Decide whether or not the relative pronoun can be omitted in the following sentences

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Ex 7. Decide whether or not the relative pronoun can be omitted in the following sentences.
1) This was the hotel that we stayed in for two weeks.
2) She showed me the emeral ds which shqhad brought back from South Africa.
8) A doctor is a person who looks af ter pe ople'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 m orning?