As you have asked about the eligibility criteria for PhD in Indian Institute of Technology (IIT) Bombay, I am giving you information about it, check below for the details

The academic programme leading to the Ph.D. degree is broadbased and involves a course credit requirement and a research project leading to thesis submission.

The Institute undertakes sponsored research and development projects from industrial and other organizations in public as well as private sector.

ELIGIBILITY CRITERION FOR PH.D ADMISSION

Master’s Degree in Engineering/Technology or equivalent degree, with First class or 60% marks (55% marks for SC/ST)
Bachelor’s degree in Engineering/Technology with First class or 60% marks
Master’s degree in Science or equivalent degree, with First class or 60% marks
Master's degree in Arts/Commerce or equivalent degree with a minimum of 55% marks (50% for SC/ST),
Candidate having an IIT B.Tech Degree and having a minimum CGPA/CPI of 8.00 (on 10.0 scale) and above are exempted from requirement of valid GATE score.

Ph.D. degrees are available in the departments of

Aerospace Engineering,
Biosciences and Bioengineering,
Chemical Engineering,
Chemistry,
Civil Engineering,
Computer Science and Engineering,
Earth Sciences,
Electrical Engineering,
Energy Science & Engineering,
Humanities and Social Sciences,
Mathematics,
Mechanical Engineering,
Metallurgical Engineering and Materials Science,
Physics,
Industrial Design Centre,
Centre for Environmental Science & Engineering,
Centre of Studies in Resources Engineering,
Centre for Research in Nanotechnology & Science
Centre for Technology Alternatives for Rural Areas
Centre for Urban Science Engineering,
Interdisciplinary Groups in Climate Studies,
Educational Technology,
Industrial Engineering & Operations Research and Systems & Control Engineering and in Shailesh J Mehta School of Management