Greetings dear Ashokkumar

Firstly, I would like to know which exam and institute you are talking about. I'm writing this answer assuming that it's for VIT Chennai campus campus. When it comes to CSE branch, the cut-off is really high as the demand is so much. Cut-off trends change every year based on the number of students attempting the exam, number of available seats, difficulty level of the exam, etc. But when it comes to a rank around 6,000, CSE or CSE with any specialization seat in Chennai campus can be easily secured within 1st fee category itself. You can even try for VIT Vellore campus 1st or 2nd category seat as the cut-off for the same was 7000 in 2016.

https://engineering.careers360.com/articles/viteee-cutoff

You can have a look at the cut-off trends from the above link.

Hope it helps!!

All the best for your counselling process