IIIT

You have a good chance of getting admission to some NITs, government engineering colleges, and IIITs, but likely not the top-ranked ones; you might need to consider lower-ranked NITs or other government colleges, depending on your branch preference and specific state cutoffs. Not enough for top NITs, but can consider lower NITs, which is local or regional NITs.

IIIT Trichy (Indian Institute of Information Technology Tiruchirappalli) has a big library, hostel, lab, and provides sports facilities to students. Indian Institute of Information Technology's library offers access to over a thousand books related to the academic and non-academic fields. The shopping centre near the campus has photocopy shops, stationery shops, food stalls, and others. 

With an OBC rank of 44,254 and a CRL rank of 133,700, you might have a shot at getting into some of the lower-ranked NITs or IIITs for a B.Tech program. Your chances are likely better for less competitive branches like Civil, Chemical, or Mechanical Engineering at these institutions.

Assuming You have a rank ~40k to ~55k, It is Not possible in general category if you are aiming for top NITs or IIITs . You may have  limited options with lower branches but  not CSE and definately not best nit's. It is possible to get into some good NITs and IIITs if you are from a  sc (scheduled caste) or st(scheduled tribe.

With 77.92 percentile in JEE Main and SC category, your SC rank would be around 12k–15k.
Chances are low for top branches like CSE in NITs/IIITs, but possible in lesser-known ones.
You may get lower branches (like Mechanical, Civil, or Production) in newer NITs.
Some IIITs with newer campuses may also be within reach.
Participate in JoSAA counseling and also consider state counseling options for better chances.