The correct option is
C Do
Option A:
The auxiliary, 'have' is used in the formation of perfect tenses. It is used along with the past participle form of the verb. The past participle form of the negative verb, 'not go' is 'not gone'. However, the simple present tense form of the verb, i.e.'not go' is used. The auxiliary, 'have' is sometimes also used to express an obligation. Eg: 'They have to go out today'. However, there is no obligation expressed in the two sentences. Hence, this option is incorrect.Option B: The auxiliary, 'are' is used along with the present continuous form of the verb. However, in the given sentence, the verb, 'not go' is in simple present tense. Hence, this option is incorrect.
Option C: The auxiliary, 'do' is used to form the negative of the simple present tense of verb. The verb in the given sentence, 'not go' is the negative form of the verb in simple present tense. However, it is incomplete and can be completed using the auxiliary, 'do'. The complete verb is: 'Do not go'. Hence, this option is correct.
Option D: The auxiliary, 'does' is used with the third person subject when it is singular. Eg: 'She does not go to the school'. However, the subject of the sentence, 'Beauty and brain' is in third person and is plural. Hence, this option is incorrect.