The correct answer is: B. The Governor of Jammu and Kashmir.
The Constitution of India, Article 217(1), states that a Judge of a High Court can resign his office by writing under his hand to the Governor of the State.
The Chief Minister is the head of the State Government, but he/she is not the head of the State. The Governor is the head of the State. The Governor is appointed by the President of India. The Governor has the power to appoint and remove Judges of the High Court.
The Council of Ministers is the body of Ministers who are responsible to the Legislative Assembly of the State. The Council of Ministers is headed by the Chief Minister. The Council of Ministers does not have the power to appoint or remove Judges of the High Court.