By which article of the constitution of india is the prime minister appointed?
According to Article 84 of the Constitution of India, which sets the principle qualification for member of Parliament, and Article 75 of the Constitution of India, which sets the qualifications for the minister in the Union Council of Ministers, and the argument that the position of Prime Minister has been described as "primus inter pares" (the first among equals), A prime minister must:
By which article of the constitution of india is the prime minister appointed by the president?
Article 75 75
Prime Minister of India
No context provided
By which article of the constitution of india is the prime minister appointed a council of ministers?
Article 74 74
Prime Minister of India
https://en.wikipedia.org/wiki/Prime%20Minister%20of%20India
There shall be a Council of Ministers with the Prime Minister at the head to aid and advise the president who shall, in the exercise of his functions, act in accordance with such advice.

— Article 74(1), Constitution of India
Prime Minister of India
The Prime Minister shall be appointed by the President and the other Ministers shall be appointed by the President on the advice of the Prime Minister.

— Article 75(1), Constitution of India
Prime Minister of India
In the Constitution of India,  Article 75 states that the Prime Minister shall be appointed by the President. Article 74 states that there shall be a Council of Ministers with the Prime Minister at the head to aid and advise the president.