You can get admission in NIT Patna in mechanical branch if you rank between 15989-20697
You can get admission in NIT Jamshedpur in mechanical branch if you rank between 13020-14011

You can also refer to below links:
engineering.careers360.com/articles/jee-main-cutoff-for-nit-jamshedpur
engineering.careers360.com/articles/jee-main-cutoff-for-nit-patna


Hope this helps you..