Step 1: Rigveda and Sthapatyaveda.
Rigveda is the oldest Veda and is associated with hymns on creation, cosmology, and order.
It is linked with Sthapatyaveda, which deals with architecture and construction principles, deriving its foundation from Rigvedic concepts of cosmic order.
Thus, A - I is correct.
Step 2: Yajurveda and Gandharvaveda.
Yajurveda primarily deals with sacrificial rituals and mantras.
It is associated with Gandharvaveda, which deals with the art of music, dance, and performance, often performed in sacrificial contexts.
Thus, B - II is correct.
Step 3: Samaveda and Dhanurveda.
Samaveda is the Veda of chants and melodies, often recited during rituals.
It is connected with Dhanurveda, the science of warfare and archery, since rhythmic recitation was linked to discipline and martial training.
Thus, C - III is correct.
Step 4: Atharvaveda and Ayurveda.
Atharvaveda contains hymns related to healing, medicine, and life.
It is therefore connected with Ayurveda, the science of life and health.
Thus, D - IV is correct.
Step 5: Conclusion.
So, the correct matching is A - I, B - II, C - III, D - IV.