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:

Rest for information on any particular college, you can dig their official site for better information

NTA Scores are given in percentile.
Percentile is calculated by the ratio of the number of values to the total number of values . You cant say/depict your actual score/rank from your percentile neither can you calculate it by only marks. To calculate the actual score/rank/percentile you would need to know the number of students who appeared in the examination and the highest score, average cut offs and the highest score. while as marks are calculated based on the right questions you have attempted, out of the total marks you have obtained for the right number of questions marks from wrong questions marked are deducted from the total.

NTA announces the result of JEE Main/Advance in the form of a percentile score in every attempt or exam of JEE Main/Advance. The All India Rank (AIR) of candidates in JEE Main is calculated by taking the best score out of four attempts and are provided after the result of fourth exam. Candidates are able to check the detailed marks vs ranks of JEE Main/Advance after the conclusion of the exam.

Two types of ranks are given at the end:

1. AIR: All India Rank
2. CR: Category Rank

AIR is the overall rank obtained by the candidate respective of their category and CR is the rank candidates got in their respective category (General/EWS/SC/ST).

Hello Aspirant,

According to the category and marks you have mentioned your rank is expected to be in the range of 6706 - 5240, you can check out marks Vs ranks Vs Percentile from the link given below :-

https://engineering.careers360.com/articles/jee-main-marks-vs-percentile

Or

You can also use JEE-Main Rank Predictor to predict your rank :-

So on such rank and category you have good chances to get the enlisted NITs :-

NIT Warangal

NIT Surathakal

NIT Jaipur

NIT Allahabad

And may more NITs as well as IIITs. You can check out previous year's cut-offs from the official website of JOSAA as given below :-

https://josaa.nic.in/Result/Result/currentorcr.aspx

Note that the above prediction is made on the basis of latest cut-offs available on official website of JOSAA or CSAB and the cut-offs are bound to change every year depending upon various factors such as the number of candidates appearing in an examination, the number of candidates qualifying an examination, difficulty level of the paper, and so on.

So you can use JEE-Main College Predictor to predict your chances of admission in different engineering colleges of India on the basis of your JEE-Main 2021 result :-

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

You can also check out the JEE-Main 2021 qualifying cut-off (expected) for JEE-Advance 2021 from the link given below :-

https://engineering.careers360.com/articles/jee-main-cutoff

I hope this information helps you.

Good Luck!!