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 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:

Hi ! No you can't get any nit with that rank. To get a nit you must rank within 50,000. Nit Agartala is a very good college and one of the good college in India. Still you can predict the college which you will get with your rank predictor of career360 whose link is given below. So hope you understand and best of luck to you.

https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/jee-main-college-predictor&ved=2ahUKEwjV9Ii3xNniAhX763MBHcG3BNEQFjABegQIAxAB&usg=AOvVaw1pTMu5LewXe0n3JPiA8V2U

Hey Aspirant.
See the rank u have secured in the JEE mains is not enough for u to bag a seat in the good colleges like NITs IIITs or GFTIs for pursuing ur higher studies in the field of ur interest under the btech courses as the cut off rank is about 50k. U should be going for private Institution like LPU , MANIPAL , KIIT , VIT , etc for ur btech career. I m providing u a link for ur help.
https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/articles/nits-cutoff-for-top-btech-branches/amp&ved=2ahUKEwjy4639hKLiAhUF6nMBHa0HBQMQFjAJegQIAhAB&usg=AOvVaw2OXl9cMS4B7GJ9DfTIJZCg&ampcf=1
Ask if any query. Good luck

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