Final answer:
The appropriate object pronouns for the given sentences are 'le' and 'les' respectively.
Step-by-step explanation:
In sentence a, the appropriate object pronoun for the student giving an apple to his teacher would be le, as it refers to a singular person, his teacher.
In sentence b, the appropriate object pronoun for the student giving apples to multiple people would be les, as it refers to a plural group of people.
Learn more about Object pronouns in Spanish