The first Open University in India was set up in the State of

Concept

An open university is a degree-granting institution created specifically for open and distance learning — admission without the usual formal entry qualification, study at the learner’s own pace, and self-instructional course material. Such a university comes into existence only through its own founding statute: either an Act of a State legislature (a State Open University) or an Act of Parliament (a national open university). "First", therefore, is settled by the date of that founding statute, not by an institution’s later size, reach or fame.

Application

Applying that test to the states named in this item, the earliest founding statute for an open university in India was passed by the Andhra Pradesh legislature, which created the Andhra Pradesh Open University at Hyderabad in 1982. It was renamed Dr. B. R. Ambedkar Open University in 1991. So the state in which India’s first open university was set up is Andhra Pradesh.

Cross-check and contrast

Placing the other states’ institutions on the same timeline confirms the ordering:

IGNOU is the first national open university and is the usual source of confusion here, but its founding statute followed the Andhra Pradesh one by three years.

Hence India’s first open university was set up in Andhra Pradesh.