Open-cast mining is a common method used for the extraction of:

Coal
Oil
Limestone
Sillimanite

The correct answer is: a) Coal.

Open-cast mining is a surface mining technique in which mineral ores and coal are extracted from the earth by removing overlying rock and soil. It is the most common form of mining for coal and other minerals that are close to the surface.

Open-cast mining is a relatively inexpensive and efficient way to extract minerals, but it can have a significant impact on the environment. The process of removing the overburden can damage land and water resources, and the dust and noise from the mining operation can be a nuisance to nearby residents.

Coal is a fossil fuel that is formed from the remains of ancient plants and animals. It is a major source of energy in the world, and it is used to generate electricity, power transportation, and heat homes and businesses.

Oil is a non-renewable energy source that is formed from the remains of ancient marine organisms. It is a liquid hydrocarbon that is found in underground reservoirs. Oil is used to produce gasoline, diesel fuel, and other petroleum products.

Limestone is a sedimentary rock that is composed of calcium carbonate. It is a common building material, and it is also used in the production of cement and other products.

Sillimanite is a mineral that is composed of aluminum silicate. It is used in the production of ceramics, glass, and other products.