IIT Mumbai is a sort of public institute. It was recognized in 1958. It is placed in Powai, Mumbai, Maharashtra, India.

Departments offering Post graduate Admissions:
Aerospace Engineering
Biosciences & Bioengineering
Chemical Engineering
Civil Engineering
Computer Science & Engineering
Earth Sciences
Electrical Engineering
Mechanical Engineering
Metallurgical Engineering & Materials Science (MM)
Cross Departmental Programme- Materials, Manufacturing and Modeling (MMM)
Center of Studies in Resources Engineering
Energy Science & Engineering
Industrial Engineering & Operations Research
Systems & Control Engineering
Environmental Science & Engineering
Centre For Technology Alternatives For Rural Areas(CTARA) (Technology And Development)

As you have asked about the cut offs of OBC in GATE for M. Tech Admissions in IITB here I am giving you cut off for various departments

Cut off for OBC’s in GATE:
Electrical Engineering Department: 459
Computer science and Engineering Department: 675
Civil Engineering: 495/450
Aerospace Engineering: 342/441/486/540
Chemical Engineering: 540
Mechanical Engineering: 540