7.

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

UPSC - 2019

8.

Each of the six different faces of a cube has been coated with a different colour i.e., V, I, B, G, Y and O. Following information is given:

1. Colours Y, O and B are on adjacent faces.

2. Colours I, G and Y are on adjacent faces.

3. Colours B, G and Y are on adjacent faces.

4. Colours O, V and B are on adjacent faces.

Which is the colour of the face opposite to the face coloured with O?

UPSC - 2015

9.

A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube. The number of small cubes with only one of the sides painted is:

UPSC - 2016

10.

A dice is numbered from 1 to 6 in different ways. If 1 is adjacent to 2, 3 and 5, then which of the following statements is necessarily true?

A.

3 is opposite to 5

B.

2 is opposite to 6

C.

1 is adjacent to 3

D.

3 is adjacent to 5

11.

Four positions of the same dice are shown. Select the number that will be on the face opposite to the one showing ‘3’.

12.

Which number is in opposite of 2 ?