I have qualified jee mains and 87.8% in boards. Is there any formalities before counselling to take admission in any nit

Yes. Before counselling you have to register with JoSAA. JoSAA is Joint Seat Allocation Authority. The procedure starts by second week of June. While registering you have to give the contact details. Then you have to fill the choices you are interested in. You can choose options based on your preference. While mock allotment come, you will get to know about the colleges you may get. And after two rounds of mock allotment you will have real allotment. Allotment is based on the rank list which you can predict based on the previous year cut-off.

You can refer https://engineering.careers360.com/articles/josaa  for more details.

Hello,

After counselling you are required to lock the seat in the institute. JoSAA is the authority that admits candidates, so may partially lock and go for higher options or freeze the option/course that you got. There is verification of documents during counselling. After such procedures are over, you should reach college with required documents on said date.