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Agniveer Army CEE Cube & Dice

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This page covers Agniveer Army CEE Cube & Dice with complete concept notes, 6 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Cube & Dice— Rules & Concept

Core ConceptRead this first — the foundation of the topic

A cube is a three-dimensional object with 6 faces, 12 edges, and 8 vertices. Each face is a square. In SSC CGL exams, cube and dice questions test your ability to visualize how a flat pattern folds into a 3D shape or how a cube looks when rotated. Key Rules for Cubes:

1. Opposite faces never touch each other when the cube is folded 2. Adjacent faces share a common edge

3. When a cube is cut, count the pieces formed 4. In dice problems, opposite faces always add up to 7 (1-6, 2-5, 3-4)

Main Question Types: - Net to Cube: Given a flat pattern, identify which cube it forms

- Cube Views: Different views of the same cube from various angles - Dice Problems: Find opposite faces or adjacent faces

- Cube Cutting: Calculate pieces when cube is cut by planes Shortcut for Net Problems:

Use the 'Corner Method' - pick any corner in the net and trace which three faces meet at that corner. In the answer choices, the same three faces must meet at one corner. This eliminates wrong options quickly.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Identify which faces are opposite to each other in the net.

2
Step 2

Faces that are separated by exactly one face in between are opposite.

3
Step 3

In the net A-B-C-D, face A is opposite to face C (one face B in between).

4
Step 4

Face E is above B, so E is opposite to F (which is below C).

5
Step 5

Face B is opposite to face D.

6
Step 6

Since A is at bottom, its opposite face C will be at top. Answer: Face C For Dice Problems: Remember the standard dice pattern: 1 opposite 6, 2 opposite 5, 3 opposite 4. If you see faces 1, 2, 3 meeting at a corner, you know 6, 5, 4 meet at the opposite corner. Cube Cutting Formula: If a cube is cut by n planes parallel to faces: Total pieces = (n₁ + 1) × (n₂ + 1) × (n₃ + 1), where n₁, n₂, n₃ are cuts along length, breadth, and height.

Exam TrapsCommon mistakes students make — avoid these

Students often confuse adjacent faces with opposite faces. Remember - opposite faces never appear together in any single view of a cube. If two faces are visible together in a view, they cannot be opposite faces.

Key Points to Remember

  • A cube has 6 faces, 12 edges, and 8 vertices with each face being a perfect square
  • Opposite faces in a cube never share an edge or vertex with each other
  • In standard dice, opposite faces always sum to 7: (1,6), (2,5), (3,4)
  • Net to cube problems: faces separated by one face in between are opposite
  • Corner method: three faces meeting at any corner must be consistent in all views
  • Cube cutting formula: pieces = (cuts+1) along each dimension multiplied together
  • Adjacent faces share a common edge and can be seen together in cube views
  • If two faces appear together in any view, they cannot be opposite faces

Exam-Specific Tips

  • Standard dice opposite pairs sum to 7: 1-6, 2-5, 3-4
  • A cube has exactly 6 faces, 12 edges, and 8 vertices
  • Each vertex of a cube is formed by exactly 3 faces meeting together
  • Maximum 3 faces of a cube can be visible from any single viewpoint
  • In net problems, faces separated by exactly one face are opposite
  • Cube cutting by n parallel planes creates (n+1) pieces in that direction
  • Each face of a cube is adjacent to exactly 4 other faces
  • Each edge of a cube is shared by exactly 2 faces
Practice MCQs

Cube & Dice — Practice Questions

6graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

A standard cube has its faces numbered 1 to 6, where opposite faces always sum to 7. If face 1 is on top and face 2 is facing you, which face is on the bottom?

Practice 2easy

A die is placed on a table with face 3 touching the surface. Face 5 is facing north. Which face is facing south?

Practice 3medium

When a standard die is rolled, the sum of the top and bottom faces is always 7. If the left face shows 4 and the die is rotated to bring the left face to the top, what is the sum of the new left and right faces?

Practice 4medium

A cube has six faces. If one corner vertex touches three faces labeled A, B, and C, how many other vertices of the cube also touch exactly three faces each?

Practice 5medium

A standard die has faces numbered 1 to 6, where opposite faces always sum to 7. If a die is positioned with 2 on top and 3 facing you, which number is on the bottom?

Practice 6hard

A standard cube has its six faces numbered 1 through 6, where opposite faces always sum to 7. When the cube is positioned so that face 2 is on top and face 3 faces you directly, which face is on the bottom?

60-Second Revision — Cube & Dice

  • Remember: Opposite faces never appear together in any cube view
  • Formula: Dice opposite pairs always sum to 7 (1-6, 2-5, 3-4)
  • Trick: Use corner method - trace three faces meeting at any corner
  • Pattern: In nets, faces with one face gap between them are opposite
  • Cutting: Total pieces = (cuts+1) multiplied for each dimension
  • Trap: Don't confuse adjacent faces with opposite faces
  • Quick check: Maximum 3 faces visible from any single angle
←Counting Figures
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