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 To be:  The verb to be is occasionally used as a modal auxiliary. but it is a strange verb, as it can have either a value of futurity, or a value of obligation , or something between the two supposition.

To be + Infinitive :  This expression is used to

(A)  Express plan : -

• I am to make a speech tomorrow.

In the question : -

1. She _____________  leave for the States after marriage.

In this sentence , is to is the correct modal that can be placed in the blank part as it is used to express about plan .

2. I ___________ make three of these cakes .

In this sentence , am to is the correct modal that can be placed in the blank part as it is used to express necessity .

3. I ____________  work in London next year .

In this sentence , am to is the correct modal that can be placed in the blank part as it is used to express necessity .

Thus , the Correct Option is D , which is 1. Is to 2. Am to 3. Am to .

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 To be:  The verb to be is occasionally used as a modal auxiliary. but it is a strange verb, as it can have either a value of futurity, or a value of obligation , or something between the two supposition.

To be + Infinitive :  This expression is used to

(A)  Express plan : -

• I am to make a speech tomorrow.

In the question : -

1. The train ___________  leave at 8.

In this sentence , was to is the correct modal that can be placed in the blank part as it means the train was supposed to leave .

2. She __________  leave for the States for higher study.

In this sentence , was to is the correct modal that can be placed in the blank part as it is used to express plan .

3. You _____________  get better marks next time. 

In this sentence , are to is the correct modal that can be placed in the blank part as it is used to express mild obligation .

Thus , the Correct Option is A , which is 1. Was to 2. Was to 3. Are to .

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 To be:  The verb to be is occasionally used as a modal auxiliary. but it is a strange verb, as it can have either a value of futurity, or a value of obligation , or something between the two supposition.

To be + Infinitive :  This expression is used to

(A)  Express plan : -

• I am to make a speech tomorrow.

In the question : -

1. The servant ___________  remain in the house till we return .

In this sentence , Is to is the correct modal that can be placed in the blank part as it is used to express order .

2. She ___________  leave for the States for higher study .

In this sentence , Was to is the correct modal that can be placed in the blank part as it is used to express plan .

Thus , the Correct Option is C , which is 1. Is to 2. Was to .