Final answer:
The correct answer is 'a. to live'. The pattern 'to be + adjective/noun + to-infinitive' is used to express desires or feelings. 'To live' is the correct form in this case.
Step-by-step explanation:
The correct answer is a. to live.
When expressing our desires or feelings, we use the pattern 'to be + adjective/noun + to-infinitive'. In this case, the adjective 'happy' is followed by the noun 'to live', indicating the student's desire or happiness to live in India. The other options are incorrect because they do not follow this pattern. For example, 'to have lived' implies that the student is happy for a past action, 'to be lived' implies that something else is happy to be lived, and 'to be living' implies ongoing happiness. Therefore, the correct answer is 'to live'.