Hello student,
You have not mentioned which state you belong to. With a score of 420, it becomes difficult to procure a seat in the government medical colleges when comparing the results of previous years. But it mainly depends on the state you choose. For example, With this score you may get a seat in the government medical colleges of Uttar Pradesh while it is not so in the case of states like Tamilnadu and Rajasthan. Also,  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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