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For last year, the closing rank for MBBS - Bachelor of Medicine and Bachelor of Surgery was 6483 which is very close to this range. This was for general category under All India quota. Unless the candidate belongs to some other category or domicile, one cannot afford to score less than this. With this rank, there is a probability of getting admission however since, the cut offs keep changing year on year, it is advisable to try to score better ranks to increase your chances of getting admission in Bangalore Medical College and Research Institute.