Hello aspirant,

Yes, you can take part in both government as well as deemed universities as they both come under All India Counselling. If you wish to apply for both, other than the application fee of INR 5000, you will have to pay INR 2,00,000 as a security fee and will be adjusted in your first-year fee if you get allotted a deemed college or refunded if not allotted any (only after the counseling is over)

Hope it helps!