Kuchipudi dance is accompanied by which system of music?

The correct answer is Carnatic music. Kuchipudi, the classical dance of Andhra Pradesh, is performed to Carnatic music, the classical music tradition of South India. Bharatanatyam of Tamil Nadu is also performed to Carnatic music.

A Kuchipudi performance is accompanied by a small ensemble of musicians. It usually includes a vocalist, who sings the songs; a mridangam player, who provides the rhythm; a violin or veena player and a flute player, who provide the melody; and a nattuvanar (or conductor), who recites the rhythmic syllables and plays the cymbals. The songs are mostly in Telugu, along with some in Sanskrit, and they are set in Carnatic ragas and talas. Many of the songs used in Kuchipudi come from the works of great composers and poets, such as the padams of Kshetrayya, the kirtanas of Annamacharya and Tyagaraja, and the Krishna Leela Tarangini of Narayana Tirtha, which is used for the famous Tarangam item. Unlike most other classical dances, Kuchipudi dancers sometimes also speak or sing parts of their own lines, which reflects the dance-drama origins of the form.

Kuchipudi is named after the village of Kuchipudi in the Krishna district of Andhra Pradesh. It was given its traditional form by Siddhendra Yogi in the 17th century, who wrote the dance-drama Bhama Kalapam. In the 20th century, Vempati Chinna Satyam reshaped it for the solo stage.

About the other options:

Hindustani music is the classical music of North India. It accompanies Kathak.

Rabindra Sangeet is the body of songs composed by Rabindranath Tagore. It is used in Rabindra Nritya.

Sufi music, such as qawwali, comes from the mystical tradition of Islam and is not used as the accompaniment of Kuchipudi.