AIIMS Patna was founded and started it's academic schedule in 2012. It's a fairly new institution, currently mentored by AIIMS New Delhi. Being an AIIMS, it will definitely be one of the top institutes within the coming 5-6 years.
It usually takes a medical college 5-6 years, that is, until the first batch passes out to gain a strong foothold.
KMC Manipal, on the contrary has been a top private college(the second best private institution in the nation, only behind CMC Vellore). It costs a lot more to study at KMC. However, currently, it is better to go for Kasturba Medical College, Manipal if money is not a problem
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