Each face of a cube can be painted in black or white colours. In how many different ways can the cube be painted?

Correct Answer: (B) 10

By Burnside's Lemma for 2 colors on the 6 faces of a cube under 24 rotational symmetries: the sum of cycle indices is $2^6 + 6(2^3) + 3(2^4) + 6(2^3) + 8(2^2) = 64 + 48 + 48 + 48 + 32 = 240$. Dividing by 24 gives $\frac{240}{24}=10$$\frac{240}{24}$ = 10 distinct coloring patterns.