There are two objects in this sentence: “des questions” (indefinite plural noun) and “au professeur” (indirect object).
We replace “des questions” with the pronoun “en” — it replaces quantities or indefinite nouns introduced by “de.”
“Au professeur” is an indirect object introduced by “à” and referring to a person, so we replace it with “lui.”
The correct order of pronouns is: lui en.
So the sentence becomes: Mathilde lui en pose.