Fill in the blank with the appropriate verb.
You have done your work. You _______ go home.
(a)will
(b)could
(c)may
(d)must

Hint: Look for pointers suggesting which modal auxiliary to use. The action has occurred in the given sentence, i.e. it occurred in the past. The next sentence refers to permission. These pointers are indicators of certain situations.

Complete answer: A modal verb is a type of verb that is used to indicate
modality – that is: likelihood, ability, permission, request, capacity, suggestions, order,
obligation, or advice. We need to find the verb from the options that indicates possibility/likelihood.

We can discern whether the actions are happening right now by certain pointers that are
given in the sentence in the question. So, let us deconstruct the given sentence.
In the first part, the sentence is telling the subject that his work is complete. So, the second sentence should surely tell us that the subject is free to go. So, the second sentence should use a modal auxiliary which gives permission.
Now, we know exactly what we are looking for. Let’s look at the given options:
(a)will - This modal auxiliary is most often used to express a strong desire. This does not fit into the context of the given sentence as it does not indicate permission. This is not the required answer. So, this is an incorrect option.
(b)could - This modal auxiliary is most often used to express past ability. This does not fit into the context of the given sentence as it does not indicate permission. This is not the required answer. So, this is an incorrect option.
(c)may - This modal auxiliary is most often used to express permission. This fits into the given sentence perfectly. This is the required answer. So, this is the correct answer.
(d)must - This modal auxiliary is most often used to express a possibility. This does not fit into the context of the given sentence as it does not indicate permission. This is not the required answer. So, this is an incorrect option.

Note:Choose the most appropriate option given the context of the sentence. Make sure all the forms of verbs are aligning with each other and work with each other perfectly.