Your father used to be the principal of this college,

The correct answer is option -C

The given sentence is of question tag.

Question tag is used to reconfirm the question or the statement.

If the main sentence is positive, question tag will be negative and vice -versa.

Here the given sentence is positive,so question tag will be negative.

The sentence is in the past form.`Used to' we use as a simple present tense but  to indicate the things happened in the past.

Ex-I used to go by bus.

As the sentence is in the past form,usage of `did' will be correct.

`Did' is the past form of the `Do'

Option A- Did he ? Will be wrong.Because given sentence is in the positive form,so question tag will be negative.

Option B- Does he?- Will be wrong.Because the given sentence is in the past tense & `Does' is use for 3rd person singular & when sentence is in present form.

Option D- Doesn't he? - Will be wrong.Because the given sentence is in present tense.Though the question tag is negative,it is wrong.Because `Does' is used when the sentence is in the present tense & subject is 3rd person singular.