Step 1: Understanding the Concept:
Plant diseases are caused by specific fungal pathogens, and matching them requires knowledge of plant pathology.
Step 3: Detailed Explanation:
1. Root rot of cotton (A): Caused by Rhizoctonia bataticola (also known as Macrophomina phaseolina). It leads to sudden wilting and drying of plants. (Matches III).
2. Rhizome rot of ginger (B): Primarily caused by Pythium myriotylum. This is a soil-borne water mold that causes soft rot of the rhizomes. (Matches I).
3. Root rot of apple (C): Specifically, white root rot is caused by Rosellinia necatrix. It causes a cottony white growth on the root surface. (Matches II).
4. Black scurf of potato (D): Caused by Rhizoctonia solani. It is characterized by black sclerotia on the tuber surface which do not wash off. (Matches IV).
Step 4: Final Answer:
Matching the pairs: A-III, B-I, C-II, D-IV. This corresponds to Option (C).