The most common form of closing a letter to a close relative is :

The correct answer is Yours affectionately.

Key Points

• Yours faithfully/truly/sincerely/obediently is used in Formal Letters. 
  • A letter that contains official information and messages is known as formal letter. 
• While yours lovingly/affectionately is used in closing letter to a close relative i.e. Informal letter. 
  • An informal letter is a non-official letter which we usually use to write to our friends, family or relatives.

Thus, Option 2 is the most common form of closing a letter to a close relative.