Explanation:

- Correct Answer: Option 1 - Bharatanatyam

- 'Alarippu' is a traditional dance piece that is often performed as the opening number in a Bharatanatyam recital. It is a dance of rhythm and includes synchronized movements of the body and head with intricate patterns aligned with the beats of the music.

- Option 2 - Kathakali

- Kathakali is a classical dance-drama from Kerala known for its elaborate costumes, detailed gestures, and well-defined body movements. It primarily focuses on storytelling and enactment of mythological narratives rather than pieces like 'Alarippu.'

- Option 3 - Odissi

- Odissi is a dance form from Odisha, characterized by its fluid movements, expressions, and sculpturesque poses. It does not traditionally feature a piece called 'Alarippu.'

- Option 4 - Kathak

- Kathak is a dance form from North India, known for its intricate footwork and spins. Like Odissi and Kathakali, Kathak does not include 'Alarippu' in its repertoire.