Hi Arijit,

40K is a pretty good rank.As per last few years ranks ranks within 50K might get into NIT's as well. So coming to your question you can easily get into a very good private college with 40K rank. Counseling in private colleges with JEE Mains rank is done a bit late because they give preference to the ones applying through their individual tests. But don't worry you might get a good private college with your choice of branch.

Let's hope for the best.