Correct option is A
The correct statements about the qualification and appointment of the Governor are:
A. He is a citizen of India. This is a basic requirement for the appointment of a Governor in India.
The other statements have inaccuracies:
B. He has completed the age of 25 years. This is incorrect; the Governor must have completed the age of 35 years.
C. He is appointed by the Prime Minister. This is incorrect; the Governor is appointed by the President of India.
D. He holds the office of Governor for a term of 6 years. This is incorrect; the term of office for a Governor is 5 years.
E. He resigns from his office, by writing under his hand addressed to the Prime Minister. This is incorrect; the Governor resigns by writing under his hand addressed to the President.
Therefore, the correct answer is (a) A only.