Question 1

A cube is painted on all six faces with different colors. The cube is then cut into 8 smaller cubes of equal size. How many of the smaller cubes have exactly 3 colored faces?

Accepted Answer

This question tests understanding of how a cube divides when cut into smaller cubes and which pieces have painted faces.

Question 2

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

Accepted Answer

This question tests the fundamental property of opposite faces on a standard die/cube. On a standard cube, opposite faces always sum to 7. If face 1 is on top, face 6 must be on the bottom. The constraint that face 2 is facing you helps confirm the cube's orientation but does not change this rule.

Question 3

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. Which face is at the bottom?

Accepted Answer

This question tests the ability to visualize cube orientation and deduce the opposite face using the constraint that opposite faces on a standard die sum to 7.

Question 4

When a cube is unfolded, one face shows a star (★), one shows a circle (●), and one shows a square (■). If the star and circle are on opposite faces, and the square is adjacent to the star, how many faces are adjacent to the circle?

Accepted Answer

This question tests spatial reasoning about cube adjacency: understanding that each face has exactly 4 adjacent faces and 1 opposite face.

Question 5

A cube has six faces. Three faces meeting at one corner are colored red, blue, and green respectively. How many faces are NOT colored?

Accepted Answer

This question tests the ability to visualize a cube's structure and count uncolored faces when three faces meeting at a corner are colored.

Question 6

A cube has six faces. On one face, the number 1 is written; on the opposite face, 6 is written. On another face, 2 is written; on its opposite face, 5 is written. The remaining two opposite faces have 3 and 4 written on them respectively. If the cube is placed such that face 1 is on top and face 2 is facing you, which face is on the bottom?

Accepted Answer

This question tests the ability to visualize a cube's structure and determine opposite faces using the given constraints. Students must track which faces are opposite to each other and use spatial reasoning to determine the bottom face when two faces are fixed in position.

Question 7

A cube has six faces. On one face is a star, on the opposite face is a circle, and on another face is a triangle. The remaining three faces are blank. When the cube is positioned such that the star is on top and the triangle is facing you, which face is on the bottom?

Accepted Answer

Step 1: Identify the three pairs of opposite faces:
- Pair 1: Star (top position given) is opposite to Circle
- Pair 2: Triangle (facing us) is opposite to one blank face
- Pair 3: Two remaining blank faces are opposite to each other

Step 2: Since Star is on top (given), Circle must be on the bottom (opposite faces of a cube are mutually exclusive).

Step 3: Triangle is facing us (front face), so a blank face is at the back (opposite to triangle).

Step 4: The remaining two blank faces are on the left and right sides, opposite to each other.

Step 5: Therefore, when star is on top and triangle faces you, the bottom face is the Circle.

Common Error 1 (Option C): Students might assume the blank face is on bottom, forgetting that opposite faces must pair correctly.

Common Error 2 (Option D): Some might think triangle could be on bottom if they misread the orientation.

Common Error 3 (Option A): Confusing which face is opposite to the star.

Question 8

A cube is unfolded into a net. The net shows: a central square labeled 'A', with squares labeled 'B' (above A), 'C' (right of A), 'D' (below A), 'E' (left of A), and 'F' (above B). When the net is folded into a cube, which two faces are opposite to each other?

Accepted Answer

This question tests the ability to visualize a 3D cube from a 2D net, specifically identifying which faces are opposite when the net is folded. This requires understanding the spatial relationships in the unfolding pattern.

Question 9

A standard die shows opposite faces summing to 7. A die is placed on a table with face 4 on top. It is then rolled forward 3 times, then rolled to the right 2 times, then rolled backward 1 time. Which face is now on top?

Accepted Answer

This question tests sequential tracking of die rotations in different directions. Students must maintain a mental model of which face is on top after each roll, accounting for the constraint that opposite faces sum to 7.

Question 10

A cube has six faces painted with different colors: Red, Blue, Green, Yellow, Orange, and Purple. When Red is on top and Blue is facing you, Green is on your right. When the cube is rotated such that Green is on top and Blue is still facing you, which color is on your left?

Accepted Answer

This question tests the ability to track face positions through a rotation while keeping one face constant, and then determine a third face's position. It requires understanding the spatial relationships between three faces and how they change with rotation.

Question 11

A cube has six faces. On one face, the number 1 is written; on the opposite face, 6 is written. On another face, 2 is written; on its opposite face, 5 is written. The remaining two opposite faces have 3 and 4 written on them respectively. When the cube is placed such that face 1 is on top and face 2 faces you, which face is on the bottom?

Accepted Answer

This question tests the ability to mentally rotate a cube and track opposite face relationships while maintaining spatial orientation constraints.

RRB NTPC Cube & Dice

Cube & Dice— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Cube & Dice — Practice Questions

60-Second Revision — Cube & Dice