The boy was incorrigible and a constant source of trouble to his mother.

The correct answer is B. inveterate.

An inveterate person is someone who is habitually bad or addicted to something. In this case, the boy is habitually bad and a constant source of trouble to his mother.

The other options are incorrect because:

• A truant is a person who stays away from school without permission.
• A rash person is someone who acts without thinking.
• A dishonest person is someone who is not truthful.

I hope this helps!