The correct option is
C debated
In order to fill in the blank with the most appropriate verb, we must understand the 'subject and verb agreement'. A subject is a person, thing, or a concept, in a sentence. A sentence always describes a person, thing or a concept and that is called 'subject' of the sentence. The rest of the sentence is a complement (which has the object in it). A subject and a verb should always agree in a sentence. If the subject is singular (example: Raj), the verb will also be singular (does). If the subject is plural (We), the verb will also be plural (do).NOTE: The given sentence doesn't specify any tense.
Option A - 'Debate' is a plural verb and can be used with a plural subject only. Though 'committee' has a lot of people in it, it is considered to be as one body, and hence it is a singular subject. Thus option A is incorrect.
Option B - 'Has debate' is grammatically incorrect. In present perfect tense, we use 'has/have' with the past participle form of the verb and not the original form of the verb. 'Debate' is not the past participle form of the verb. Hence, option B is incorrect.
Option D - 'To debate' can't be used here, as it doesn't specify any tense. Also, as the sentence is in the active voice, we can't use the infinitive with 'to'. Hence, option D is incorrect.
Option C - 'Debated' can be used with both singular and plural subjects. Also, it specifies that the sentence is in the past tense. Hence, option C is the correct answer.
'The committee debated these questions carefully.'