Hello dear student, 

As you have asked for the cut off rank so far for the Aiims for OBC category. So last rank at which seats where filled in first round counselling in aiims was 2016 while expected cut off of second round counselling is 2567 . I am also sharing a link with you kindly check it. May be that will be helpful to you 

https://www.google.com/amp/s/medicine.careers360.com/articles/aiims-mbbs-counselling/amp

I hope this was helpful to you