The correct answer is option 'D': Prime minister.

The keystone of the cabinet arch refers to the most important or central figure within the cabinet of ministers. In the context of this question, the term "cabinet arch" is used metaphorically to represent the entire cabinet, which is a group of senior government officials chosen by the head of government (in this case, the Prime minister) to lead various government departments and assist in decision-making.

Here is a detailed explanation of why the Prime minister is considered the keystone of the cabinet arch:

1. Role of the Prime Minister:
- The Prime minister is the head of government and holds the highest executive office in many parliamentary democracies, including India.
- They are responsible for leading the government, formulating policies, making important decisions, and representing the country both nationally and internationally.
- The Prime minister is usually the leader of the political party or coalition that holds the majority in the parliament.

2. Appointment and Power:
- The Prime minister is appointed by the President or the Monarch (in countries with a constitutional monarchy) after a general election or in a parliamentary system.
- They have significant powers, including the authority to appoint and dismiss cabinet ministers, allocate portfolios, and shape policies.
- The Prime minister also acts as the principal advisor to the President or Monarch and provides recommendations on key appointments and legislative matters.

3. Leadership and Coordination:
- The Prime minister plays a crucial role in coordinating the activities of various government departments and ensuring that policies are implemented effectively.
- They preside over cabinet meetings, where ministers discuss and decide on important issues, and provide overall direction to the government.
- The Prime minister's leadership and decision-making skills are essential in maintaining the unity and coherence of the cabinet.

4. Representative of the Government:
- The Prime minister represents the government in interactions with the President, parliament, judiciary, and other branches of the state.
- They are the spokesperson for the government's policies and are accountable to the parliament and the public.
- The Prime minister often addresses the nation on important matters, participates in international summits, and represents the country's interests in diplomatic negotiations.

In summary, the Prime minister is considered the keystone of the cabinet arch because of their central role in leading the government, making key decisions, coordinating the activities of various departments, and representing the government nationally and internationally.