Explanation:

The Rashtrapati Bhavan announced a slew of gubernatorial appointments, including that of Union Minister for Social Justice and Empowerment Thawarchand Gehlot as the Governor of Karnataka, replacing Vajubhai Vala.

• Governor is the head of the executive of the state.
• He/she is appointed by President of India.

Qualifications and conditions for appointment

• Should be a citizen of India.
• Should have completed 35 years of age.
• Should not hold any office of profit under the union govt. or state govt. or any local Authority or any other public authority.
• Should not be a member of either house of parliament or a house of the state legislature.

Tenure

• Governor holds office for a term of 5 years from the date on which he assumes office. This term of 5 years is subject to the pleasure of president.
• He/she can resign anytime by addressing a resignation letter to the president.
• Oath: The oath of office to the governor is administered by the chief justice of concerned HC and in his absence by the senior-most judge of the HC available.
• By 7th Constitution Amendment Act of 1956, same person can be appointed as governor of 2 or more states.

Hence both statements 1&2 are correct.