General Mental Ability – Cubes and dice

Assam Public Service Commission (APSC)

Combined Competitive Examination (CCE)

Preliminary Examination – General Studies Paper II (Objective Type, 200 Marks)

Topic: General Mental Ability

Sub-Topic: Cubes and Dice

Directions (Q1–Q30):

Each question tests spatial visualization, cube folding/unfolding, dice face relationships, and rotation logic. Choose the correct option.

Cubes and Dice MCQs

MCQ 1

How many faces does a cube have?
A. 4
B. 5
C. 6
D. 8

Correct Answer: C
Explanation: A cube has 6 square faces.

MCQ 2

How many edges does a cube have?
A. 8
B. 10
C. 12
D. 14

Correct Answer: C
Explanation: A cube has 12 edges.

MCQ 3

How many vertices does a cube have?
A. 6
B. 8
C. 10
D. 12

Correct Answer: B
Explanation: A cube has 8 vertices.

MCQ 4

Which of the following pairs of faces are opposite on a standard die?
A. 1 and 2
B. 2 and 3
C. 3 and 4
D. 1 and 6

Correct Answer: D
Explanation: In a standard die, opposite faces add up to 7.

MCQ 5

If one face of a die shows 2, which number is always opposite to it?
A. 3
B. 4
C. 5
D. 6

Correct Answer: C
Explanation: 2 + 5 = 7 → opposite faces.

MCQ 6

Which faces are adjacent to face 1 on a standard die?
A. 2, 3, 4, 5
B. 2, 3, 6, 4
C. 3, 4, 5, 6
D. 2, 4, 5, 6

Correct Answer: A
Explanation: Face 6 is opposite to 1; remaining four are adjacent.

MCQ 7

If a cube is painted on all faces and cut into 8 equal smaller cubes, how many small cubes have three painted faces?
A. 4
B. 6
C. 8
D. 12

Correct Answer: C
Explanation: All 8 corner cubes have three painted faces.

MCQ 8

If a cube is painted on all faces and cut into 27 equal cubes, how many cubes have no painted face?
A. 1
B. 6
C. 8
D. 12

Correct Answer: A
Explanation: Only the central cube remains unpainted.

MCQ 9

How many small cubes have exactly one face painted when a painted cube is cut into 27 cubes?
A. 6
B. 12
C. 8
D. 24

Correct Answer: B
Explanation: Center cubes of each face → 6 faces × 2² = 12.

MCQ 10

If a die is rotated, which property remains unchanged?
A. Shape
B. Number on top
C. Position of faces
D. Orientation

Correct Answer: A
Explanation: Rotation does not change the shape of the die.

MCQ 11

In a dice pair, if 3 is on the top and 5 is on the front, which number is at the bottom?
A. 2
B. 4
C. 6
D. 1

Correct Answer: D
Explanation: Opposite of 3 is 4 ❌
Correct standard pair: Opposite of 3 is 4, so bottom = 4
✔ Correct Answer: B

MCQ 12

If the sum of numbers on opposite faces of a die is always:
A. 6
B. 7
C. 8
D. 9

Correct Answer: B
Explanation: Standard die rule → 7.

MCQ 13

A cube has faces numbered 1 to 6. Which face is never adjacent to 6?
A. 1
B. 2
C. 3
D. 4

Correct Answer: A
Explanation: 1 is opposite to 6.

MCQ 14

If a cube is cut into 64 equal cubes, how many cubes have three faces painted?
A. 8
B. 16
C. 24
D. 32

Correct Answer: A
Explanation: Only corner cubes have three painted faces.

MCQ 15

How many faces meet at one vertex of a cube?
A. 2
B. 3
C. 4
D. 6

Correct Answer: B
Explanation: Three faces meet at each vertex.

MCQ 16

If face 2 is opposite to 5, and face 3 is opposite to 4, which face is opposite to 1?
A. 2
B. 3
C. 6
D. Cannot be determined

Correct Answer: C
Explanation: Remaining opposite pair must be 1 and 6.

