It depends upon the JEE Main and JEE Advance cut offs, If You manage to qualify the exam by achieving the cut off, You can apply for JOSAA Counselling. It should be noted the cut off for EWS/SC/ST/FEMALES/OBC category is lower than the general category
However It is usually advised to fill the choices as per the preference of colleges and departments, for example CSE in NIT Trichy is your priority followed by CSE in NIT Warangal, you can fill CSE at NIT Trichy at serial number 1 and CSE at NIT Warangal at serial number 2 and so on and so forth. However to get any NIT, you must have qualified JEE Mains and to get any IIT, you must have qualifies JEE Advanced

But the previous cut offs of colleges should be taken in consideration, it is better to research over the cut off of colleges then make a preference list of colleges and fill accordingly

For the college preferences and the courses provided by these colleges and to know which colleges participate in the JOSAA counselling, please go to the below mentioned link: https://engineering.careers360.com/articles/josaa-participating-institutes/amp

For college prediction as per your marks and rank, please go through the below mentioned link:

Hello Tanmay. You mentioned you are a general candidate and you are interested to know whether you can get admission to Computer Science and Engineering at any government college. Well, based on previous years' data and your performance in JEE Main 2021, it is difficult for you to get admission to CSE at most of the top-rated government colleges in India apart from NITs or IIITs. However, there is slight possibility for you to get chance at Shivpuri Institute of Technology, Madhya Pradesh if only the seats are available till the last round or they conduct any mop-up rounds.

In 2020, JEE Main Cutoff Rank prescribed for admission to CSE for General, Home State candidates was 7,41,869 (in Round 2 - Final Round).

To get a personalized report on your eligibility of getting a college, you can use the JEE Main 2021 College Predictor , it will show you complete list of colleges which you can get on the basis of the category you belong to,  your home state, your gender etc, the link for JEE Main College 2021 Predictor is provided below

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

I hope this information is enough to help you out.

I wish you all the best for your future.

Thank you.