One of the boys who always give/gives the correct answer is Samuel.
As per rule, one of is followed by plural noun/pronoun and singular helping verb, so we should be using gives in the sentence. But the answer is give.
Learn English – One of is followed by plural noun/pronoun and singular helping verb
subject-verb-agreement
Related Solutions
Whilst a dictionary search shows that the word is singular but plural in form, it is most commonly used (in my experience) with a verb in singular form.
Math(ematic)s is my least favourite subject.
Math(ematic)s is really hard.
This Ngram viewer helps:
EDIT: As @Araucaria points out, the "mathematics are" examples in the Ngram above are not really relevant. See his comment below.
The second, as the subject "Bob and Alice" is plural. The adverb doesn't change that.
It would, of course be possible to rephrase "Bob drives a BMW and Alice (drives) a Lexus". The repeated verb can be dropped.
The adverb "respectively" is sometimes misused, even where it is grammatically correct. Grammarist.com gives examples of good and bad use of "respective".
Best Answer
Samuel is one member of some group. This explains why the verb of the matrix clause is "is". Without the relative clause, the sentence is simply:
The original sentence does include a relative clause, and the subject of that clause is the relative pronoun "who". By itself, "who" doesn't have a grammatical number. The relative pronoun must have an antecedent. Whatever "who" references, that is the thing that will have a grammatical number.
There are two possible antecedents: "one" and "boys".
In the first sentence, the phrase "of the boys" and the clause "who always gives the correct answer" each independently modify the subject "one". The "who" refers to "one", and so the verb "gives" agrees with its singular subject.
In the second sentence, the clause "who always give the correct answer" modifies the object "the boys". The "who" refers to "boys", and so the verb "give" agrees with its plural subject.
The example sentence matches this second possibility. Several boys always give the correct answer, and Samuel is a member of this group.
Both possibilities are grammatically sound. Each possibility has a different meaning, so the correctness of the form of the verb "to give" depends on which meaning is intended.
Without further context, the second possibility seems more likely and more useful. "Samuel" is a traditionally masculine name. If the entire prepositional phrase is "of the boys", that hardly counts as useful information about him. However, if the prepositional phrase is "of the boys who always give the correct answer", that certainly counts as useful information about him.