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dear candidate,
since i dont know your state so i cannot say anything about getting a medical seat via state quota but with a score of 580 and most importantly with a rank of 13021 it is bit difficult since the cut off rank for previous year general category at most was around 10,000 (odisha) so you may have a chance via state quota but slim chance via all india quota. i am adding the link for all india quota cut off of previous year. you have a fair chance to secure a dental college. previous year one college of mainpur had cut off of 17,000.
https://medicine.careers360.com/articles/neet-cut-off-for-government-colleges?utm_source=newsletter&utm_medium=neet-ug-email&utm_campaign=medicine
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Hello candidate !!
With cut off increasing this year , and a score of 580 , you have decent chances of getting a college through AIQ in the second round . Just chose the colleges accordingly where you think you can get a seat .
State quota will be better because the cut off is less than that of AIQ, and you can get almost any college except KGMC.
Here is a link with list of colleges and their cut off in 2018-
https://medicine.careers360.com/articles/neet-cutoff-up
All the best.
Hope this helps.
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