Explanation:

- Correct Answer: Option 2 - Bharatanatyam

- T Balasaraswati was an iconic figure in the realm of classical Indian dance, remarkable for her mastery and innovation in Bharatanatyam.

- She played a pivotal role in popularizing Bharatanatyam, which originates from Tamil Nadu in South India, marked by intricate footwork, expressive hand gestures (mudras), and facial expressions.

- Option 1 - Kuchipudi

- A dance style from Andhra Pradesh, known for its graceful movements and strong narrative element through drama.

- Option 3 - Kathak

- Originates from Northern India, Kathak is distinguished by its precise footwork, spins, and storytelling through dance.

- Option 4 - Kathakali

- A dance-drama from Kerala, characterized by elaborate costumes, heavy makeup, and intricate facial expressions.