Modals: They are verbs which are used before the main verb to express ability, possibility, obligation, permission, suggestion, request, certainty or necessity.They indicate the attitude, intention and the mood of the speaker.

• They cannot be used alone in a sentence.
• In case of Questions they are used alone.
• They are not affected by the change in person i.e. first, second or third form.
• Present Participle or Past Participle form of a verb is never used with a modal.

May and Might:

Use of May

1. To show or ask for permission. e.g.

       May I borrow two books from the library ?

Use of Might:

1. The use of might for request expresses more politeness, hesitation or lack of confidence of the  speaker. e.g.

       Might I borrow your golden necklace?

In the question : -

1. You __________ have a cookie after you finish your dinner.

In this sentence , may is the correct modal that can be placed in the blank part as it is used to ask for permission .

2. ___________ I borrow your pen ?

In this sentence , might is the correct modal that can be placed in the blank part as it is used to ask for permission .

Thus , the Correct Option is D, which is 1. May 2. Might .

Modals: They are verbs which are used before the main verb to express ability, possibility, obligation, permission, suggestion, request, certainty or necessity.They indicate the attitude, intention and the mood of the speaker.

• They cannot be used alone in a sentence.
• In case of Questions they are used alone.
• They are not affected by the change in person i.e. first, second or third form.
• Present Participle or Past Participle form of a verb is never used with a modal.

May and Might:

Use of May

1. To show or ask for permission. e.g.

       May I borrow two books from the library ?

Use of Might:

1. The use of might for request expresses more politeness, hesitation or lack of confidence of the  speaker. e.g.

       Might I borrow your golden necklace?

In the question : -

1. Shivani ___________  failed the exam because she was sick.

In this sentence , may have is the correct modal that can be placed in the blank part as it show express possibility in the past .

2. It ___________ rain later on. We’d better take an umbrella.

In this sentence , may is the correct modal that can be placed in the blank part as it expresses more possibility .

3. Mr Hunt is late. He _____________  missed his train.

In this sentence , may have is the correct modal that can be placed in the blank part as it express possibility in the past .

Thus , the Correct Option is A , which is 1. May have 2. May 3. May have .

Modals: They are verbs which are used before the main verb to express ability, possibility, obligation, permission, suggestion, request, certainty or necessity.They indicate the attitude, intention and the mood of the speaker.

• They cannot be used alone in a sentence.
• In case of Questions they are used alone.
• They are not affected by the change in person i.e. first, second or third form.
• Present Participle or Past Participle form of a verb is never used with a modal.

May and Might:

Use of May

1. To show or ask for permission. e.g.

       May I borrow two books from the library ?

Use of Might:

1. The use of might for request expresses more politeness, hesitation or lack of confidence of the  speaker. e.g.

       Might I borrow your golden necklace?

In the question : -

1. Do you think the company _____________ hire more people next year ?

In this sentence , might is the correct modal that can be placed in the blank part as it show possibility .

2. We ___________ go out later. I’m not sure. 

In this sentence , may is the correct modal that can be placed in the blank part as it show possibility .

3. Tom ___________ win this game. He’s been playing very well recently.

In this sentence , might is the correct modal that can be placed in the blank part as it show possibility .

Thus , the Correct Option is C , which is 1. Might 2. May 3. Might .