Hello student,
You have not mentioned which category you belong to. With a score of 421,it becomes difficult to secure a seat in the government medical colleges when comparing the results of previous years. Usually Tamilnadu has a highest cut off range. Last year,  a score of 593 was required to secure a seat in Rajah Muthaiah medical college, Annamalai nagar in General category under the state quota. But scores and ranks vary each year with toughness of the exam 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

Yes, chances are likely to get a govt college, but based on the results.. he may get pudukottai, thiruvarur, thiruvannamalai, sivagangai

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