Will they not have solved one of the questions?

Will one of the questions not have been solved by them?

Was one of the questions not have been solved by them?

Can one of the questions not have been solved by them?

Should one of the questions not have been solved by them?

All of the above

This is an interrogative sentence of Future Perfect Tense.

Active verb form: will/shall + have + past participle form of the verb

Passive verb form: will/shall + have been + past participle form of the verb