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

The six orthodox systems (shad-darshana) are Nyaya, Vaisheshika, Samkhya, Yoga, Purva Mimamsa and Vedanta (Uttara Mimamsa). Option C is the odd one out because neither Lokayata nor Kapalika belongs to this list.

• A is correct: Mimamsa and Vedanta are both among the six.
• B is correct: Nyaya (Gautama) and Vaisheshika (Kanada) form a standard pair.
• D is correct: Samkhya (Kapila) and Yoga (Patanjali) are both orthodox systems.
• C does not form part of the six: Lokayata, also called Charvaka, is a materialist school that rejects the Vedas. Kapalika is a Shaiva ascetic sect linked to tantric practice, not a darshana.

The core concept is the astika and nastika divide. Schools that accept Vedic authority are astika. Charvaka, Jainism and Buddhism are nastika. This distinction matters for Mains GS-1 on Indian thought and for the Bhakti and Buddhist sections of the culture syllabus.

Trap: Aspirants treat Lokayata as a darshana simply because it is a famous school of thought. Remember that the six-darshana list is fixed and Charvaka sits outside it.