The best pair of tropisms that describe the responses of a plant with deep roots and tendrils wrapping around objects are geotropism and thigmotropism.
- Geotropism refers to the plant's growth response to gravity, which is why the roots grow downwards.
- Thigmotropism refers to the plant's growth response to touch, which explains how the tendrils wrap around objects.
So the correct answer is geotropism and thigmotropism.