Explanation:

Only statements 2&3 are correct.

• Ministers are appointed by the President on the advice of the Prime Minister.Hence statement 1st is incorrect.

• Article 74 of the Constitution deals with the status of the council of ministers while Article 75 deals with the appointment, tenure, responsibility, qualification, oath and salaries and allowances of the ministers.

• Article 74 (COM to aid and advise President): The advice tendered by Ministers to the President shall not be inquired into in any court.

• The appointment criteria of the council ministers are just like the President. The President of India appoints them on the advice of the Prime Minister. The Council Ministers function with the representation to different regions and hold different positions in the prime minister’s cabinet

• The COM consists of three categories of ministers, namely, cabinet ministers, ministers of state, and deputy ministers. At the top of all these ministers stands the Prime Minister.

• The word ‘Cabinet’ wasn’t in the Constitution until the year 1978. The next year, 1979 saw the 44th Amendment to the Constitution coming into force. According to this, the President cannot issue a National Emergency unless the Union Cabinet makes the decision, and sends it in writing.

• The word 'Cabinet' is mentioned only once in the Indian Constitution in Article 352(3) which states that "the President shall not issue a proclamation unless the Union Cabinet communicates him in writing that such a proclamation may be issued".

Hence option 3rd is correct.