This question tests the correct grammatical structure after the adjective "fortunate". The word "fortunate" is typically followed by an infinitive (to + verb) to explain why the person is fortunate.

Let's analyze the structure:

Subject (Janet) + be verb (is) + adjective (fortunate) + infinitive phrase (to have been given)

The action of "being given the scholarship" happened in the past relative to the present state of "being fortunate". Therefore, we need the perfect infinitive passive form: "to have been given". This form indicates a completed action that happened before the present time.

Step 1: Identify the required structure after "fortunate". It is an infinitive (to + verb). This immediately rules out options that do not start with "to".

Step 2: From the remaining options, determine the correct verb form. The giving of the scholarship is a past event, so we need the perfect form ("to have been given") rather than the simple form ("to be given").

Final Answer: The most appropriate word is to have been given.
The complete sentence is: Janet is fortunate to have been given a scholarship.

Related Concepts & Theory

Adjective + Infinitive: Many adjectives, such as fortunate, lucky, happy, glad, surprised, etc., are commonly followed by an infinitive clause to explain the reason for the feeling or state.

• I was surprised to see you.
• She will be happy to help.

Perfect Infinitive: The perfect infinitive (to have + past participle) is used to show that the action of the infinitive happened before the time of the main verb.

• He seems to have forgotten the meeting. (He forgot it before now.)

Passive Infinitive: The passive infinitive (to be + past participle) is used when the subject of the main clause is the receiver of the infinitive's action.

• The package is to be delivered tomorrow.

In this question, both concepts are combined into the perfect passive infinitive: "to have been given".

Applicable Formulae (Grammar Rules)

Rule 1: Subject + be + adjective + to-infinitive

Rule 2: For an action in the infinitive that is complete, use to have + past participle (Perfect Infinitive).

Rule 3: If the subject receives the action of the infinitive, use the passive voice: to be + past participle or to have been + past participle.