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SSC MTS Cube & Dice

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This page covers SSC MTS Cube & Dice with complete concept notes, 13 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

13graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

A cube has faces numbered 1 to 6. When face 1 is on top and face 2 is facing you, which face is at the bottom?

Practice 2easy

Two dice are placed side by side. The left die shows 2 on top and 3 facing you. The right die shows 5 on top and 4 facing you. What is the sum of the bottom faces of both dice?

Practice 3easy

A cube has six faces labeled with colors: Red, Blue, Green, Yellow, Orange, and Purple. Red is opposite to Blue. Green is opposite to Yellow. If Orange is on top and Red is facing you, which color is on the bottom?

Practice 4easy

A die shows face 6 on top. When you rotate the die 90 degrees to the right (tilting it toward your right side), which face comes to the top?

Practice 5medium

A cube is unfolded into a net. The net shows: a central square with squares attached to all four sides, and one square attached above the top square. If the central square is the base, which face is opposite to the base?

Practice 6medium

A cube has faces numbered 1 through 6. When the cube is positioned with face 1 on top and face 2 facing north, face 3 is on the right. The cube is then rotated 90° clockwise (when viewed from above). After this rotation, which face is now facing north?

Practice 7medium

A standard die has opposite faces summing to 7. If a die shows face 2 on top and face 3 facing north, which face is facing west?

Practice 8hard

A cube has faces labeled with numbers 1 through 6, where opposite faces sum to 7. A die is positioned with 3 on top and 4 facing you. The die is rolled to the right, then rolled forward, then rolled to the left. After these three rolls, what is the sum of the numbers on the top and front faces?

Practice 9hard

A cube has faces numbered 1 to 6. When face 1 is on top and face 2 is facing you, face 3 is on your right. If the cube is rolled forward (away from you) once, then rolled to the right once, what face is now facing you?

Practice 10hard

A standard die has opposite faces summing to 7. A die is placed with 1 on top and 2 facing you. The die is rolled away from you (forward), then rolled to your left, then rolled toward you (backward). After these three rolls, which number is now facing you?

Practice 11hard

A cube has six faces with symbols: ★, ●, ■, ▲, ◆, and ○. From the given views: View 1 shows ★ opposite to ●, View 2 shows ■ opposite to ▲, and View 3 shows ◆ opposite to ○. If ★ is on top and ■ is facing you, which symbol is on your right?

Practice 12hard

A transparent cube has colored faces: Red, Blue, Green, Yellow, Orange, and Purple. When Red is facing you and Blue is on top, Green is on your right. The cube is then rotated 180° around the vertical axis (top-bottom axis). After this rotation, if you want Green to be facing you again, how many 90° rotations around the front-back axis are needed?

Practice 13hard

An unfolded cube net shows: Top face = A, Bottom face = B, Front face = C, Back face = D, Left face = E, Right face = F. The net is folded into a cube. If face A is placed on a table (bottom), and the cube is rotated 90° clockwise when viewed from above, which face is now on the table?

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
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