The correct word to fill in the blank is who.
The word "who is used to refer to a person. In this sentence, the speaker is referring to a specific girl who is going to IIT, Delhi. The other options are not as appropriate.
- Which is used to refer to a thing. In this sentence, the speaker is not referring to a thing, but to a person.
- That can be used to refer to a person or a thing. However, it is more commonly used to refer to a thing. In this sentence, the speaker is specifically referring to a person, so it would not be appropriate to use the word "that."
- Whom is the objective case of the word "who." It is used when the person is the object of the verb. In this sentence, the person is not the object of the verb, so it would not be appropriate to use the word "whom."
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