No, you will not get CSE in NIT Trichy with a 10000 JEE main rank. But you will get to pursue CSE from NIT Jalandhar, NIT Hamirpur, etc. Your rank is quite good but it will not be enough to get admitted to NIT Trichy. However, you might get admitted to other branches in NIT Trichy such as Production, ICE, MME, etc. You can also prepare for JEE Advanced and try your luck with the IITs. Do not lose hope because NIT Tricbhy is not the only best institute in the country to pursue CSE. Also, CSE is not the only course that will lead you to a successful path. There are many other colleges and many other courses that are equally good. Research and take your time. You will surely do great. All the best!
I know I might sound blunt, but you cannot get into NIT Trichy CSE unless you belong to a reserved category. The expected opening and closing rank for the B.Tech CSE course at NIT Trichy for the academic session 2022 was around 400 to 5300. This year there might be only a slight difference. However, your rank of 10000 has no chance considering the cutoff.
Don’t get discouraged as here is the bright side. You might not get into NIT Trichy CSE but you surely might get into NIT Jalandhar, NIT Hamirpur which are quite good institutes if not as good as Trichy. In fact, NIT Jalandhar was ranked among the top 5 NITs in NIRF rankings (placement-wise).
You can't get NIT Trichy's CSE, but don't worry you can still get CSE at NIT Jalandhar, NIT Hamirpur, etc. Believe me, they are also good institutions. Talking about NITJ it was ranked among top 5 NITs in NIRF rankings placement-wise.
Another option is to apply at your home state institute. For instance, if you are from Delhi, go for DTU or NSIT. While the choice of Institute does matter, the majority depends on your own persistence.
The required cutoff for CSE in NIT Trichy was 714 (round 6, open category) for 2021. As per the recent cutoff trends, it will be difficult to get CSE in any of the top 10 NITs with a JEE Main rank of 10000. You may get CSE in NITs like NIT Jamshedpur, NIT Andra Pradesh, NIT Jaipur.
There is very little possibility of getting Computer Science at NIT Trichy with a rank of 10000. As there will be Reservation, state quota, and PwD reservations, so there is less possibility of getting Computer Science. You may get other branches with your rank.
Although a rank of 10000 in JEE Main will get Computer Science in other low ranked NITs but not NIT Trichy. The JEE Mains cutoff for the General category in Computer Science for All India was 1000-4358 in 2020, at NIT Trichy. With a rank of 10000, you will be getting branches like ICE, MME, Production, etc.
It’s better if you don’t bother about NIT and prepare well for the JEE Advance examination.