Complete the sentence with suitable alternative: The son asked his mother if

This is reported speech. The reporting verb "asked" is in the past, so the verb in the reported clause should move back one step in time. Options A and B are present-tense forms and would break that sequence. "Might" is the past of "may", which is what you get from a direct question like "May I go out?"

• A) can go out: "Can" would backshift to "could", not stay as "can". Keeping the present form breaks the sequence of tenses.
• B) may go out: "May" is also a present form and should shift to "might" after a past reporting verb.
• D) did go out: "Did" is a past auxiliary used for questions and past actions. It does not express permission, so the meaning changes.

Core concept: sequence of tenses and backshifting in reported speech, applied to modal verbs of permission. Mains angle: precision in official drafting and correspondence, where the choice of tense and modal changes the meaning of a report.

Trap: choosing "may" because it looks like the natural permission verb, and forgetting that the reporting verb is in the past. The question gives no direct speech, so the answer rests on the standard backshifted form.