As far as IIIT Hyderabad is concerned, it has no Mechanical Department as such. The institute specializes in technologies like AI, Computer and Electronics Technology, Robotics and Automation.

NIT Jamshedpur, is perhaps one of the best institutes in Eastern India for Mechanical Engineering, next to IIT Kharagpur and IIEST Shibpur. The institute has good infrastructure, faculty and employer outlook. Unless you are from Home State, you need a Rank of about 20k (GEN), to confirm your seat at NIT JSR Mechanical. For Home State Aspirants, a rank of atleast 30k is desired for confirming your seat at NIT JSR Mechanical. For more information regarding cutoff do follow the link below

https://engineering.careers360.com/articles/jee-main-cutoff-for-nit-jamshedpur/amp