Firstly, as per your rank and category the college cut-off of the student will be given. As you said that you have got 50% of marks in jee mains you have chances in getting in some popular colleges.

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

PH :- 0.0096375 percentile

According to your percentage you have chances to get in :

NIT Trichy- Tiruchirappalli, Tamil Nadu

National Institute of Technology - [NIT] - Rourkela, Orissa

National Institute of Technology - [NIT]  - Warangal, Telangana

Birla Institute of Technology - [BIT Mesra]  - Ranchi, Jharkhand

National Institute of Technology - [NIT] - Durgapur, West Bengal

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