Ph.D

Yes,  PhD is available at Woxsen University. This programme is offered to students with a focus on research and academia. Moreover, this programme is offered in full-time and part-time modes. Candidates seeking admission can check the below table to know more about the programme:

Note: The above information is taken from official sources. However, it is subject to change.

I don't know about the placement scenarios for PhD from TIFR Bombay, but for IIT Kharagpur, pursuing PhD can be a very good choice, as IIT Kharagpur has Top Research facilities. if you want to do research, you will get the best resources of the country, and also many PhD students get placed during the Campus placement cycle, so there are various Job opportunities. And, a PhD from IIT KGP is flexible than any other institute.

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Yes, IIT Dhanbad (ISM) does accept the UGC NET scorecard for Ph.D. admission in Psychology. A valid UGC NET score, along with a Master's degree in Psychology (like yours from Patna University), is a requirement for eligibility. Essentially, a valid UGC NET score is a prerequisite for being considered for Ph.D. admission in Psychology at IIT Dhanbad. 

A doctorate degree in Automobile Engg. spans 3 to 6 years, depending on the research topic chosen by you, the institute's requirements, the amount of coursework to be completed, your research progress, and the supervisor's guidance.
If you want to get into research and development in the automobile sector and contribute something unique to the existing vehicle and engine designs, you can surely think of opting for a PhD degree, as it will be worth the time and money invested in the program.

No, PhD is not compulsory for the JK SET exam. However, PhD degree holders who did their Master's degree or post-graduation by September 19,  1991 get relaxation of 5% for appearing in JKSET exam. In this case, the date of declaration of Master's degree result is not applicable.