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You want to do PhD course after MBA in Distance Education so for PhD course candidate must have Master degree and MBA is master degree that’s why after MBA through distance learning you can do PhD in Management. Here is list of institutes in India offer PhD in Management:

1. Alliance University - Ph. D
2. Apeejay Institute of Management Technical Campus - Doctor of Philosophy in Management
3. Bhavnagar University - Doctor of Philosophy in Business Adminintration
4. Department of Pharmaceutical Education and Research - Doctor of Philosophy in Management
5. Dibrugarh University, Dibrugarh - Doctor Of Philosophy in Business Administration
6. Faculty of Management Studies, Banaras Hindu University (FMSBHU) - Doctoral Program in Management Studies
7. G.L.A. Institute of Business Management, Mathura - Doctorate Of Philosophy in Management
8. Gauhati University - Doctor of Philosophy in Business Administration
9. Goa University - Doctor of Philosophy in Business Adminstration
10. Guru Ghasidas Vishwavidyalaya - Post Doctorial In Business Administration
11. Himachal Pradesh University (HPU), Shimla - Doctor of Philosophy in Business Administration
12. Indian Institute of Business Management & Studies, Mumbai (IIBMS) - Professional Laureate in Management ( PLM)
13. Indian Institute of Business Management & Studies, Mumbai (IIBMS) - Professional Doctorate in Management (PDM)
14. Jain University - Doctor of Philosophy in Management
15. Jaipur National University (JNU) - Doctor of Philosophy in Management
16. KIIT School of Management - Bhubaneswar - Doctor Of Philosophy
17. Lal Bahadur Shastri Institute of Management & Development Studies - Lucknow - Doctoral Programme In Management (PhD)
18. Loyola Institute of Business Administration - Ph.D. Degree in Business Administration
19. Maharishi Markandeshwar Institute of Management - Mullana - Post Doctoral In Business Administration
20. Mohanlal Sukhadia University (MLSU), Udaipur - Doctor Of Philosophy In Business Administration
21. National Institute of Management (NIM), Mumbai - Professional Doctorate in Management Studies
22. Pondicherry University - Doctor Of Philosophy In Management
23. Pune University - Doctor of Philosophy In Management
24. Rizvi Institute of Management Studies & Research - Doctorate of Philosophy in Management Studies
25. S.N.S College of Technology - Doctor of Philosophy in Business Administration

Hi Deepali,
There are no fixed official GMAT dates, you can choose any date according to your convenience and availability. The exam date that you choose should be at least two months before your first application deadline. This will give you plenty of time to work on your applications, and in case you need to retake the GMAT exam you can do so after 31 days.
Your target test date for taking the GMAT should be at least two months before your first application deadline. So if the deadline for your application is November, you should take the exam by September. If you feel the need to retake GMAT, you can take it in October again.
Their is no direct negative marking. If you leave the complete section unattempted then their is negative marking.
You can refer the link for more required information:
https://studyabroad.shiksha.com/gmat-important-dates-abroadexam321
Hope it helps. Please feel free to revert. Click on the thumbs up if you found this useful.
Wish You Luck!