Based on this score NEET 2018 the chances seems to be less to get a seat under All India Quota seats but the chances are decent to get a seat under state quota seats. You can also use NEET UG college predictor tool to know your chances.

https://medicine.careers360.com/neet-ug-college-predictor?icn=neet-clgpd&ici=qna-answer

Good Luck!

Greetings!

According to the cut off of last year, the last closing rank was 10,978 with the score of 550. If the same pattern is to be believed for this year too, then there are very few chances of getting a government college in UP. 

Hope this helps. All the best!

Thanks for the question. 

Since the candidates have increased from the previous years, hence the competition has become stiffer. 

Your relative can get private medical colleges only with this rank.