In the sentence below:
The teachers discussed Jim, one of whose problems was poor study habits.
was is used in the adjective clauses?
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The discussion took place in the past, so the issue being discussed is described in the past tense. It may be that Jim still has that problem, but that isn't relevant to the sentence as it stands.
I see from your heading that you mean 'why is were not used?' - that is because only one problem is mentioned.