Challenge Prelims V1.0 – Day 64 – CSAT Paper

1. A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other 4 cubes are big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted? (UPSC 2019)

2. The figure below shows the opened up version of a cube with numbers on each face

What is the number on the face opposite to that containing the number 5?

3. A dice is numbered from 1 to 6. If 1 is adjacent to 2, 3 and 4, then which of the following is necessarily true?

4. Two opposite sides of a cube is painted red. The cube is then cut into 64 number of identical smaller cubes. Then, what is the ratio of the number of smaller cubes which have at least one side painted to the number of smaller cubes which is not painted at all?

5. Two positions of dice are shown below. How many dots will appear on the face opposite to face containing 4 dots?