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Yes, you can apply for AIAPGET state counselling in Uttarakhand, subject to their eligibility rules.
Many states allow open candidates (other-state students) under management or All India quota seats.
You must check the Uttarakhand AYUSH counselling brochure for seat matrix, domicile rules, and registration details. This subject is offered in many private and government AYUSH colleges across India, including some in Uttarakhand. This subject is offered in many private and government AYUSH colleges across India, including some in Uttarakhand.