Are there any conditions under which such functions can be entrusted?
Yes, there are conditions under which such functions can be entrusted. According to Article 258A of the Constitution: "The Governor of a State may, with the consent of the Government of India, entrust either conditionally or unconditionally to that Government or to its officers functions in relation to any matter to which the executive power of the State extends." This means that the Governor can only entrust such functions with the consent of the Government of India.