The correct answer is Option 2 - President of India
The Governor is appointed by the President of India (acting on the advice of the Central Government). However, the Governor functions with the aid and advice of the Council of Ministers of the state, which holds real executive power. The Supreme Court has ruled that the Governor is not under the control of the Central Government for day-to-day functioning.
Articles Related to Governor at a Glance:
Article 153: Governors of states
Article 154: Executive power of state
Article 155: Appointment of Governor
Article 156: Term of office of Governor
Article 157: Qualifications for appointment as Governor
Article 158: Conditions of Governor’s office
Article 159: Oath or affirmation by the Governor
Article 160: Discharge of the functions of the Governor in certain contingencies
Article 161: Power of the Governor to grant pardons and others
Article 162: Extent of executive power of state
Article 163: Council of Ministers to aid and advice the Governor
Article 164: Other provisions as to ministers like appointments, term, salaries, and others
Article 165: Advocate-General for the State
Article 166: Conduct of business of the government of a state
Article 167: Duties of the Chief Minister regarding furnishing of information to the Governor, and so on
Article 174: Sessions of the state legislature, prorogation and dissolution
Article 175: Right of the Governor to address and send messages to the house or houses of state legislature
Article 176: Special address by the Governor
Article 200: Assent to bills (i.e. assent of the Governor to the bills passed by the state legislature)
Article 201: Bills reserved by the Governor for consideration of the President
Article 213: Power of Governor to promulgate ordinances
Article 217: Governor being consulted by the President in the matter of the appointments of the judges of the High Courts
Article 233: Appointment of district judges by the Governor
Article 234: Appointments of persons (other than district judges) to the judicial service of the state by the Governor. | 
