Ans: B

Exp:

• Statement 1 is incorrect: The Constitution does not contain any specific procedure for the selection and appointment of the Prime Minister. As per Article 75, the Prime Minister shall be appointed by the President. However, this does not imply that the president is free to appoint anyone as prime minister. 
• Statement 2 is incorrect: In accordance with the conventions of the parliamentary system of government (not according to the constitution), the President has to appoint the leader of the majority party in the Lok Sabha as the Prime Minister. But, when no party has a clear majority in the Lok Sabha, then the President may exercise his personal discretion in the selection and appointment of the Prime Minister
• Statement 3 is correct: In 1997, the Supreme Court held that a person who is not a member of either House of Parliament can be appointed Prime Minister for six months, i.e., he does not necessarily have to be a member of parliament, within which, he should become a member of either House of Parliament; otherwise, he ceases to be the Prime Minister.
• Reference : Laxmikant, Chapter 19 

Ans: B

Exp:

• Statement 1 is incorrect: In India, the Prime Minister is the head of government and is appointed by the President. The term of the Prime Minister is not fixed, and  there is no strict limit on the number of terms he can serve. The Prime Minister is typically the leader of the political party or coalition with the majority of seats in the lower house of Parliament, known as the Lok Sabha.
• Statement 2 is correct: The prime minister holds office at the pleasure of the president. However, this does not mean that the president can dismiss the Prime Minister at any time. So long as the Prime Minister enjoys the majority support in the Lok Sabha, he cannot be dismissed by the President. Statement 3 is correct: if the Prime Minister loses the confidence of the Lok Sabha, they are required to resign from their position, or the President can dismiss him. The Prime Minister’s position is dependent on having the support of the majority of the members in the Lok Sabha.
• Reference: Laxmikant, Chapter 19 

Ans: D

Exp:

• Both statements 1 and 2 are incorrect: The oath of office of the Prime Minister of India is administered by the President of India, not the Speaker of the Lok Sabha. The salary and allowances of the Prime Minister are determined by Parliament from time to time. He gets the salary and allowances that are payable to a member of Parliament. Additionally, he gets a sumptuary allowance, free accommodation, travelling allowance, medical facilities, etc.
• Reference: Laxmikant, Chapter 19 

Ans: A

Exp:

• Statement-I is correct: The Prime Minister stands at the head of the council of ministers, the other ministers cannot function when the Prime Minister resigns or dies. In other words, the resignation or death of an incumbent Prime Minister automatically dissolves the council of ministers and thereby generates a vacuum.
• Statement-II is correct: Prime Minister is the head of the council of ministers, and He recommends persons who can be appointed as ministers by the president. The President can appoint only those persons as ministers who are recommended by the Prime Minister.
• Hence ,Both Statement-I and Statement-II are correct and Statement-II is the correct
  explanation for Statement-I
• Reference : Laxmikant,Chapter 19 

Ans: C

Exp:

• The councils are often formed to address specific policy issues, coordinate government actions, and provide advice to the Prime Minister.  Some of the notable councils that the Prime Minister of India chairs include.
  • NITI Ayog (which succeeded the planning commission) 
  • National Integration Council 
  • Inter-State Council, 
  • National Water Resources Council
• Zonal councils are created by the State Reorganisation Act, 1956. They are chaired by the Home Minister of India.
• Reference: Laxmikant, Chapter 19