Cube & Dice

3 practice questions on Cube & Dice for MP Police PC, with answers

Shishya's practice questions, written with AI. Each answer was checked by an automated second pass, not by a person.

1. 1.A cube is painted red on all faces. It is then cut into 64 smaller identical cubes. How many smaller cubes have exactly two faces painted?

   • (A)24
   • (B)8
   • (C)12
   • (D)16
   Show the answer and solution

   Answer: (A) 24

   Solution: When a cube is cut into 64 smaller identical cubes, it means each edge is divided into 4 equal parts (because 4 x 4 x 4 = 64). So the original cube becomes a 4x4x4 arrangement of smaller cubes. Cubes with exactly two faces painted are located along the edges of the original cube, but not at the corners. Each edge of the original cube has 4 smaller cubes. Of these, 2 are at corners (having 3 faces painted) and 2 are in the middle of the edge (having exactly 2 faces painted). A cube has 12 edges. So the number of smaller cubes with exactly two faces painted = 12 edges x 2 cubes per edge = 24.

   Report an error

2. 2.A dice is thrown four times and its positions are shown below: Position 1 shows faces 2, 3, and 5; Position 2 shows faces 1, 3, and 6; Position 3 shows faces 2, 4, and 6; Position 4 shows faces 1, 4, and 5. What number is opposite to face 3?

   • (A)6
   • (B)4
   • (C)5
   • (D)2
   Show the answer and solution

   Answer: (B) 4

   Solution: From Position 1 and Position 2, faces 1, 2, 5, and 6 are adjacent to face 3. Since a dice has 6 faces and faces 1, 2, 5, 6 are adjacent to 3, the remaining face 4 must be opposite to face 3.

   Report an error

3. 3.A cube of side 6 cm is painted on all faces and then cut into smaller cubes of side 1 cm. How many smaller cubes will have no face painted?

   • (A)64
   • (B)48
   • (C)36
   • (D)24
   Show the answer and solution

   Answer: (A) 64

   Solution: The original cube has side 6 cm. When cut into smaller cubes of side 1 cm, we get 6 x 6 x 6 = 216 smaller cubes in total. Cubes with no face painted are those completely inside the original cube, not touching any outer face. After cutting, the inner unpainted cubes form a smaller cube. Since the outer layer (1 cm thick) on all sides is painted, the inner unpainted cube has side = 6 - 2 = 4 cm (we subtract 2 because we remove 1 cm from each of two opposite sides). Number of smaller cubes with no face painted = 4 x 4 x 4 = 64.

   Report an error