Residuary powers are the powers that aren`t explicitly given to either the federal or provincial governments by the constitution. They`re generally given to the authority that can best handle them. According to the Government of India Act of 1935, these residuary powers were given to the Governor General. Here`s why other options aren`t correct:

Option 1: The Federal Legislature was responsible for making laws on matters listed in the Federal List, not for exercising residuary powers.

Option 3: The Provincial Legislature had defined powers to make laws in areas listed in the provincial list. They didn`t possess residuary powers.

Option 4: The Provincial Governors were not vested with residuary powers; they basically acted as heads of their provinces.

So, the correct answer is Option 2 - Governor General, who was granted residuary powers to handle any matters not dealt with by the other authorities.