Which of the following provisions in the Indian Constitution deals with the duty of the State to separate the judiciary from the executive?

The correct option is Article 50.

Explanation:
Article 50 of the Indian Constitution, contained within the Directive Principles of State Policy (DPSP) under Part IV, deals with the separation of the judiciary from the executive. It states: "The State shall take steps to separate the judiciary from the executive in the public services of the State."
This separation is vital for maintaining the independence of the judiciary, ensuring that the judicial system functions without any interference or influence from the executive branch of the government.

Let us also look at the other options to understand their provisions:
1. Article 51: Deals with the promotion of international peace and security.
2. Article 44: Directs the State to secure a Uniform Civil Code for the citizens throughout the territory of India.
3. Article 48A: Focuses on the protection and improvement of the environment and safeguarding of forests and wildlife.