The Constitution of India provides for a parliamentary form of government, both at the Centre and in the states.
The parliamentary system of government is the one in which the executive is responsible to the legislature for its policies and acts.

2 and 3 are incorrect.
The Constitution of India is neither rigid nor flexible but a synthesis of both.
Article 368 provides for two types of amendments:
(a) Some provisions can be amended by a special majority of the Parliament, i.e., a two-third majority of the
members of each House present and voting, and a majority (that is, more than 50 per cent), of the total
membership of each House.
(b) Some other provisions can be amended by a special majority of the Parliament and with the ratification by half of the total states.
At the same time, some provisions of the Constitution can be amended by a simple majority of the Parliament in the manner of ordinary legislative process. Notably, these amendments do not come under Article 368.
The Constitution of India establishes a federal system of government. It contains all the usual features of a federation, viz., two government, division of powers, written Constitution, supremacy of Constitution, rigidity of Constitution, independent judiciary and bicameralism.
Flexibility of Constitution is a unitary or non-federal feature.

The 42nd Amendment Act of 1976 added four new Directive Principles to the original list. They require the State:
(i) To secure opportunities for healthy development of children (Article 39).
(ii) To promote equal justice and to provide free legal aid to the poor (Article 39 A).
(iii) To take steps to secure the participation of workers in the management of industries (Article 43 A).
(iv) To protect and improve the environment and to safeguard forests and wild life (Article 48 A)

Only 1 is correct.
Part III of the Constitution is rightly described as the Magna Carta of India. It contains a very long and comprehensive list of ‘justiciable’ Fundamental Rights. In fact, the Fundamental Rights in our Constitution are more elaborate than those found in the Constitution of any other country in the world, including the USA.
The Fundamental Rights are named so because they are guaranteed and protected by the Constitution, which is the fundamental law of the land.

All 1, 2 and 3 are correct.
Constitution is the supreme law that determines the relationship among citizens and also the relationship between the citizens and government. Moreover:
• First, it generates a degree of trust and coordination that is necessary for different kind of people to live together;
• Second, it specifies how the government will be constituted, for e.g. by democratic elections.
• Third, it lays down limits on the powers of the government and tells us what the rights of the citizens are; and
• Fourth, it expresses the aspirations of the people, for e.g. by preamble and DPSP.