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You had a chance to get admission in some of the good CFTIs but it's too late to apply for it now. You should try to inquired in some state universities and private colleges.

Based on the search results, it seems that there may not be any specific universities that will allow a Ph.D. after completing distance learning PGDM courses. However, it depends on the university's accreditation and recognition by regulatory bodies such as UGC, AICTE, or AIU. It's important to consider factors such as the credibility, reputation, and recognition of the PGDM course and the university when planning to pursue a Ph.D. Additionally, Ph.D. admission requirements may vary by university, so it's best to check with individual universities for their specific requirements and criteria.