**Explanation:**

The correct answer is option B, which states that the president convenes and prorogues all sessions of Parliament in consultation with the prime minister.

**Convening and Proroguing Parliament:**

1. The term "convene" refers to the act of summoning Parliament for a session. It involves calling Members of Parliament (MPs) to assemble and begin the legislative proceedings.

2. The term "prorogue" refers to the act of ending a session of Parliament without dissolving it completely. It marks the conclusion of a session and allows for a new session to begin at a later date.

**Role of the President:**

1. The President of India is the constitutional head and the highest authority in the country. As per Article 85 of the Indian Constitution, the President has the power to summon, prorogue, and dissolve Parliament.

2. The President exercises these powers on the advice of the Council of Ministers, headed by the Prime Minister. The President acts as a titular head and performs these functions based on the advice received from the government.

**Consultation with the Prime Minister:**

1. The President, while exercising the powers to convene and prorogue Parliament, consults with the Prime Minister. This consultation is done to ensure the smooth functioning of the Parliament and to align with the government's legislative agenda.

2. The Prime Minister, as the head of the government and the leader of the ruling party or coalition, is responsible for coordinating and advising the President on matters related to the functioning of Parliament.

3. The Prime Minister's input is crucial as they are well-versed with the government's priorities, legislative proposals, and the overall political situation in the country.

**Role of the Speaker and Leader of the Opposition:**

1. The Speaker of the Lok Sabha (the lower house of Parliament) is responsible for maintaining order and presiding over the proceedings. However, the Speaker does not have the authority to convene or prorogue Parliament.

2. The Leader of the Opposition, as the leader of the largest opposition party in the Lok Sabha, plays an important role in voicing the concerns and opinions of the opposition. However, their consultation is not required for convening or proroguing Parliament.

In conclusion, while the Speaker and the Leader of the Opposition have significant roles in the functioning of Parliament, the President convenes and prorogues Parliament in consultation with the Prime Minister, as the head of the government. The Prime Minister's advice is crucial to ensure coordination with the government's legislative agenda.

The prime minister