The correct pair of tropisms that describe the responses of a plant with deep roots and tendrils wrapping around objects is geotropism and thigmotropism.
- Geotropism (or gravitropism) describes the growth response of a plant in relation to gravity, which would explain the deep roots growing downward.
- Thigmotropism refers to the growth response of a plant to touch or physical contact, which explains the tendrils wrapping around objects.
Thus, the answer is hydrotropism and geotropism.