Option 1 -> Mismatches all sentences; (A) doesn't fit with (I), and the other pairings are incorrect.
Option 2 -> (A)-(IV): "He spoke to me in a rude manner, but I still forgave him" ✓; (B)-(I): "I will go and talk to the Manager in an impressive way so that he agrees to our suggestions" ✓; (C)-(II): "Rohit continues to commit mistakes as he works without any care" ✓; (D)-(III): "Shobha won the race because she ran with great speed" ✓
Option 3 -> Incorrect pairings; (C) with (IV) doesn't make grammatical sense.
Option 4 -> All matches are contextually inappropriate; (A) with (III) doesn't fit the sentence structure.
Hence, Option 2: (A) - (IV), (B) - (I), (C) - (II), (D) - (III) -> Each adverbial phrase correctly completes its corresponding sentence with proper grammar and logical context. The phrases describe manner, purpose, carelessness, and speed respectively, matching perfectly with the intent of each sentence. -> correct