Harshit, in 2019, a rank of 1176  secured a seat in Veterinary College under ST Category. We do not have HK Specific Cut offs. Considering the fact that there are only 5 Veterinary Colleges that participate in KCET Counselling, a seat in Veterinary science with a rank of 10,882 might be tad difficult. But again this is 2019 data and cut offs change every year. For example, in 2018, a General rank of 8997 secured a seat in B.V.Sc. Going by that, you might have a chance with ST-HK Quota. We would suggest you to wait atleast until the Extended round.