The first Inter-University Centre established by the UGC in 1984 is the

The first inter-university centre set up in 1984 was the accelerator centre once called the Nuclear Science Centre.

Treating the Nuclear Science Centre as its present name overlooks that this title was its earlier designation.

The centre for astronomy and astrophysics was established later, not first.

Since the centre is identified, 'none of the above' does not apply.

It provides advanced accelerator facilities shared across universities.

It was renamed the Inter-University Accelerator Centre in 2005.