Hi

I am assuming you from general category.

With 66 percentile

• Your crl rank will be  around  347820 - 391000 as  per our rank predictor at

  JEE Main Rank Predictor 2021 - Predict your JEE Main ...

  JEE Main Rank Predictor - Know your expected IIT JEE Main 2021 Rank by ...

With this rank, your chances of getting a seat in NIT, IIITs is very low.  Even to get into lower NITs under other state you should have got at least around 45000 - 50,000 rank i. e 95.5 - 96 percentile.

Some of the   engineering colleges in which you hold a good chance are listed below along with their previous year cut off percentile :-

----------)Budge Budge Institute of Technology, Kolkata :- civil engineering :- 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

----------)Imperial College of Engineering and Research, Pune :- mechanical engineering b https://www.careers360.com/colleges/imperial-college-of-engineering-and-research-pune/cut-off?college_id=4117&exam_sub_exam_id=2&ici=college_view_cutoffs

----------)Bengal College of Engineering and Technology, Durgapur :- electrical engineering https://www.careers360.com/colleges/bengal-college-of-engineering-and-technology-durgapur/cut-off?college_id=4831&exam_sub_exam_id=2&ici=college_view_cutoffs

To have  a personalised and complete list of colleges which you can get on the basis of the category you belong to,  your home state, your gender etc we have jee main college predictor  for which link is provided below

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

To help you further,

To give you an idea of qualifying cut off, JEE mains 2020  qualifying  CUT OFF percentile to be eligible for jee advanced is given below for different category

>>>> General :-     90.3765335

>>>> GEN-EWS :-  70.2435518

>>>> OBC-NCL :-  72.8887969

>>>> SC     :-           50.1760245

>>>> ST :-                39.0696101

>>>> PwD :-            0.0618524

You can check the same at our page the link is provided below

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

Thank you