Hello there , hope you are doing well . As per your query ,I'll provide you the list of government medical Colleges in Karnataka along with the closing AIRs through All India Quota Counselling in Round 2 below .Please note that the closing AIRs are with respect to general category.

1. Bangalore Medical College, Bangalore - 1,566
2. Belgaum Inst. of Medical Sciences,Belgaum- 10,954
3. Bidar Inst. of Medical Sciences,Bidar- 12,755
4. C. Inst. of Medical Sciences,Chamarajanagar- 12,446
5. ESI-MC & PGIMS&R, Bangalore- 8,565
6. Bowring Lady Curzon Medical College and Research Institute, Bangalore- 9,020
7. ESI MC,Gulbarga- 12,149
8. Gulbarga Institute of Medical Sciences,Gulbarga- 12,883
9. Gadag Inst. of Medical Sciences,Gadag- 13,424
10. Hassan Inst. of Medical Sciences,Hassan- 10,502
11. Karnataka Inst. of Medical Sciences,Hubli- 9,394
12. Karwar Inst. of Medical Sciences,Karwar- 12,762
13. Kodagu Inst. of Medical Sciences,Kodagu- 10,844
14. Koppal Institute of Medical Sciences,Koppal- 13,537
15. Mysore Medical College & Research Institute,Mysore- 4,987
16. Mandya Inst. of Medical Sciences,Mandya- 9,505
17. Raichur Inst. of Medical Sciences,Raichur- 13,302
18. Shimoga Inst. of Medical Sciences,Shimoga- 11,414

19.Vijaynagar Inst. of Medical Sciences,Bellary- 11,915

From the above list you can see that the closing AIR for a government medical college in Karnataka through All India Quota Counselling was 13,537.

Hope my answer helped.