Step 1: Understanding the Concept:
This question requires knowledge of the Fundamental Rights and Directive Principles of State Policy (DPSP) enshrined in the Constitution of India.
Step 2: Detailed Explanation:
1. Article 14: Guarantees "Equality before the law" and equal protection of the laws within the territory of India. So, (A) matches (III).
2. Article 21: States that no person shall be deprived of his life or personal liberty except according to procedure established by law. So, (B) matches (I).
3. Article 24: Prohibits the employment of children below the age of 14 years in factories, mines, or any other hazardous employment. So, (C) matches (II).
4. Article 50: This DPSP directs the State to take steps to separate the judiciary from the executive in the public services of the State. So, (D) matches (IV).
Step 3: Final Answer:
The correct matching sequence is (A)-(III), (B)-(I), (C)-(II), (D)-(IV).