As per the constitution of India, the Prime Minister of India is addressed as the head of the government and the President of India is the formal head of the state of India and the Prime Minister and the council of ministers. 

As per the Indian Parliamentary System the head of the government is the Prime Minister of India and the head of state i.e. the President of India holds a ceremonial position and on most matters acts only on the advice of the Prime Minister of India.

(the prime minister of India Mr Narendra modi)

The Prime Minister of India is the head of the council of ministers and is also the chief adviser to the President of India. The Prime Minister of India can be a member of any of the two houses of the Parliament of India i.e. the Lok Sabha (House of the People) and the Rajya Sabha (Council of the States). The Prime Minister of India must be a member of a political party or coalition having a majority in Lok Sabha. Since the Prime Minister is the leader of the Executive of the Government of India and being the senior most member of the cabinet can select and dismiss members of the cabinet. He allocates portfolios to the members within the government. The Prime Minister submits his resignation to the President of India if he is not having confidence of majority in the Lok Sabha.

(president of India Mr ram Nath Kovind)

The President of the Republic of India is appointed indirectly by the members comprising the Parliament of India (both the houses) and the Legislative Assemblies of each of the Indian states and territories for a term of five years. The President of the Republic of India enjoys executive, judiciary, legislative and emergency powers and is the commander-in-chief of the Indian Armed Forces. The President of India has the power to appoint and remove the Prime Minister of India, other members of the Union, the Attorney General of India, the Comptroller and Auditor General of India, the Chief Justice and the Judges of the Supreme Court, the Chief Justice and Judges of the High Court of the states, the Governor of states, the Chief Election Commissioner and other Election Commissioners of India, the Chairman and members of the Union Public Service Commission (UPSC). The President submits his resignation to the Vice President of India.