The correct option is A Yours obediently
Option A: 'Yours obediently' is a suitable salutation in a formal letter in terms of its tone and style. Hence A is the correct option.
Options B and C: 'Your's obediently' and 'Your's sincerely' are both not suitable closings because 'your's' is grammatically incorrect. The possessive adjective 'your' already indicates possession by
modifying the noun that follows, 'your bag', for example. It does not
use an apostrophe s ('s) to indicate possession.
Hence options B and C are incorrect.
Option D: 'Yours truly' is generally used when one writes a letter to someone that one does not know very well. But here, the student has written a letter to his principal. Hence, this option is not preferable.