GST Liability under RCM for Transportation Services Provided to University - Goods and Services Tax - GST

We are a private university established through the State University Act by a sponsoring body. As per the Act, the university may be classified as a body corporate. At our university campus, we have arranged transportation services from a third-party supplier for the pickup and drop-off of staff and students between the campus and the city on a monthly fixed charge of Rs. 1 lakh (fuel charges borne by the university). We recently received an invoice from the supplier for passenger transportation services provided for the month of September 2024. We seek clarification on whether the GST is applicable under the Reverse Charge Mechanism (RCM) on this service as per Notification No. 13/2017-Central Tax (Rate) , which covers GST applicability on passenger transportation services. Kindly provide your expert opinion on whether we, as a university can be considered as a body corporate for GST purposes, and are liable to pay GST on a reverse charge basis for these transportation services. Also Supplier already has turnover more than 20 lakhs and not taken GST No