names with their botanical nomenclature is a foundational requirement in horticulture.
Step 2: Detailed Explanation:
Let us match each common name with its corresponding scientific name:
(A) Sword bean is botanically classified as Canavalia gladiata, so (A) matches with (IV).
(B) Ivy gourd is botanically classified as Coccinia indica (or Coccinia grandis), so (B) matches with (III).
(C) Cowpea is botanically classified as Vigna unguiculata, so (C) matches with (II).
(D) Snake gourd is botanically classified as Trichosanthes anguina (or Trichosanthes cucumerina), so (D) matches with (I).
Combining these gives the sequence: (A)-(IV), (B)-(III), (C)-(II), (D)-(I).
Step 3: Final Answer:
Hence, the correct option is (C).