Consider the following pairs: [Fundamental Rights]

Provision in the Constitution of India	Stated under
I. Separation of Judiciary from the Executive in the public services of the State	The Directive Principles of the State Policy
II. Valuing and preserving of the rich heritage of our composite culture	The Fundamental Duties
III. Prohibition of employment of children below the age of 14 years in factories	The Fundamental Rights

How many of the above pairs are correctly matched?

The correct answer is All the three.

Let us analyze each pair step-by-step to understand why all three pairs are correctly matched according to the Constitution of India:

1. Pair I: Separation of Judiciary from the Executive in the public services of the State – Stated under The Directive Principles of State Policy (DPSP)
Article 50 of the Constitution of India, which is part of Part IV (Directive Principles of State Policy), explicitly directs the State to take steps to separate the judiciary from the executive in the public services of the State. Therefore, this pair is correctly matched.

2. Pair II: Valuing and preserving of the rich heritage of our composite culture – Stated under The Fundamental Duties
Article 51A of the Constitution of India, which is part of Part IVA (Fundamental Duties), details the citizens' fundamental duties. Specifically, Article 51A(f) states that it is the duty of every citizen of India "to value and preserve the rich heritage of our composite culture". Therefore, this pair is correctly matched.

3. Pair III: Prohibition of employment of children below the age of 14 years in factories – Stated under The Fundamental Rights
Article 24 of the Constitution of India, which is part of Part III (Fundamental Rights) under the Right against Exploitation, prohibits the employment of children below the age of 14 years in any factory, mine, or other hazardous employment. Therefore, this pair is also correctly matched.

Since all three pairs (I, II, and III) are correctly matched, the correct option is indeed All the three.