Hello aspirant,

Yes, even if doing your undergraduate from a private college, be it CMC Vellore or any other, you can complete your Post graduation from a government college. It does not matter where you completed your undergraduate from. Once you obtain your UG degree, you will have to give the NEXT/INICET/DNB CET exam or any other exam you wish to, and get a good score and rank. During the counseling procedure, you can select the government colleges you wish to complete your PG from and if you have a good rank, you can certainly get into the respective college.

Hope it helps!