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.

Use of 'Need' : As a model auxiliary verb in negative terms, it indicates absence of obligation. It expresses the speaker's authority or advice and is used for the present and the future. For example :

You needn't type this letter.   (The speaker is the authority; could be his boss.) .

In the question : -

1. Nobody ____________ know the name of the person who made the complaint .

In this sentence , need is the correct modal that can be placed in the blank part as it is used to denotes an unnecessary action which was nevertheless performed.

2. You ___________ take off your shoes.

In this sentence , needn't  is the correct modal that can be placed in the blank part as it is used mostly in the negative form to indicate that there is no obligation or necessity to do something .

Thus , the Correct Option is D , which is 1. Need 2. Needn't .

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.

Use of 'Need' : As a model auxiliary verb in negative terms, it indicates absence of obligation. It expresses the speaker's authority or advice and is used for the present and the future. For example :

You needn't type this letter.   (The speaker is the authority; could be his boss.) .

In the question : -

1. Not a thing ___________ change on this page.

In this sentence , need is the correct modal that can be placed in the blank part as it is used to show no obligation or necessity to do something .

2. Let’s forget about it. No one ___________ know about it.

In this sentence , need is the correct modal that can be placed in the blank part as it is used to show no obligation or necessity to do something .

Thus , the Correct Option is A , which is 1. Need 2. Need .

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.

Use of 'Need' : As a model auxiliary verb in negative terms, it indicates absence of obligation. It expresses the speaker's authority or advice and is used for the present and the future. For example :

You needn't type this letter.   (The speaker is the authority; could be his boss.) .

In the question : -

1. You _________ bought so much food. There are only three of us staying for the weekend .

In this sentence , needn't have is the correct modal that can be placed in the blank part as it is used to denotes an unnecessary action which was nevertheless performed .

2. You don’t _______ to mention this to your father.

In this sentence , need is the correct modal that can be placed in the blank part as it is used to show an unnecessary action which was nevertheless performed .

3. Does it _____________ to be so dark in here?

In this sentence , need is the correct modal that can be placed in the blank part as it is used to ask about a question  whether an action is necessary or not .

Thus , the Correct Option is D , which is 1. Needn't have 2. Need 3. Need .