Correct Option (C)
The pair Lokayata and Kapalika does not form part of the six orthodox systems of Indian Philosophy (Shad-darshanas).
- Lokayata, also known as Charvaka, is a heterodox, materialistic school of thought. It rejects the authority of the Vedas and spiritual concepts, thus standing outside the orthodox framework.
- Kapalika refers to a heterodox Tantric sect, known for its specific rituals and practices, rather than a formal philosophical system in the context of the Shad-darshanas.
Incorrect Options:
- Mimamsa and Vedanta: These are two of the six orthodox systems. Mimamsa focuses on the interpretation of Vedic rituals and dharma, while Vedanta explores the ultimate nature of reality (Brahman) and the self (Atman) based on the Upanishads.
- Nyaya and Vaisheshika: These are also orthodox systems. Nyaya is a school of logic and epistemology, concerned with valid knowledge. Vaisheshika is a naturalistic school of atomism and metaphysics, postulating categories of existence.
- Sankhya and Yoga: These are complementary orthodox systems. Sankhya is a dualistic philosophy distinguishing between Purusha (consciousness) and Prakriti (matter). Yoga is a practical discipline for achieving liberation, based on the metaphysical framework of Sankhya.