U.P.’s first Open University is located in

Agra
Allahabad
Gorakhpur
Jhansi

The correct answer is (b) Allahabad.

The Dr. APJ Abdul Kalam Technical University (AKTU), formerly known as Uttar Pradesh Technical University (UPTU), is a public state university located in Allahabad, Uttar Pradesh, India. It was established in 1998 by the Government of Uttar Pradesh. AKTU is the largest technical university in India in terms of student enrollment. It offers undergraduate, postgraduate, and doctoral programs in engineering, technology, management, and computer science.

The other options are incorrect because:

(a) Agra is a city in the northern Indian state of Uttar Pradesh. It is the administrative headquarters of Agra district and Agra division. Agra is a major tourist destination because of its many historical monuments, including the Taj Mahal.
(c) Gorakhpur is a city in the eastern Indian state of Uttar Pradesh. It is the administrative headquarters of Gorakhpur district and Gorakhpur division. Gorakhpur is a major religious and educational center.
(d) Jhansi is a city in the northern Indian state of Uttar Pradesh. It is the administrative headquarters of Jhansi district and Jhansi division. Jhansi is a major tourist destination because of its many historical monuments, including the Jhansi Fort.