It's not based on first come first serve . It's purely on merit. Even the management seats are properly counselled for. In Rajasthan no college has fee structure less than 12 lakh. With your marks u'll get admission in private medical colleges but fees will be high. I am not talking about management seats. There fees are more. U can try for comedk, colleges in mp have low fees, karnataka also. 

Dear student

The fee for private colleges vary from college to college and from state to state, with 360 marks in neet, any private college in india won't provide a seat in no less that 10 lacs+ /year and for general category the chances are even low and it all depends on first come first get basis.
So you can talk to the college authorities about the fees and in anyway if the can help you.

Wish you good luck.

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