Sure, let's go through each question and provide the correct answers along with explanations:

1. **When I last saw him, he ___ in London.**
- **C. was living**
- Explanation: The past continuous tense "was living" is used to describe an action that was ongoing in the past when another action occurred.

2. **We ___ Dorothy since last Saturday.**
- **B. haven’t seen**
- Explanation: The present perfect tense "haven’t seen" is used to describe an action that has not occurred up to the present moment.

3. **The train ___ half an hour ago.**
- **B. left**
- Explanation: The simple past tense "left" is used to describe a completed action in the past.

4. **My sister ___ for you since yesterday.**
- **C. has been looking**
- Explanation: The present perfect continuous tense "has been looking" is used to describe an action that started in the past and is still ongoing.

5. **Christopher Columbus ___ America more than 500 years ago.**
- **A. discovered**
- Explanation: The simple past tense "discovered" is used to describe a completed action in the past.

6. **He fell down when he ___ towards the church.**
- **C. was running**
- Explanation: The past continuous tense "was running" is used to describe an ongoing action in the past that was interrupted by another action.

7. **I’ll come and see you before I ___ for the States.**
- **A. leave**
- Explanation: The simple present tense "leave" is used in a time clause to describe a future action.

8. **John ___ a book when I saw him.**
- **C. was reading**
- Explanation: The past continuous tense "was reading" is used to describe an ongoing action in the past when another action occurred.

9. **Her brother ___ in Canada at present.**
- **C. is working**
- Explanation: The present continuous tense "is working" is used to describe an action that is currently happening.

10. **I ___ to the same barber since last year.**
- **B. have been going**
- Explanation: The present perfect continuous tense "have been going" is used to describe an action that started in the past and continues to the present.

11. **Her father ___ when she was a small girl.**
- **B. died**
- Explanation: The simple past tense "died" is used to describe a completed action in the past.

12. **Almost everyone ___ for home by the time we arrived.**
- **D. had left**
- Explanation: The past perfect tense "had left" is used to describe an action that was completed before another action in the past.

13. **I couldn’t cut the grass because the lawn mower ___ a few days previously.**
- **C. had broken down**
- Explanation: The past perfect tense "had broken down" is used to describe an action that was completed before another action in the past.

14. **Since ___, I have heard nothing from him.**
- **B. he left**
- Explanation: The simple past tense "left" is used to describe a completed action in the past.

15. **After I ___ lunch, I looked for my bag.**
- **B. had had**
- Explanation: The past perfect tense "had had" is used to describe an action that was completed before another action in the past.

16. **By the end of next year, George ___ English for two years.**
- **A. will have learned**
- Explanation: The future perfect tense "will have learned" is used to describe an action that will be completed by a certain time in the future.

17. **Henry ___ into the restaurant when the writer was having dinner.**
- **B. went**
- Explanation: The simple past tense "went" is used to describe a completed action in the past.

18. **He will take the dog out for a walk as soon as he ___ dinner.**
- **B. finishes**
- Explanation: The simple present tense "finishes" is used in a time clause to describe a future action.

19. **I ___ from him since he ___ two years ago.**
- **B. haven't heard; disappeared**
- Explanation: The present perfect tense "haven't heard" is used to describe an action that has not occurred up to the present moment, and the simple past tense "disappeared" is used to describe a completed action in the past.

20. **After the guests ___, she ___ back into the living-room and ___ off the light.**
- **D. had left; went; turned**
- Explanation: The past perfect tense "had left" is used to describe an action that was completed before another action in the past, and the simple past tense "went" and "turned" are used to describe completed actions in the past.

21. **By the time you finish cooking they ___ their homework.**
- **A. will have finished**
- Explanation: The future perfect tense "will have finished" is used to describe an action that will be completed by a certain time in the future.

22. **I will tell John about it ___.**
- **B. when I see him this afternoon.**
- Explanation: The simple present tense "see" is used in a time clause to describe a future action.

23. **I have heard nothing from him since he ___ school.**
- **B. left**
- Explanation: The simple past tense "left" is used to describe a completed action in the past.

24. **He fell down while he ___ towards the church.**
- **C. was running**
- Explanation: The past continuous tense "was running" is used to describe an ongoing action in the past that was interrupted by another action.

25. **Bill’s mother won’t let him go out with his friends ___.**
- **D. until he has finished his homework**
- Explanation: The present perfect tense "has finished" is used to describe an action that must be completed before another action can occur.

26. **Her academic performance has greatly improved since she ___ her study methods.**
- **B. changed**
- Explanation: The simple past tense "changed" is used to describe a completed action in the past.

27. **You may not see how important your family is ___.**
- **C. until you live far from home**
- Explanation: The simple present tense "live" is used to describe a condition that must be met before understanding occurs.

28. **The city has changed a lot since I last ___ it.**
- **A. visited**
- Explanation: The simple past tense "visited" is used to describe a completed action in the past.

29. **He will take the dog out for a walk ___.**
- **C. as soon as he has finished**
- Explanation: The present perfect tense "has finished" is used to describe an action that must be completed before another action can occur.

30. **Ask her to come and see me ___.**
- **B. when she has finished her work**
- Explanation: The present perfect tense "has finished" is used to describe an action that must be completed before another action can occur.