Question

Fill in the blank with a suitable modal:
If you need some help with your homework, you___ go to the library.
A. Should
B. Mustn’t
C. Had to
D. Shouldn’t

Answer 1

Hint: A modal verb is a verb that expresses modality, such as probability, ability, permission, request, power, recommendations, order, duty, or advice. Modal verbs are often used in conjunction with the base form of another semantic verb.

Complete answer:
The questions demands to complete the sentence with the most apt helping verb.
Option A) Should: It can be used to convey an opinion, suggestion, expectation, or complaint about a previous action, or it can be used to request advice. It's a contraction of ‘must not,' and it's used to talk about things we can stop doing, such as: Shouldn’t: It's used to express a need felt by the speaker in the past. It's a contraction of the word ‘shouldn’t'; it's a negative word. We can see in the query that the speaker is making a recommendation, which is to go to the library if he or she needs assistance.
It's important to remember that this is a conditional sentence. It's the First Conditional Sentence in particular — in first conditional sentences, we use ‘should' to express a slight probability.
Option B) mustn’t isn't acceptable here since it's a suggestion, not an obligation or anything that can be prevented.
Option C) Since the sentence is not in the past tense, the word 'had to' is inappropriate.
Option D) The sentence is in the positive form, so ‘shouldn’t' isn't appropriate; similarly, telling someone they shouldn't go to the library if they wanted help with their homework would be meaningless.

Thus the correct answer is option ‘A’.

Note: Auxiliary verbs add functional or grammatical sense to the clause in which they appear, such as tense, aspect, modality, expression, focus, and so on. Auxiliary verbs are generally found next to an infinitive verb or a participle, which provide the clause's key semantic material.