National Institute of Technology, NIT H

https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7476690
Check out this link.
Hope this helps.
Best of Luck!

https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7476690
Kindly visit this link.

See, NIT is a better option than any other normal college but on the other side, ECE is a bit tough. Also, its not just your level of interest to opt for your B.Tech, post that you should be in a position.
To get placed quickly, it depends on based on your college reputation and campus selection. Mainly, your option will be based on your career plan post B.Tech.

Hello Nikhil,
Your rank is far beyond to get any of your desired branch at NIT, Hamirpur, however, check here to know more: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.
All the best.

You will not get this college because your rank is very low. You can get government colleges with this rank. Try JEE college predictor to get more information and insight about college & branch which you can get on the basis of your rank:-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=4067795.

Yes, you can take admission.

Depends on what college you want admission into. You can get into a lot of NITs with that rank, mainly you will be able to get branches such as Mechanical, Electrical, Civil. Cut off for CSE and ECE is generally very low for NITs so chances you get those branches are low, but you can hope to get one of those branches in internal shuffling once you secure admission into a college.

As it is an NIT, getting admission would be quite difficult there as you don't have any quota except the home state one. I can not say for sure that you will be able to get admission into ECE. So, I would recommend that you apply for other branches or look into other colleges. You can also apply for IIIT Una which has the same faculty and campus as NIT Hamirpur and has the CSE, ECE and IT branches. With your rank, there is a chance that you can get admission into IT or ECE in IIIT Una.