Two insulting materials of thermal conductivity $$K$$ and $$2K$$ are available for lagging a pipe carrying a hot fluid. If the radial thickness of each material is same

Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A.$$ The ratio of power which can be transmitted by shaft $$A$$ to that of shaft $$B$$ is

Only $$4$$ pairs can be matched :

The process of hot extrusion is used to produce