Hello Bheeshma,

If you are mentioning 20k as your all india rann, then it's a good score. You do not need to apply for management quota because you can get a free seat though conveyor quota may be under non local category. But if you are assuming your state wise rank as 20k , then definitely you have to try for management quota. You can check the below article for cut off details of various colleges and categories in karnataka

https://www.google.com/url?sa=t&source=web&rct=j&url=https://medicine.careers360.com/articles/neet-cutoff-karnataka/amp&ved=2ahUKEwiAjNLH9aPsAhVU7HMBHR_hDqoQFjADegQIARAB&usg=AOvVaw2U6_E3o02t4YOQdt068Ave&ampcf=1

You can use college predictor tool attached below to predict your possible college which helps you get an idea about which colleges to fill during web options

https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer

Hope you found this helpful.

All the best!

Cheese:)