Omitting Relative Pronouns

Decide whether or not the relative pronoun can be omitted in the following sentences. ANSWERS
1) This was the hotel that we stayed in for two weeks.
2) She showed me the emeralds which she had brought back from South Africa.
3) The smartphone that costs £200 is very good.
4) Mrs. Smith, who is very smart, lives on the fourth floor.
5) This is the car that John bought at an auction.
6) My colleague with whom I'm doing the project should be here as soon as possible.
7) That's the woman whose house has been broken into.
8) A doctor is a person who looks after people's health.
9) My new motorbike, which I paid a few thousand euros for, is not running well.
10) Where is the letter that arrived this morning?