Nucleate pool boiling is a process in which bubbles are formed at a heated surface submerged in a pool of liquid. The heat transfer in this process is primarily governed by the liquid properties and the condition of the surface. Let's discuss each option in detail to understand why option 'A' is the correct answer.

a) Liquid properties, material, and condition of the surface:
- Liquid properties: The heat flux in nucleate pool boiling depends on the thermophysical properties of the liquid, such as its viscosity, thermal conductivity, and specific heat capacity. These properties determine how efficiently heat can be transferred from the surface to the liquid.
- Material: The material of the surface also plays a significant role in the heat transfer process. Different materials have different thermal conductivities, which affect the rate at which heat is conducted through the surface. Additionally, the surface material can influence the wettability of the liquid, which affects bubble formation and heat transfer.
- Condition of the surface: The condition of the surface, including its roughness, cleanliness, and presence of any coatings, can significantly impact the heat transfer. A rough surface can enhance boiling heat transfer by providing nucleation sites for bubble formation. Surface coatings can also alter the wetting characteristics and affect bubble dynamics.

b) Material of the surface only:
- This option oversimplifies the factors influencing heat transfer in nucleate pool boiling. Heat transfer is a complex process that involves the interaction between the liquid and the surface. Ignoring the liquid properties would lead to an incomplete understanding of the phenomenon.

c) Material and roughness of the surface:
- While the material and roughness of the surface are important factors, they alone do not determine the heat flux in nucleate pool boiling. The liquid properties also play a crucial role in determining the heat transfer rate.

d) Liquid properties and material of the surface:
- This option correctly identifies the key factors influencing heat transfer in nucleate pool boiling. Both the liquid properties and the material of the surface are essential in determining the heat flux. The liquid properties dictate how efficiently heat can be transferred, while the surface material influences the thermal conductivity and wettability.

In summary, option 'A' is the correct answer because the heat flux in nucleate pool boiling depends on a combination of liquid properties, material, and condition of the surface. Ignoring any of these factors would lead to an incomplete understanding of the heat transfer process.