Choose the correct option for ending an application to the authority:

The correct answer is Option (3) → Yours faithfully

Closing a formal letter:

• An application to an authority (a principal, an officer) is a formal letter, usually addressed as "Sir" or "Madam".
• Such a letter closes with Yours faithfully (or Yours obediently in a student's application).
• Yours is a possessive pronoun and is written without an apostrophe.
  Example: The letter to the Municipal Commissioner ended with "Yours faithfully".

Why the Other Options are Incorrect?

Option 1: Your's sincerely — Incorrect.

• "Your's" is a spelling error; possessive pronouns take no apostrophe.
• Yours sincerely is used when the reader is addressed by name, not in an application to an authority.

Option 2: Your's faithfully — Incorrect. The close is right, but "Your's" is wrongly written with an apostrophe.

Option 4: Yours lovingly — Incorrect. Yours lovingly is an informal close for letters to family and close friends.

Contrast: Yours faithfully when the letter opens with "Sir" or "Madam"; Yours sincerely when the reader is addressed by name.