The correct answer is option 'A' - 1950.

Establishment of the Supreme Court:
The Supreme Court of India, the highest judicial body in the country, was established on January 26, 1950. It came into existence under the Constitution of India, which was adopted on this day. The establishment of the Supreme Court marked an important milestone in the history of India's judiciary.

Reasons for the Establishment:
1. Need for an independent judiciary: After gaining independence from British colonial rule in 1947, India needed a strong and independent judiciary to safeguard the rights and liberties of its citizens. The establishment of the Supreme Court was a significant step towards achieving this objective.

2. Replacing the Privy Council: Prior to the establishment of the Supreme Court, the highest court of appeal for Indians was the Judicial Committee of the Privy Council in London, which was the final appellate authority in British India. With the formation of the Supreme Court, India replaced the Privy Council as the highest judicial body within the country.

3. Implementing the Constitution: The Supreme Court was established to interpret and enforce the provisions of the newly adopted Constitution of India. It plays a crucial role in upholding the principles of justice, equality, and rule of law enshrined in the Constitution.

Role and Functions of the Supreme Court:
1. Guardian of the Constitution: The Supreme Court acts as the guardian of the Constitution and ensures that the government and its agencies function within the limits set by the Constitution. It has the power of judicial review, which allows it to strike down any law or action that violates the fundamental rights or the constitutional provisions.

2. Final Court of Appeal: The Supreme Court is the highest court of appeal in India. It hears appeals from lower courts and tribunals and has the power to review their decisions.

3. Constitutional Interpretation: The Supreme Court interprets the provisions of the Constitution and clarifies their meaning and scope. It provides authoritative guidance on constitutional matters and resolves disputes related to constitutional interpretation.

4. Upholding Fundamental Rights: The Supreme Court protects and upholds the fundamental rights of citizens guaranteed by the Constitution. It ensures that these rights are not violated by the government or any other entity.

5. Resolving Disputes: The Supreme Court resolves disputes between the central government and state governments, between different states, and between individuals and the government. It provides a platform for peaceful resolution of conflicts.

Conclusion:
The establishment of the Supreme Court in 1950 played a crucial role in ensuring the independence and integrity of the Indian judiciary. It has been instrumental in upholding the rule of law, protecting fundamental rights, and maintaining the balance of power between the three branches of the government. The Supreme Court continues to serve as the guardian of the Constitution and the final arbiter of justice in the country.