Can a paper 1 and paper 2 qualified student of the JEE Mains participate in the counselling for both of those paper's ranks?

Hello,
JOSAA counseling is done for both JEE Mains paper 1 and paper 2 qualified students as well as students who qualified in JEE Advanced.

Since you have appeared for both paper 1 and paper 2 in JEE Mains, you can sit for the Counseling for both the papers in JEE Mains.

Please note that JEE Mains paper 1 is for engineering undergraduate courses and JEE Mains paper 2 is for architecture and planning bachelor's courses.
Through JOSAA counseling, you can get admission into government engineering colleges like NITs IIITs and GFTIs through paper 1 and into NITs, GFTIs and SPAs through paper 2.

Please visit this link for detailed information about JOSAA counseling for JEE Mains for paper 1 and paper 2.

Please visit this link to use the JEE Mains college predictor
Hope it helps