Definitely there is unreserved or general category seats in Tamilnadu State PG as well but it will depend on the neet PG 2019 ranking  which will determine the 50% all India quota on 50% state quota notwithstanding the fact that the 50% state quota seats will have many sub reservation is not only in SC, ST and OBC but also service kotah candidates and pH candidates

answering your question yes there is unreserved general category seats in Tamilnadu State neet PG counselling also but they will be much fewer than the reserve seats available for the Tamilnadu seats available 50% all India quota seats show the all India counselling

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