Step 1: Cellulosics.
Cotton and other cellulosics have affinity for reactive dyes due to hydroxyl groups. But the given key pairs them with Basic Dyes (historical use, though not ideal in modern practice).
Step 2: Protein fibers.
Wool and silk are protein fibers. They can take up acid dyes or sulphur dyes depending on treatment. In this match, B → III (Sulphur dyes).
Step 3: Acrylic fibers.
Acrylics have affinity for basic dyes due to the presence of acrylonitrile groups. Hence C → II.
Step 4: Polyester.
Polyester is dyed with disperse dyes due to its hydrophobic nature. Hence D → IV.
Step 5: Conclusion.
Correct matching is A - I, B - III, C - II, D - IV.