Which one of the following was the first to be declared as a Central University?

The correct answer is (d), University of Allahabad. It was established in 1887

as Muir Central College, and was declared a central university in 1921. The other options are:

(a) Aligarh Muslim University, Aligarh: Established in 1875 as Mohammedan Anglo-Oriental College, it was declared a central university

in 1920.
(b) Dr. Bhimrao Ambedkar University, Lucknow: Established in 1920 as the University of Lucknow, it was renamed in 1995 after Dr. Bhimrao Ambedkar, the chief architect of the Indian Constitution.
(c) Banaras Hindu University, Varanasi: Established in 1916, it is one of the oldest and most prestigious universities in India. It is not a central university, but a state university.