Fill in the Blanks

The usage of exclamatory mark itself gives the clue for 'may' to be used. 'May' in such cases means 'a wish'.

The answer of this question is to be arrived by using POE i.e., process of elimination. This is a case of present and future ability, and none other than 'can' fits the requirement of the sentence.

Falling of rain is always a matter of probability. The sentence says that 'the sky is overcast'. This means there is more probability of raining. Modal 'may' perfectly fits the requirement of the blank.

This is a case of 'hope' or 'wish'. Except 'would' all the other modals fail to support a wish. Thus, option 4. 

Though this sentence describes a general fact, but the capability of noun (rat) is depicted. As 'rat' does not have the capability to eat a cat, so 'can not' is the perfect choice. 

The auxiliary verb 'did' is used to form the simple past tense. 'I did see him' emphasizes the completed action in the past. 'Does' is present tense and would only be used with third-person subjects (he/she/it), not with the first-person 'I'.

Third-person singular subjects (he, she, it) require the auxiliary verb 'does' in present tense questions. 'Doesn't he?' is the grammatically correct tag question form. 'Don't' is used with first-person (I, we), second-person (you), and plural subjects (they).

'Did' is the past tense auxiliary verb used with all subjects (I, you, he, she, it, we, they) to form questions about completed actions. 'Does' is only for present tense with third-person singular. Without context establishing a specific timeframe, 'Did' is the correct choice for a general question.

Third-person singular subjects (he, she, it) require the auxiliary verb 'does' in present tense. 'Does she?' is grammatically correct for questions about third-person singular subjects. 'Do' is used with first-person (I, we), second-person (you), and plural subjects (they).

Third-person singular subjects (he, she, it) require 'does' in present tense questions. The structure '______ he do?' asks about a habitual or present action, so 'Does' is correct. 'Do' is used with other subjects (I, you, we, they).

The question 'Do you smoke?' uses the auxiliary 'do' with second-person 'you.' The response must maintain the same auxiliary and subject. 'Yes, I do' correctly echoes back the question structure. 'Does' would be incorrect because it's third-person singular.

After the preposition 'of,' the verb must be in the gerund form (-ing). 'Having' is the gerund of 'have.' 'Having been touched' forms the perfect passive gerund, describing an action (or lack thereof) that occurred before the statement. 'Have' and 'has' are finite verb forms and cannot follow prepositions.

Without context specifying tense, both 'Did we?' and 'Do we?' are grammatically complete tag questions. 'Did' works for past tense contexts, 'Do' for present tense. Since the question stem provides no temporal context, both auxiliaries are valid, making option C correct.

With you as the subject, the auxiliary verb for questions in present simple is do.

Question tags use the opposite polarity and tense: didn't (negative past) becomes did (positive past).