Should I use HIS or THEIR in the sentence:
Which of the students of your group does __________ homework together?
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Sign up to join this community"Their" because the subject is "which". "Which" can be either singular or plural, but in this case it is definitely to be understood as plural because of the word "together". Doing homework together certainly implies more than one participant.
The verb in the sentence should also be plural, "do". So the correct sentence should be:
Which of the students of your group do their homework together?
Their. Because it is about "the students". It is from meaning of this sentence.
From other hand, if you put "his" in this place in sentence, this would be depend on more wide context. But for this sentence, without anything else - more logical choice is "their".