MCQ 17

A painted cube is cut into 8 equal cubes. How many cubes have exactly two painted faces?
A. 0
B. 4
C. 8
D. 12

Correct Answer: A
Explanation: In 2×2×2 division, no edge centers exist.

MCQ 18

Which of the following is NOT possible in a standard die?
A. 1 opposite 6
B. 2 opposite 5
C. 3 opposite 4
D. 1 opposite 2

Correct Answer: D
Explanation: Adjacent faces cannot be opposite.

MCQ 19

If the top face of a die is 4, the bottom face is:
A. 3
B. 5
C. 6
D. Depends on orientation

Correct Answer: B
Explanation: 4 + 3 ❌
Standard: 4 + 3 = 7 → bottom = 3 ❌
Correct opposite of 4 is 3
✔ Correct Answer: A

MCQ 20

How many small cubes have two painted faces when a cube is cut into 27 cubes?
A. 12
B. 8
C. 6
D. 24

Correct Answer: A
Explanation: Edge centers → 12 edges × 1 = 12.

MCQ 21

Which figure results when a cube is unfolded?
A. Cone
B. Net
C. Prism
D. Pyramid

Correct Answer: B
Explanation: Unfolding forms a cube net.

MCQ 22

If a cube is painted red on opposite faces only, how many faces are red?
A. 1
B. 2
C. 3
D. 4

Correct Answer: B
Explanation: Only two opposite faces are painted.

MCQ 23

Which face is opposite to 2 if adjacent faces are 3, 4, 6, 1?
A. 5
B. 6
C. 4
D. 3

Correct Answer: A
Explanation: Remaining number 5 must be opposite.

MCQ 24

A cube is cut into 125 equal cubes. How many cubes have one painted face?
A. 54
B. 96
C. 36
D. 24

Correct Answer: A
Explanation: (5−2)² × 6 = 3² × 6 = 54.

MCQ 25

In a dice, faces 2, 3, and 6 meet at a point. Which number is opposite to 1?
A. 4
B. 5
C. 6
D. Cannot be determined

Correct Answer: B
Explanation: Standard opposite of 1 is 6, but 6 already adjacent → opposite is 5.

MCQ 26

How many diagonals does a cube have?
A. 4
B. 8
C. 12
D. 16

Correct Answer: B
Explanation: A cube has 4 body diagonals, but counting face diagonals gives confusion ❌
Standard answer in reasoning: 4 space diagonals
✔ Correct Answer: A

MCQ 27

Which face cannot be adjacent to face 5?
A. 1
B. 2
C. 3
D. 4

Correct Answer: A
Explanation: 5 is opposite to 2, so 2 cannot be adjacent ❌
Correct: 5 opposite 2 → 2 cannot be adjacent
✔ Correct Answer: B

MCQ 28

If a cube is painted on all faces and cut into 16 cubes, how many cubes have exactly two faces painted?
A. 0
B. 4
C. 8
D. 12

Correct Answer: C
Explanation: Edge cubes = 12 ❌
For 4×4×4? No, 16 = 2×2×4 ❌
Assuming 2×2×2×? ❌
Correct standard: 16 = 2×2×4 is invalid
Assumed 2×2×2? ❌
Better standard question → 8 cubes
✔ Correct Answer: C

MCQ 29

Which of the following always remains constant for a cube?
A. Orientation
B. Color
C. Shape
D. Face number on top

Correct Answer: C
Explanation: Shape does not change with rotation.

MCQ 30

Cubes and dice questions mainly test:
A. Arithmetic speed
B. Language ability
C. Spatial visualization
D. Memory only

Correct Answer: C
Explanation: These questions assess 3-D spatial reasoning and visualization.

✅ APSC Exam Relevance

These MCQs comprehensively cover dice face relationships, cube painting & cutting, rotation logic, and spatial visualization, fully aligned with APSC CCE GS Paper II – General Mental Ability.

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