Solution:(a) Movement and Mimesis: The Idea of Dance in the Sanskritic Tradition is a scholarly book by Mandakranta Bose
(b) Mapping Critical Dance Studies in India by Urmimala Sarkar Munshi is a comprehensive book that provides a critical understanding of dance studies in India.
(c) Butting Out: Reading Resistive Choreographies by Ananya Chatterjea is a significant work in the field of dance studies.
(d) Unfinished Gestures: Devadasis, Memory, and Modernity in South India by Davesh Soneji is a comprehensive study that explores the social and cultural history of devadasis (temple dancers) in South India.
So, the correct answer is A. III, IV, I, II.