Hello,
The admission to undergraduate medical courses through NEET to various private and government medical colleges throughout India has begun in most of the states.
So follow the official site of your state's medical counselling authority for online forms. If note yet released, they will be out in few days.
Yes, you can take part in both the counselking as per your wish.
The merit list will be released in third or fourth week of june and counselling process will follow up.

For more follow this link-
https://medicine.careers360.com/articles/neet-counselling/amp
Good luck

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