The rate of payment is made per cubic meter (% cu m) for various types of work involved in construction projects. The correct answer to the given question is option 'D', which states that the rate of payment is applicable for all the mentioned cases, including earthwork in excavation, rock cutting, and excavation in trenches for foundation.

Let's understand the explanation for this answer in detail:

a) Earthwork in excavation:
Excavation is an important part of any construction project, and it involves the removal of earth or soil from the ground to create a desired shape or level for the construction. Earthwork in excavation includes activities such as leveling the ground, digging trenches, removing unwanted materials, etc. The rate of payment for earthwork in excavation is calculated per cubic meter (% cu m) of the excavated material. This rate is determined based on factors such as the type of soil, difficulty level, depth of excavation, and equipment used.

b) Rock cutting:
Rock cutting refers to the process of excavating or removing rocks from the ground. This is often required in construction projects where the presence of rocks hinders the progress or the desired shape of the construction. Rock cutting involves the use of heavy machinery, such as rock breakers or excavators, to break the rocks into smaller pieces and remove them from the site. Similar to earthwork in excavation, the rate of payment for rock cutting is also calculated per cubic meter (% cu m) of the rock material removed. The rate may vary depending on the hardness of the rocks, the method used for cutting, and the equipment employed.

c) Excavation in trenches for foundation:
Excavation in trenches for foundation is another type of work that requires payment based on the rate per cubic meter (% cu m). Trenches are dug to create a foundation for various structures, such as buildings, bridges, or pipelines. The depth and width of the trenches may vary depending on the design and requirements of the structure. The rate of payment for excavation in trenches for foundation is determined by considering factors such as the depth and width of the trenches, the type of soil or rock encountered, and the equipment used for excavation.

d) All the above:
Option 'D' states that the rate of payment is applicable for all the cases mentioned above, i.e., earthwork in excavation, rock cutting, and excavation in trenches for foundation. This means that regardless of the type of work involved, the payment is determined based on the rate per cubic meter (% cu m) of the material excavated or removed. This allows for a standardized method of calculating the payment, considering factors such as the volume of work, the complexity of the task, and the equipment and resources utilized.

In conclusion, the correct answer to the given question is option 'D' because the rate of payment is made per cubic meter (% cu m) for all the mentioned cases, including earthwork in excavation, rock cutting, and excavation in trenches for foundation. This method provides a fair and consistent approach to determine the payment for the work done in construction projects.