Hello student,
Yes, With a score of 508 you can definitely get a seat in the government medical colleges when comparing the results of previous years. Last year, a score of 433 was enough to fetch a seat in the government medical college, Dungarpur and a score of 432 got a seat in Government medical college, Pali in St category under the state quota. So no worries! But one thing to keep in mind is that scores and ranks vary each year with difficulty level of the question paper and availability of seats. However you can predict the colleges which you are likely to get using the given link
http://medicine.careers360.com/neet-college-predictor
Good luck

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