Which value is NOT explicitly mentioned in the Preamble of the Indian…

Concept. The Preamble is the Constitution's declaration of purpose - it announces the nature of the Indian State and names, in words, the objectives the Republic resolves to secure. A value counts as explicitly mentioned only if it stands in that text; a value the Constitution pursues elsewhere, through a Directive Principle or a Fundamental Duty, is not part of the Preamble's own list.

The Preamble names four objectives:

• Justice - social, economic and political

• Liberty - of thought, expression, belief, faith and worship

• Equality - of status and of opportunity

• Fraternity - assuring the dignity of the individual and the unity and integrity of the Nation

It also describes India as a Sovereign, Socialist, Secular, Democratic Republic. That is the whole of its vocabulary.

Application. Checking the offered values against that list: Justice, Liberty and Equality each stand in the Preamble by name. Environmental protection does not appear in it at all. It entered the Constitution only in 1976, through the 42nd Amendment - as Article 48A, a Directive Principle asking the State to protect and improve the environment and to safeguard forests and wildlife, and as Article 51A(g), a Fundamental Duty of every citizen. So the value not explicitly mentioned in the Preamble is Environmental protection.

Cross-check. Where each offered value is actually written:

The same 42nd Amendment did amend the Preamble - it inserted the words Socialist, Secular and Integrity - but it added nothing there about the environment, which is why the environmental provisions sit in Part IV and Part IV-A instead.