Hi

I am assuming you from general category.

With 63.60 percentile/ nta score

• Your crl rank will be  around  372372 - 418600 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 government colleges like 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. You have try for state government colleges.

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

----------)MH Saboo Siddik College of Engineering, Mumbai :- https://www.careers360.com/colleges/mh-saboo-siddik-college-of-engineering-mumbai/cut-off?college_id=4990&exam_sub_exam_id=2&ici=college_view_cutoffs

---------) 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

----------)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

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