Let's analyze the sentences and choose the correct options:
Your passport might __ in the top drawer - did you look there?

A. be is the correct option. The sentence is expressing a possibility, and "be" is the appropriate verb form for that.
Melanie couldn't resist __ another piece of cake.

B. taking is the correct option. The verb "resist" is followed by a gerund (the -ing form of the verb).
Colin stopped __ a glass of water before he drove.

A. to drink is the correct option. The verb "stop" can be followed by a gerund to indicate an action that was stopped, or by an infinitive to indicate an action that was interrupted and then resumed. In this case, Colin stopped his current activity to drink a glass of water.
It's unusual for Thomas __ saying goodbye.

A. to leave is the correct option. The phrase "It's unusual for" is followed by an infinitive.
The house should __ tomorrow.

C. be painted is the correct option. The sentence is expressing a passive voice, indicating that the house will be painted by someone else.
I really dislike __ people mistreat animals.

A. seeing is the correct option. The verb "dislike" is followed by a gerund.
I’d prefer __ camping than staying in a hotel.

A. to go is the correct option. The verb "prefer" is followed by an infinitive.
Jemma said __ about ten thousand years.

B. she had lived is the correct option. The sentence is referring to a past event that happened before Jemma said it, so the past perfect tense is appropriate.
He accused me __ the tickets.

B. of having sold is the correct option. The verb "accused" is followed by the preposition "of" and a gerund.
Your child's behaviour is __ annoying.

D. just is the correct option. The adverb "just" is used to emphasize the degree of annoyance.
I'm __ with Philip - he won't change his mind.
A. fed up is the correct option. The phrase "fed up with" means to be irritated or annoyed by something.
I don't really like that kind __ telling you the truth.
A. of is the correct option. The phrase "that kind of" is followed by a noun or gerund.
You must __ have eaten such a big dinner last night.
A. be starving is the correct option. The sentence is expressing a logical conclusion based on the past event of eating a big dinner.
You were wasting your time __.
B. explaining is the correct option. The verb "wasting" is followed by a gerund.
I watched the bus __ disappear.
D. disappear is the correct option. The verb "watched" is followed by the base form of the verb to express an action that was seen happening.
The boss doesn’t encourage __.
A. smoking is the correct option. The verb "encourage" is followed by a gerund.
He was angry __.
D. having been is the correct option. The phrase "angry at" is followed by a gerund.
She has broken __ my favourite coffee mug.
D. in is the correct option. The phrase "broken in" means to damage or break something.
The pencil’s blunt __ sharpening.
C. at is the correct option. The phrase "blunt at" means not sharp.
Sophia attended __ having slept on the sofa.
B. in is the correct option. The phrase "attended in" means to participate or be present at something.
I cheated him __.
A. of is the correct option. The phrase "cheated someone of" means to trick someone out of something.
He was polite enough __ to allow.
C. to be is the correct option. The phrase "polite enough to" is followed by an infinitive.
I had to be careful __ pass.
A. to is the correct option. The phrase "careful to" is followed by an infinitive.
There’s no point __ about it.
B. getting upset is the correct option. The phrase "no point in" is followed by a gerund.
Will you let me __ your car for the weekend?
A. borrow is the correct option. The verb "let" is followed by the base form of the verb.