Hey there, 

As per your query I would like to tell you that according to your rank and based upon the previous year cuttoff marks for getting admission in private medical college. you are eligible for getting admission in private medical colleges at karnataka. 

Domicile isn't required for getting admission private medical colleges, it's only required for getting admission in government medical colleges under through state qouta. 

HOPEFULLY it's will usefull to you. 

GOOD LUCK. 

Dear aspirant, yes you can apply for admission in Karnataka's private colleges even if you don't have a domicile certificate. But being a general category candidate bring in lots of competition and add upon no. Of struggles along. Your admission depends on no. Of factors like which college you apply for, their official cut off, no. Of candidates applying for the same.
All the best,
Thank you.