Ph.D

You can pursue Ph.D in computer. However, doing it through distance mode is very tough as compared to part time mode.

Ideally, if you are interested in doing PhD, you must complete it along with your post graduation studies. Once you are in job motivation to do PhD will be difficult. However, Answer to your question can be better answered by any expert if you share your educational and professional career details.

Part-time PhD is available in many universities but not by distance mode.

Hello Rajesh,
A doctoral degree is typically required to work as a full-time, tenure-track university professor. You should be prepared to earn an undergraduate degree in your chosen subject area, go to graduate school, complete a Ph.D. programme, conduct independent research, and write and publish articles in scholarly journals.
As you keep on earning more experience in the field, you will become eligible to be a professor in IIIT. Check the careers section on the IIIT website for the minimum eligibility criteria to be a professor.
I hope this answers your question. If you have any further questions, kindly revert.

The following article clearly defines the difference between MBA and Ph.D and its advantages and disadvantages:
https://www.shiksha.com/mba/articles/what-is-better-phd-in-management-or-mba-blogId-5230

You may refer to following link for PhD admission at Manipal University https://manipal.edu/mu/academics/phd/admissions-to-phd-program.html
MIT is a under Manipal University.

M.Phil is offered by most of the universities in India, you need to clear the entrance test conducted by universities or NET in life sciences to get admission into M.Phil.

Yes, you can. Also, appear for GATE exam once again.