Hello Narayana,

Since you have achieved 57 marks in the gate examinations, you have a chance to get admission in the IIT's or the NIT's.
but as u mentioned in OBC category, you still might get a chance.

Also, want to tell you that what course or subject you wish to study also plays a vital role,

and for further details, you can even visit our website, where there is a detailed description of all the major courses offered by the IIT's and which one would be the best for you.

https://engineering.careers360.com/iit-mtech-admissions

few of IIT colleges for mechanical engineering

IIT Madras
IIT Bombay
Indian Institute of Technology Delhi
IIT Kharagpur
Indian Institute of Technology Kanpur
Indian Institute of Technology Roorkee
Indian Institute of Technology Guwahati
NIT (National Institute of Technology) Trichy