Hii nikhil!

No, if you are applying for counselling as per the Karnataka eligibility then your category certificate must mention that you are an ordinary resident of Karnataka not Rajasthan. This will be contradictory since you are getting eligibility through Karnataka but as per category certificate you are resident of Rajasthan.

You can submit another central category certificate which will have Karnataka as your residential place. You can ask the issuing authority to speed up the procedure. In the worst case if you were not able to get category certificate within the deadline you can apply through general category.

Hope it worked for you!