1)jack(to lose)his key.he can’t get into the house
a)has lost; b)lost
2)i(to do)a lot of work today
a)did; b)have done
3)what (to do) last weekend
a); b)
(to see ann yesterday?
a); b)
5)it’s the most interesting film i(ever/to see)
a)saw; b)have seen
(to eat)many fruit today?
a); b)

1) Jack lost his key. He can't get into the house.
In this sentence, the action of Jack losing his key is already completed in the past. Therefore, the correct answer is:
a) has lost

2) I have to do a lot of work today.
The action of doing a lot of work is happening today, so we need to use the present perfect tense. The correct answer is:
b) have done

3) What did you do last weekend?
This question is asking about the past weekend, so we need to use the past simple tense. The correct answer is:
b) did

4) Did you see Ann yesterday?
This question is also asking about a past action, specifically if the person saw Ann yesterday. Therefore, the correct answer is:
a) did

5) It's the most interesting film I have ever seen.
The action of seeing the film is completed in the past, but the impact of that action is still relevant in the present. Therefore, we use the present perfect tense. The correct answer is:
b) have seen

6) Have you eaten many fruits today?
This question is asking about the quantity of fruits eaten today, so we need to use the present perfect tense. The correct answer is:
b) have eaten