Explanation:

• First statement is correct. As Article 51 states to promote international peace and security; According to which the State shall endeavor to
• (a) Promote international peace and security;
• (b) Maintain just and honorable relations between nations;
• (c) Foster respect for international law and treaty obligations in the dealings of organized peoples with one another; and encourage settlement of international disputes by arbitration states that fraternity professed in the Preamble is not confined to National territory, but is extended towards Universal Brotherhood.
• Second statement is correct. The democratic republic envisaged in the Preamble stands for good of all the people is embodied in the concept of a welfare state which inspires the Direct Principles of State Policy. The ‘economic justice’ assured by the Preamble can hardly be achieved if the democracy envisaged by the constitution were confined to a ‘political democracy’.
• Third statement is correct.
• Article 38 directs the state to secure a social order with economic, political and social justice for the promotion and welfare of the people. Article 38(2) says that state shall strive to minimize the inequalities of income, status, facilities, opportunities etc.
• Article 15 i.e. Prohibition of discrimination on grounds of religion, race, caste, sex or place of birth states that the State shall not discriminate against any citizen on grounds only of religion, race, caste, sex, place of birth or any of them provides social justice to the people.
• Fourth is incorrect i.e. Socialism is mentioned in Preamble and the ideals of a Socialistic pattern of society are present in the Constitution.
• Some of the Directive Principles of State Policy reflect the ideology of socialism that lay down the framework of democratic socialist state, aim at providing social and economic justice and set the path towards welfare state.
• For example,
• Article 38 in The Constitution of India- State to secure a social order for the promotion of welfare of the people
• (1) 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
• (2) The State shall, in particular, strive to minimize the inequalities in income, and endeavor to eliminate inequalities in status, facilities and opportunities, not only amongst individuals but also amongst groups of people residing in different areas or engaged in different vocations
• Article 39- Certain principles of policy to be followed by the State: The State shall, in particular, direct its policy towards securing
• (a) That the citizens, men and women equally, have the right to an adequate means to livelihood;
• (b) That the ownership and control of the material resources of the community are so distributed as best to sub-serve the common good;
• (c) That the operation of the economic system does not result in the concentration of wealth and means of production to the common detriment;
• (d) That there is equal pay for equal work for both men and women;
• (e) that the health and strength of workers, men and women, and the tender age of children are not abused and that citizens are not forced by economic necessity to enter avocations unsuited to their age or strength;
• (f) That children are given opportunities and facilities to develop in a healthy manner and in conditions of freedom and dignity and that childhood and youth are protected against exploitation and against moral and material abandonment