The correct answer is option 'D' - None of the mentioned.

Explanation:
Slopes extending to infinity refer to sloping surfaces that continue indefinitely without reaching a stable or flat point. None of the options provided in the question (inclined face of Earth dams, embankments, or cuts) represent slopes that extend to infinity.

a) Inclined face of Earth dams:
An inclined face of an Earth dam is a sloping surface designed to resist the pressure of the water stored behind the dam. While the slope may be steep, it does not extend to infinity. The slope eventually reaches a stable point where it transitions into the flat top of the dam.

b) Embankments:
Embankments are constructed slopes used in various engineering applications such as roadways, railways, and canals. These slopes are designed to provide stability and prevent erosion. However, like the inclined face of Earth dams, embankments do not extend to infinity. They have a finite length and eventually reach a stable point or transition into a flat surface.

c) Cuts:
Cuts refer to excavations made in the ground surface for various purposes, such as road construction, building foundations, or mining operations. These excavations create sloping surfaces. However, similar to the previous options, cuts do not extend to infinity. They have a limited depth and length and eventually reach a stable point or transition into a flat surface.

Conclusion:
In summary, none of the options provided in the question represent slopes extending to infinity. While the inclined face of Earth dams, embankments, and cuts are all examples of sloping surfaces, they have finite lengths and eventually reach stable points or transition into flat surfaces.