Step 1: Conceptual Understanding: This task involves correlating technical terms from Indian classical dance, as defined in the Nāṭyaśāstra, with their simplified explanations.
Step 2: Detailed Explanation: We will define each term in List-I and identify the most appropriate match from List-II.
(A) Cārīs: A Cārī is a coordinated movement of the foot, calf, thigh, and hip of one leg, representing movement or gait. The most fitting description is (III) Foot & Leg Positions, as it primarily pertains to the lower limbs.
(B) Maṇḍalas: A Maṇḍala is a pattern traced on the ground by the dancer, formed by a sequence of Cārīs. These patterns can be linear, circular, or complex. (II) Circular Movements accurately describes the resulting floor patterns.
(C) Karaṇas: A Karaṇa is a fundamental unit of dance, a transitional movement combining a specific stance (sthāna), leg movement (cārī), and hand gesture (nṛtta hasta). The Nāṭyaśāstra outlines 108 Karaṇas. While it is a full-body movement and options are simplified, the Nṛtta Hasta is a key component.
(D) Aṅgāhāras: An Aṅgāhāra is an extended dance sequence composed of six, seven, eight, or nine gracefully linked Karaṇas.
Step 3: Matching and Final Answer: We will use elimination based on the most definitive matches.
(A) Cārīs clearly matches (III) Foot & Leg Positions.
(B) Maṇḍalas clearly matches (II) Circular Movements.
Option (3) is the only one containing both these matches: (A)-(III) and (B)-(II). Let's review the remaining pairings in option (3).
(C) Karaṇas is matched with (IV) Movements of Hands. This is an incomplete depiction, as a Karaṇa involves the entire body, but the Nṛtta Hasta (dance hand gesture) is a crucial element. Within the constraints of the provided options, this may be the intended, albeit simplified, association.
(D) Aṅgāhāras is matched with (I) Dance Postures. An Aṅgāhāra is a sequence of movements, not a static posture. However, given its composition of Karaṇas, which can often be interpreted as poses, this might represent the intended logic.
Considering the strong and exclusive matches for (A-III) and (B-II) in option (3), it emerges as the most probable correct answer, despite potential imprecision in the other pairings.