Sir.i have got 3782 rank in aiims and l am belong to OBC(NCL) category.and my category rank is 1026.
Yes you have fair enough chances of getting any of the aiims institution based upon your category and ranking.
Go through the below link for information regarding various aiims cutoff
AIIMS MBBS Cutoff 2018, 2017, 2016 GEN, SC, ST, OBC, PwD - ...
https://www.google.co.in/amp/s/medicine.careers360.com/articles/aiims-mbbs-cut-off%3famp
Goodluck I hope this information helps you
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