Hi

Assuming you from general category

With 60 percentile

• Your crl rank will be  around 409200 - 460000  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 or government colleges is extremely low. Even to get into lower NITs 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 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

And a few more

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 improve your score in your remaining attempts of JEE main you should focus on your preparation go through previous year question papers ,mock test papers and to help you in your preparation we have jee main knockout out for you, for which  is provided below

https://learn.careers360.com/knockout-jee-main

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