The "Basic Structure" doctrine empowers the Judiciary to review:

The correct option is Whether an amendment passed by Parliament violates the core ethos of the Constitution..

Explanation

The Basic Structure Doctrine is a judicial principle established by the Supreme Court of India in the landmark Kesavananda Bharati case (1973). It asserts that while Parliament has the power to amend the Constitution under Article 368, this power is not absolute. Parliament cannot alter, damage, or destroy the essential features or the "basic structure" of the Constitution.

Option Analysis:

• Whether an amendment passed by Parliament violates the core ethos of the Constitution. is Correct: The doctrine specifically empowers the Judiciary to review Constitutional Amendments. If an amendment passed by Parliament is found to violate the core ethos or fundamental features of the Constitution (such as democracy, rule of law, secularism, or judicial review), the Supreme Court has the power to declare such an amendment ultra vires and void.
• The Constitution every 20 years. is Incorrect: The Indian Constitution does not mandate a periodic review every 20 years. It is a living document that evolves through amendments and judicial interpretations as needed, rather than through fixed-term revisions.
• The appointment of the Prime Minister. is Incorrect: The appointment of the Prime Minister is governed by Article 75 and established parliamentary conventions. While the principle of free and fair elections is a basic feature, the specific executive act of appointment is not the primary target of the Basic Structure doctrine, which focuses on the validity of laws and amendments.
• The dissolution of the Rajya Sabha. is Incorrect: The Rajya Sabha (Council of States) is a permanent house and is not subject to dissolution under Article 83(1) of the Constitution. Therefore, the question of reviewing its dissolution does not arise.

Key Takeaway:
The Basic Structure doctrine acts as a limitation on the constituent power of Parliament, ensuring that the fundamental identity of the Constitution cannot be abrogated through the amendment process.