Under the administration of which- one of the following is the Department of Atomic Energy ?

The Department of Atomic Energy (DAE) is administered under the direct charge of the Prime Minister. The DAE website states it was set up under the direct charge of the Prime Minister by a Presidential Order dated 3 August 1954, designating that atomic energy-related business of the Government of India be transacted in the DAE [1]. The Atomic Energy Commission, created with full executive and financial powers, formulates DAE policy and the Department carries out both power and non-power atomic energy programmes, confirming its unique status outside regular ministerial control and under Prime Ministerial oversight rather than the Cabinet Secretariat, Ministry of Power, or Ministry of Science and Technology [2].

Sources

1. [1] https://dae.gov.in/
2. [2] https://dae.gov.in/about-dae/