Which one of the following pairs does not form part of the six systems of Indian Philosophy?

Mimamsa and Vedanta: These are both orthodox schools of Hindu philosophy within the six systems. Nyaya and Vaisheshika: These are also part of the six orthodox systems, known for their focus on logic and epistemology. Sankhya and Yoga: These are considered two of the six orthodox systems, with Sankhya focusing on dualism and Yoga on achieving liberation through practices like meditation.

Lokayata: This was a materialistic philosophy that is not considered part of the six orthodox systems of Hindu philosophy. It emphasized materialism and scepticism towards spiritual concepts. Kapalika: While the exact nature and origin of Kapalika are debated, it's generally not considered among the six orthodox systems. It's associated with tantric practices and rituals that deviate from the mainstream Hindu philosophy.

Therefore, Lokayata and Kapalika are not part of the six established systems of Indian philosophy.