As you have asked about the Phd programme offered by Shailesh J Mehta School of Management (SJSOM) at IIT Bombay, I am giving you information about it, check below for the details

The School offers a programme leading to the PhD degree in all areas of management.
Admission to this program is open to individuals from a range of academic disciplines, including
Engineering,
Natural science,
Humanities and
The social sciences

IIT Bombay accepts applications for Ph.D. Programme round the year.
However, they are processed twice a year (i.e. Autumn Semester (July session) and Spring Semester (January session)

After applying for the program, shortlisted applicants will be called for a written test followed by an interview.
The written test is based on aptitude test.

Candidates applying to SJMSOM are required to submit a sample of their recently published writings on relevant topics

OR

A 1500 word proposal on proposed area of research
The proposal should contain
1. Title
2. Keywords
3. Problem Identification
4. Review of Literature
5. Proposed methodology

Contact:
Shailesh J. Mehta School of Management,
IIT Bombay, Powai,
Mumbai 400076
Office - +91 22 2576 7781
Fax - +91 22 25722872 / +91 22 25723480