Which part of the Constitution of India declares the ideal of Welfare State?

The correct option is Directive Principles of State Policy.

The concept of a "Welfare State" is a core philosophy of the Indian Constitution, and it is explicitly declared and detailed in Part IV of the Constitution, which contains the Directive Principles of State Policy (DPSP).

Here is a step-by-step explanation of why this option is correct:
1. Definition of Welfare State: A welfare state is a concept of government in which the state plays a key role in the protection and promotion of the economic and social well-being of its citizens. It is based on the principles of equality of opportunity, equitable distribution of wealth, and public responsibility for those unable to avail themselves of the minimal provisions for a good life.
2. Role of DPSP (Articles 36 to 51): The Directive Principles are guidelines or principles given to the federal institutes governing the State of India, to be kept in citation while framing laws and policies. Article 38 of the Constitution explicitly states that the State shall strive to promote the welfare of the people by securing and protecting as effectively as it may a social order in which justice—social, economic, and political—shall inform all the institutions of the national life.
3. Distinction from other options:
- Fundamental Rights (Part III): These provide political democracy and protect individual liberties against state encroachment, rather than establishing economic and social welfare systems.
- Preamble: While the Preamble mentions justice, liberty, equality, and fraternity, which are the foundations of a welfare state, the concrete declaration and framework for achieving a welfare state are operationalized specifically through the DPSP.
- Seventh Schedule: This schedule merely deals with the division of legislative powers between the Union and the States (Union List, State List, and Concurrent List).