Opening rank means the first student which get admission it that Branch and the closing rank means the last student get admission in that branch according to rank.in jee mains you get home state quota and other state quota.

https://engineering.careers360.com/articles/jee-main-cutoff-for-nit-calicut

Opening rank means the maximum score and closing rank means the minimum score which got admitted in the particular college.

You can check the NITs and IITs cut off below -

JEE Main Cutoff 2017

JEE Advanced Cutoff 2017

Hope this helps!!!