Direction: Fill in the blank with the most appropriate option.
No sooner _________ the sun risen than the fog disappeared.

The correct structure follows the adverbial inversion rule for "No sooner... than".
When a sentence begins with "No sooner", the auxiliary verb is inverted before the subject:

$$\text{No sooner}+\text{had}+\text{subject}+{\text{V}}_3\cdots +\text{than}+\text{subject}+{\text{V}}_2$$

Since the verb risen is in its past participle form (${\text{V}}_3$), the auxiliary verb had must be used. If the verb were in its base form (rise), did would be used.