IIT

Based on the information you have given, you have fewer chances of getting admission into IIT. However, you can try getting admission into government colleges, NITs, IIITs, and private colleges that accept JEE scores. According to your rank, I am suggesting some colleges. The list of colleges is given below.
1-NIT Silchar-National Institute of Technology
2-IIIT Guwahati-Indian Institute of Information Technology, Assam
3-DTU-Delhi Technological University
4-NIT Calicut National Institute of Technology
5-NIT Trichy-National Institute of Technology
If you want more information regarding the college, course, or anything else, kindly visit the given link (https://www.shiksha.com/engineering/jee-main-college-predictor). .

I have completed 2 years in NIT Uttarakhand. So, I can give you a brief idea about life of an average student at National Institute of Technology Uttarakhand. You will get a tag of NITian and you can participate in inter NIT competitions (both Sports and Technical). The faculty is good but most of them are Assistant Professors. Currently, they don't have any Associate Professors or Professor, some recruitment have been made this year maybe some Associate Professors might join the Mechanical Department. Being a newly established NIT not much has been done yet in the field of Research and Development but students are doing quite well. "Kalam Lab" body specifically working on the development of innovative ideas into a reality. Govind Vajpayee student of NIT UK has recently won the Inter NIT innovation challenge. Placements are not as good as it should be. Considering lack of resources and remote location of college. We are doing quite well in Placements and graph is increasing every year. Major Core and IT companies visit us every year. If you are looking for a huge campus then my friend NIT UK is not for you because their temporary campus is in government. Poly. Srinagar and it ends before it starts. Still, they don't have the permanent land allotment.

If your category rank (OBC Rank) is 3032, then the IITs available to you are:-
1] IIT Dhanbad - Geophysics (5 Y)
2] IIT BHU - Bio (5 Y)
3] IIT Kharagpur - Applied Geology (5 Y)
Unless you need the IIT Tag to flaunt in front of your relatives and unless you have some specific interest in these fields or unless you are planning to work hard to get a vertical branch transfer, go for NITs on the basis of your Mains rank or go for a drop. If your Open Rank is 3032, then you have a lot to choose from: - (The best options in no specific order, according to me are chosen as there are 50 and more branches open)
1] IIT Delhi Chemical (Dual Degree)
2] IIT Bombay Civil Engineering
3] IIT Madras Aerospace
4] IIT BHU Electrical Engineering
5] IIT Jodhpur Artificial Intelligence
6] IIT Guwahati Mechanical
7] IIT Bombay Metallurgical
8] IIT Bhubaneswar CS (5 Y) CS from all the newest IITs
9] IIT Indore Electrical Engineering
10] IIT Delhi Production Engineering
But if I were you, I had pick IITM Aerospace
PS - Data based on JEE 2020.

First of all, congratulations on your results. The JEE Main Cutoff for 2022 was recently released, and usually this cutoff is of two types: the qualifying cutoff and the admission cutoff. The admission cutoff for JEE Main will be the opening and closing ranks for each government institute like NIT and will be released by JoSAA (joint seat allocation authority). Based on the information you have given, you have fewer chances of getting into NITs or IIITs. Depending on the course-based cut-off, you may be able to get into institutes such as NIT Agartala for specific branches. However, you can try getting admission into government colleges in your state that accept JEE scores. For instance, some colleges in Telangana, Karnataka, and Rajasthan accept JEE scores. You can also use the Shiksha platform's JEE Main College Predictor 2022 (https://www.shiksha.com/engineering/jee-main-college-predictor) to get more specific recommendations based on courses, fees, and rank. Here you need to enter your JEE rank or percentile, gender, category, and domicile to get recommendations of possible good colleges.