Step 1: Understanding the Concept:
This question requires matching technical terms from Indian classical dance, as codified in the Nāṭyaśāstra, with their simplified descriptions.
Step 2: Detailed Explanation:
Let's define each term in List-I and find the best fit from List-II.
(A) Cārīs: A Cārī is a coordinated movement of the foot, calf, thigh, and hip of one leg. It represents the movement or gait. The most fitting description is (III) Foot \& Leg Positions, as it primarily concerns the lower limbs.
(B) Maṇḍalas: A Maṇḍala is a pattern traced on the ground by the dancer, created by a series of Cārīs. These patterns can be linear, circular, or complex. (II) Circular Movements is a suitable description for the resulting floor patterns.
(C) Karaṇas: A Karaṇa is a fundamental unit of dance, a transitionary movement combining a specific stance (sthāna), leg movement (cārī), and hand gesture (nṛtta hasta). The Nāṭyaśāstra describes 108 such Karaṇas. While it's a full-body movement, the options are simplified. Between (I) and (IV), both are components. However, often a Karaṇa culminates in a pose.
(D) Aṅgāhāras: An Aṅgāhāra is a longer sequence of dance, composed of six, seven, eight, or nine Karaṇas strung together gracefully.
Step 3: Matching and Final Answer:
Let's use the process of elimination with the clearest matches.
(A) Cārīs definitely matches (III) Foot \& Leg Positions.
(B) Maṇḍalas definitely matches (II) Circular Movements.
Only option (3) has both of these matches: (A)-(III) and (B)-(II). Let's examine the rest of option (3).
(C) Karaṇas is matched with (IV) Movements of Hands. This is an incomplete description, as a Karaṇa involves the entire body, but the Nṛtta Hasta (dance hand gesture) is a critical component. In the context of the given limited choices, this might be the intended, albeit simplified, match.
(D) Aṅgāhāras is matched with (I) Dance Postures. An Aṅgāhāra is a sequence of movements, not a single posture. However, as it is composed of Karaṇas (which are often viewed as poses), this could be the intended logic.
Given that the first two matches (A-III, B-II) are strong and unique to option (3), it is the most plausible correct answer despite the imprecision in the other two pairings.