In 1949, the Gopalaswami Ayyangar Committee while recommending a restructuring of the Central Secretariat, suggested that a Department should be identified with a Secretary’s charge and a Ministry should be identified with a Minister’s charge.​
​A department of the Government of India may be defined as an
an organizational unit consisting of a secretary to the Government of India, together with a part of the central secretariat under his administrative control, to which responsibility for the performance of specified functions of the Government of India has been assigned under Rules of Business framed for this purpose.
A ministry of the Government of India may be defined as ordinarily
consisting of a department of the Government of India and the minister-in-charge of such department.
A formal distinction of this kind was new and the committee found it necessary that a department and a ministry should be respectively identified ordinarily with secretary's charge and a minister's
charge.
The nature of the work to be performed by a minister should not be identical with that of a secretary and, therefore, what may constitute a manageable charge for a minister is not always necessarily a manageable charge for secretary. Hence statement 1 is not correct.
In 1954, on the recommendation of Paul H. Appleby report, an Organisation and Methods (O&M) Division was set up in the Cabinet Secretariat. In 1964, the O&M Division was transferred to the Ministry of Home Affairs, under the newly created Department of Administrative Reforms.
In 1970, on the basis of the recommendations of the Administrative Reforms Commission, the Department of Personnel was set up in the Cabinet Secretariat. Since the Cabinet secretariat falls under the Prime Minister, it is safe to say the DoPT was placed under PM’s Charge. Hence, statement 2 is correct.