Hey, there are entrance exam centers in Kerala and Tamilnadu for Hyderabad University.

In Kerela -

• Department of Polymer Science & Rubber Technology, Cochin University of Science and Technology, Kochi – 682022 – Kerala
• The Zamorin’s Guruvayurappan College, Kozhikode, P.O. GA College, Calicut 673014

In Tamil Nadu -

• Kendriya Vidyalaya Annanagar, G.P.R.A. Campus, Thirumangalam, Chennai – 600 040
• Kendriya Vidyalaya, Meena Estate, Sowripalayam Coimbatore – 641 028
• SRR Govt. Arts & Science College Karimnagar, Jagtial Road, Karimnagar

For Osmania University, the exam center is only in and around Telangana State.

Check our link for more info

https://university.careers360.com/articles/oucet-exam-centres

i hope this helped.

Best wishes