The question asks to identify the specific article in the Indian Constitution that mandates the separation of the judiciary from the executive within the state's public services.
Article 50 of the Constitution of India is a Directive Principle of State Policy (DPSP). It explicitly states: "The State shall take steps to separate the judiciary from the executive in the public services of the State."
Therefore, Article 50 is the correct provision addressing the separation of the judiciary and the executive.
Comparing this with the options provided:
Thus, the correct option is Article 50.
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