Hello aspirant,

With a 10500 rank holder and hailing from BC-E category, the chances for getting a free seat in veterinary science seem to be less as the cutoff rank in veterinary science for BC-E category candidates from last year AP EAMCET results ranged from 5579 to 10841. Well, this is an assumption based on the previous year results and your rank. So, don't need to get worried. The cutoff list differs from year to year and changes according to the situation. Also, you may also try your luck in the private institutes offering veterinary science programs. I'm providing you the link given below. You can check your chances of getting a seat in the branch of your choice.

www.careers360.com/ap-eamcet-college-predictor

Hope, this answer helps you. Good Luck!