The correct answer is:
1. My little brother wants to be an actor.(Here in the given sentence, it has been asked to mention the finite and non-finite verb, 'to be' is finite and 'wants' is an infinitive verb)
2. She worked hard to p. the test.(Here in the given sentence, it has been asked to mention the finite and non-finite verb, 'to' is finite and (p) is an infinitive verb)
3. I couldn't solve the problem.(Here in the given sentence, it has been asked to mention the finite and non-finite verb, 'couldn't' is finite and 'solve' is an infinitive verb)
Note:- An non-finite verb is has a preposition before it. (p) denotes passed.