1) You ought to take it to the police station as soon as possible.
Explanation: The modal verb "ought to" is used here to express a strong recommendation or moral obligation. In this context, returning a found briefcase is the right thing to do, so "ought to" fits better than "can," which simply expresses possibility.
2) No, I didn’t need to. I had enough in my wallet.
Explanation: "Didn’t need to" is the correct choice because it refers to the fact that there was no necessity to get money from the bank (and the action didn’t happen). "Needn’t" is not suitable because it typically describes a lack of necessity for a future or present action, not a past one.
3) You should wear a watch.
Explanation: "Should" is used to give advice or a suggestion. In this case, the speaker is suggesting that wearing a watch would help avoid lateness in the future. "Might" would imply possibility, which doesn't fit the context of giving advice.
4) They can’t have got lost because I gave them a map.
Explanation: "Can’t" is used to express a strong impossibility based on logical reasoning. Since the speaker gave them a map, it is highly unlikely that Paul and Jim got lost, making "can’t" the appropriate choice. "Mustn’t" refers to prohibition, which is irrelevant here.
5) Could I use your mobile phone, please?
Explanation: "Could" is more polite and formal than "would" when making a request. While "would" can also be used for polite requests, "could" is more commonly employed in this specific context to ask for permission.
6) We needn’t go shopping this week, we’ve got plenty of food.
Explanation: "Needn’t" means that there is no necessity to do something. Since there’s already plenty of food, going shopping is unnecessary. "Mustn’t" would imply prohibition, which is not the intended meaning here.
7) You can call in tomorrow if you like.
Explanation: "Can" is used to express permission or possibility. In this case, the speaker is offering permission for the other person to visit tomorrow. "Might" would express uncertainty, which doesn’t fit the context of giving an invitation or suggesting a time to visit.