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
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 off 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

Hello,

As per cutoff trends, you rank is very high to get a seat in JoSSA counselling, i will suggest you to go for other private colleges as there are many reputed ones in India. You can also use the college predictor tool to know about all possible colleges you might get with this rank.

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