The National Development Council (NDC) was constituted by a resolution of the Union Cabinet, which means that option 3 is the correct answer. The NDC was established in 1952 with the aim of promoting and coordinating developmental efforts in India. It serves as a platform for interaction and consultation between the central and state governments on matters related to national planning and policy-making.

Option 1, which states that the NDC was constituted by an Act of Parliament, is incorrect. There is no specific legislation that established the NDC.

Option 2, which states that the NDC was constituted as a voluntary association of states and union territories, is also incorrect. While the NDC does involve the participation of states and union territories, it was not constituted solely as a voluntary association.

Option 4, which suggests that the NDC is an attached office of the PMO (Prime Minister`s Office), is also incorrect. The NDC is an independent entity and not directly attached to the PMO.