Dear Navneet, 

Yes you can apply for NITs if you want. 

You can participate in JOSAA Counselling though you are not qualified for JEE Advanced. 

You can check your colleges on Careers 360 College Predictor 

https://engineering.careers360.com/jee-main-college-predictor

Hello Naveen,

To be honest with you, with this rank you can't get any seat in any of the nits. Even home state quota etc also won't work.

But don't get disappointed. You might have given other entrance test also so you can try something from there. If you have given VIT , MIT, UPSEE , comedk, SRM etc .

I am attaching a link with this answer , u can check the chances and choices available to u for different colleges. Careers360 is very accurate in this domain, even I have tried the same during my counselling days. There are lot of good private colleges try out there.

Hoping the best for you. Let me know if u have any query just comment me I will answer soon.

https://engineering.careers360.com/jee-main-college-predictor