Fill in the blank with most appropriate word-
_________ I come in, Sir?
a) Can
b) Shall
c) May
d) Could

Hint: Read the given phrase/sentence carefully. Try to make out the meaning of it and find the subject or the predicate or the main object of the sentence.

Complete answer:
The given sentence shows gratitude and moral values. We will have to fill in the blank with a modal verb. Modal Verbs show us the attitude of the speaker to what is being said or done. The term "modal" means expressing mood and mood is a way to express the attitude of the speaker.
Now, let us examine all the given options to find out the correct option -
Option ‘a’ is Can. It cannot be the correct option as it is not as polite or full of gratitude as is “may”. So, we cannot use this as the correct option and we will eliminate this option.
Option ‘b’ is Shall. It won’t fit in the given blank and it cannot be the correct answer. It is not as polite and respectful. So, we will eliminate this option.
Option ‘c’ is May. This is the most appropriate option as it fits in the given blank correctly and is polite and generous enough.
Option ‘d’ is Could. It cannot be the correct option as it expresses an ability that was supposed to show in the past. So, we will eliminate this option as well. Hence, option ‘c' is the correct option.

Note:
All the other options are plausible distractions. Option ‘a’ suggests an ability; and option ‘b’ expresses certainty or assurance with which a certain act is to be done in the future.