The correct pair of tropisms that describe the plant's responses of having deep roots and tendrils that wrap around objects is hydrotropism and thigmotropism.
- Hydrotropism refers to the growth of plant roots toward moisture or water sources (deep roots).
- Thigmotropism is the growth response to touch or physical contact, which explains the tendrils wrapping around objects.
Therefore, the best answer is: hydrotropism and thigmotropism.