The correct answer is Chief Justice of High Court of the state.

The Chief Justice of the state or the union territory or High Court administers the oath to the governor as per Article 159.

• A governor is the executive of the state or union territory level of government.
• The governor administers the oath to the Chief Minister and other Ministers of the state.

Oath taken by the governor is–

"I, A. B., do solemnly affirm (or swear) that I will faithfully execute the office of Governor (or discharge the functions of the Governor) of (name of the State) and will to the best of my ability preserve, protect, and defend the Constitution and the law and that I will devote myself to the service and well-being of the people of (name of the State).”

• Chief Minister’s oath is administered by the governor of that state.
• President of India’s oath is administered by the Chief Justice of India. The President administers the oath of the Prime Minister of the country and other Member of Parliament.
• State Lokayukta is appointed by the Chief Minister of the state after consultation with the Chief Judge of the High Court or the state.

• Article 159 of the Constitution is the same as Article 136 of the Draft Constitution 1948.