Hello

Your profile suggests that your home state is Bihar

With 77k rank,

You have extremely low chance in any NITs .

For example,

When we go through previous year trend then ,

- -------------) Under your homestate

Under Bihar home state quota, In the 6th round of josaa counselling 2020 , 6835 ews rank was   the closing rank/last rank for ews category in NIT Patna  and it was for civil engineering

- --------------) Under other state

Under other state quota , closing rank for some of the nits for which closing rank goes low are listed below along with their closing rank in the 6th round of josaa counselling 2020   :-

---------) NIT Nagaland :- Electronics and Instrumentation Engineering  :- 8007 EWS rank

---------) NIT Raipur :- biotechnology :- 8096 ews rank

---------) National Institute of Technology Agartala:- production engineering :- 8629 ews rank

You can verify the above at

https://josaa.nic.in/Result/Result/currentorcr.aspx

So, to get a seat in NIT you should get at least around 8000 ews rank

But yes,

Some of the  engineering colleges in which you hold a chance on the basis of past year closing rank are listed below along with the link for their previous year cutoff :-

---------) Techno Engineering College, Banipur:- https://www.careers360.com/colleges/techno-engineering-college-banipur/cut-off?college_id=4247&exam_sub_exam_id=2&ici=college_view_cutoffs

----------)Shri Ram College of Engineering and Management, Palwal :- https://www.careers360.com/colleges/shri-ram-college-of-engineering-and-management-palwal/cut-off?college_id=2281&exam_sub_exam_id=2&ici=college_view_cutoffs

----------)Budge Budge Institute of Technology, Kolkata :- https://www.careers360.com/colleges/budge-budge-institute-of-technology-kolkata/cut-off?college_id=4747&exam_sub_exam_id=2&ici=college_view_cutoffs

This prediction of colleges is  based of past year data but  cut off or closing rank changes every year depending upon many factors like the number of students that give the examination, difficulty level of the JEE main  for different shifts etc so

To have a personalised report on your chances of getting a college you can go through our college predictor, it will give you complete list of colleges which you can get on the basis of the category you belong to,  your home state, your gender etc, the link for  jee main college predictor is provided below

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

To help you  further,

Minimum percentile in jee main 2021 to qualify it to  be eligible for jee advanced 2021 is given below :-

--------) general :-87.8992241 percentile

--------) EWS:- 66.2214845 percentile

--------) OBC-NCL :- 68.0234447 percentile

--------) SC :- 46.8825338 percentile

--------) ST:- 34.6728999 percentile

--------) PWD :- 0.0096375 percentile

Thank you