Analysis of sentences using context-dependent phrasal verbs:
- (A) She was very cut up with him for his offensive remarks on women in politics.
In this sentence, "cut up" signifies being emotionally distressed or deeply affected. - (B) I have plenty of interesting books to give away to book lovers.
"Give away" is fitting, meaning to distribute or offer for free. - (C) Strange that people easily give in to temptation and ruin their reputation!
"Give in" denotes succumbing or yielding, which aligns with the sentence's context. - (D) Rahul is trying to cut down on his smoking.
"Cut down" is appropriate, meaning to reduce intake.
Based on this analysis, the correct matches are (A) - (III), (B) - (I), (C) - (IV), and (D) - (II), accurately correlating contextually appropriate phrasal verbs.