MAT - DICE PROBLEMS - MCQs - 7

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🎲 3D Dice Reasoning – NMMS & NTSE MCQ Quiz

1. Analyzing the two 3D orientations of the dice below, which face sits opposite to face 6?

Orientation A

Orientation B

A) 1 dot B) 2 dots C) 4 dots D) 5 dots

Correct Answer: B (2 dots)

Detailed Explanation: Face 6 is adjacent to faces with 1, 3, 4, and 5 dots. The only remaining face that cannot be adjacent is 2 dots, making 2 opposite to 6.

2. In a standard fair die (where opposite faces sum to 7 dots), which face lies opposite to 3 dots?

Standard Die View

A) 1 dot B) 2 dots C) 4 dots D) 5 dots

Correct Answer: C (4 dots)

Detailed Explanation: By definition, the sum of dots on opposite faces of any standard die equals 7. Thus, 7 − 3 = 4 dots.

3. If face 1 dot shares edges with faces of 2, 3, 4, and 5 dots, how many dots are on the opposite face?

Top Face (1 Dot)

A) 6 dots B) 5 dots C) 2 dots D) 3 dots

Correct Answer: A (6 dots)

Detailed Explanation: A single face on a 6-sided die can only have 4 adjacent faces. Since 2, 3, 4, and 5 are adjacent to 1, face 6 dots must be the opposite face.

4. From the two positions shown below, deduce which face lies opposite to 3 dots:

Position A

Position B

A) 4 dots B) 2 dots C) 5 dots D) 1 dot

Correct Answer: D (1 dot)

Detailed Explanation: The adjacent dot counts to 3 across both views are 2, 5, 4, and 6. Therefore, 1 dot must be directly opposite 3 dots.

5. What fixed total is obtained when summing the dot counts of any two opposing faces on a standard die?

Standard 3D Cube

A) 6 B) 7 C) 8 D) 9

Correct Answer: B (7)

Detailed Explanation: Standard dice pairs are always structured as (1,6), (2,5), and (3,4). Each pair sums to 7 dots.

6. Given two dice positions sharing common faces with 1 and 3 dots, what face lies directly opposite 5 dots?

Position A

Position B

A) 3 dots B) 2 dots C) 6 dots D) 1 dot

Correct Answer: C (6 dots)

Detailed Explanation: When two dice share two common face values (1 and 3), the remaining uncommon faces on each die are opposite to each other. Hence, 5 dots is opposite to 6 dots.

7. Geometrically, how many total faces directly border/touch any single selected face on a cube?

3D Cube Geometry

A) 2 B) 3 C) 5 D) 4

Correct Answer: D (4)

Detailed Explanation: A cube has 6 faces in total. For any given face, 1 face is opposite to it and the remaining 4 faces are adjacent to it.

8. Analyzing the given dice orientations, determine which number of dots sits opposite to face 3 dots:

Position A

Position B

A) 6 dots B) 4 dots C) 2 dots D) 1 dot

Correct Answer: A (6 dots)

Detailed Explanation: The faces adjacent to 3 dots are 1, 2, 4, and 5. The only remaining face that can be opposite to 3 dots is 6 dots.

9. A colored die has opposite pairs (Red-White) and (Blue-Yellow). What color must be opposite to Green?

3D Color Cube

A) Red B) Yellow C) Black D) White

Correct Answer: C (Black)

Detailed Explanation: Since 4 of the 6 colors are already paired up into opposite sets (Red-White, Blue-Yellow), Green must be paired with the remaining 6th color (Black).

10. If a die is rotated such that face 2 dots moves into position 5 dots, what happens to the spatial location of adjacent face 1 dot?

Initial State (Face 2 Top)

Rotated State (Face 5 Top)

A) It changes position B) It stays in place C) It flips D) None of these

Correct Answer: A (It changes position)

Detailed Explanation: Rotating a 3D solid body changes the orientation of all non-axis faces. Thus, face 1 dot shifts position along with the rotation.