Hello Sadhana, in Karnataka as per the last year cut off students with more than 300 marks were got seat in following colleges. So for ST category below are some colleges where you can get seat.

Mandya Institute of Medical Sciences, Mandya

Hassan Institute of Medical Sciences, Hassan

Karnataka Institute of Medical Sciences, Hubli

Belgaum Institute of Medical Sciences, Belgaum

Bidar Institute of Medical Sciences, Bidar

Vijayanagar Institute of Medical Sciences, Bellary

Raichur Institute of Medical Sciences, Raichur

These are some colleges. There are also other colleges  for you. 

I hope it will help.

Thanks.

Hello student,
With a score of 360 in the SC category, you can secure a seat in the government medical colleges of Karnataka when comparing the results of previous years. Last year, a score of 283 was enough to fetch a seat in Raichur medical college, Raichur in SC category under the state quota. But scores and ranks vary each year with difficulty level of the question paper and availability of seats. However you can predict the colleges which you are likely to get using the given link
http://medicine.careers360.com/neet-college-predictor
Good luck

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