Hello student

you didn't specify your domain so here's the list of both Medical and engineering government colleges in Karnataka

Medical-

Bangalore medical college

Karnataka institute of medical sciences Hubli

Mysore medical college

Vijayanagar institute of medical sciences Bellary

Belgaum institute of medical sciences

Mandya institute of medical sciences

Hassan institute of medical sciences

Shimoga institute of medical sciences

Bidar institute of medical sciences

Raichur institute of medical sciences

https://medicine.careers360.com/colleges/list-of-government-medical-colleges-in-karnataka

engineering colleges-

1. NIT Surathkal
2. IIIT Bangalore
3. RV college of engineering.(Autonomous).
4. PES university(Deemed university now) .
5. BMS College of engineering(Autonomous).
6. UVCE College(Government College).
7. JSS Mysore(Autonomous).
8. MS ramaiah University.(Deemed now)
9. SIR MV IT .(VTU affiliated).
10. Bangalore institute of technology(BIT) (VTU affiliated).

https://engineering.careers360.com/colleges/ranking/top-engineering-colleges-in-karnataka