Hello Aryan !!

Since you belong to Uttarakhand and I think that you don't have Karnataka state domicile, you can get a private college in Karnataka through All India quota only.

The dates for registration in the second round has already passed, if you have not registered you can still go for mop up round.

But if you got seat in first or second round of counselling then you can not register yourself in mop round.

All the best.

Hope this helps.