Due to less seats and high competition BCD non former quota, it is highly unlikely that you will secure a veterinary seat in the last round of counselling, even considering the possibility of a few seats opening up in the last round; your rank is likely too high for most veterinary colleges in this category.

Usually upto rank 3k most of the students get seat in veterinary colleges.however you should participate in counselling process till the last round you might get the seat.