MCQ
Reasoning: Cubes & Dice MCQ - Practice Questions with Answers
Solve 25 Reasoning: Cubes & Dice questions for RAS/RPSC preparation.
Practice questions
Q1The same die is shown in two positions. In the first position, the visible faces are 1, 2 and 3. In the second position, the visible faces are 1, 2 and 6. Which number is opposite to 3?
In both positions, the faces 1 and 2 are common. When two views of the same die have two common visible faces, the remaining visible faces in those two views are opposite to each other. In the first view the remaining face is 3, and in the second view the remaining face is 6. Therefore, the number opposite to 3 is 6.
Q2Three views of the same die are shown below: View 1: top 2, front 4, right 6 View 2: top 2, front 6, right 3 View 3: top 5, front 4, right 1 Which number is opposite 4?
A face shown with 4 in the same view is adjacent to 4. In the first view, 2 and 6 are adjacent to 4. In the third view, 5 and 1 are adjacent to 4. Thus 4 is adjacent to 1, 2, 5 and 6. A cube face has exactly four adjacent faces and one opposite face. The only remaining number is 3, so 3 is opposite 4.
Q3Read the Assertion and Reason, then choose the correct option. Assertion: If a cube is cut into 2 equal parts along each edge, 8 smaller cubes are obtained. Reason: When each edge of a cube is divided into n equal parts, the total number of smaller cubes is n x n x n.
If each edge of a cube is divided into 2 equal parts, then the cuts create 2 layers in length, 2 layers in breadth and 2 layers in height. The total number of smaller cubes is found by multiplying these three counts: 2 x 2 x 2 = 8. The Reason states the same general rule: for n equal parts on each edge, the number of smaller cubes is n x n x n. Putting n = 2 proves the Assertion, so the Reason correctly explains it.
Q4A cube is made from a net in which four squares A-B-C-D are in a straight row. Square E is attached above B and square F is attached below B. Match the faces with their opposite faces.
Take B as the front face. Then A folds to the left of B and C folds to the right of B, so A and C become opposite faces. D is attached beyond C, so after folding it comes opposite B. The two squares attached above and below B become the top and bottom faces, so E and F are opposite. Thus the matching pairs are A-C, B-D and E-F.
Q5A cube has 4 on the face opposite 1, 5 on the face opposite 2, and 6 on the face opposite 3. If the cube is placed with 1 on the top and 2 on the front, which number will be on the bottom face?
Opposite pairs are fixed: 1-4, 2-5 and 3-6. The bottom face is always opposite the top face. Since 1 is on the top, the face directly below it must carry the number opposite 1. The given opposite pair for 1 is 4. The front face, 2, only tells us that 5 is at the back; it does not change the top-bottom pair. Therefore the bottom face has 4.
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More questions
6A cube of side 5 cm is painted on all its faces and cut into small cubes of side 1 cm each. Match List I with List II. List I: I. three painted faces, II. two painted faces, III. one painted face. List II: 1. 36, 2. 8, 3. 54.
7The net of a cube has 3 in the centre; 1 is to the left of 3, 5 is to the right of 3, 2 is above 3, 4 is below 3, and 6 is to the right of 5. When the net is folded into a cube, which pair is not a pair of opposite faces?
8A cube of side 3 cm is painted on all its faces and cut into smaller cubes of side 1 cm each. Which one of the following statements is incorrect?
9Two positions of the same dice are shown. In the first position, 1 is on the top, 2 is on the front and 3 is on the right. In the second position, 1 is on the top, 3 is on the front and 4 is on the right. Which number is opposite to 2?
10A large cube is painted on all faces and then cut into 125 equal small cubes. Match List I with List II. List I I. Small cubes with no painted face II. Small cubes with exactly one painted face III. Small cubes with exactly two painted faces IV. Small cubes with exactly three painted faces List II 1. 54 2. 36 3. 8 4. 27
11A cube of side 5 cm is painted on all faces and cut into small cubes of side 1 cm each. Match the type of small cube with its number. I. No painted face II. Exactly one painted face III. Exactly three painted faces. Numbers: 1. 8 2. 27 3. 54
12Consider the following assertion and reason about a standard dice. Assertion: If the numbers 2, 3, 4 and 5 are all adjacent to 1, then 6 is opposite to 1. Reason: On a cube, each face has exactly four adjacent faces and exactly one opposite face. Choose the correct option.
13A wooden cube of side 3 cm is painted red on all its faces and then cut into small cubes of side 1 cm each. How many small cubes will have no face painted?
14For a standard die, the sum of the numbers on opposite faces is 7. Read the assertion and reason, then choose the correct answer. Assertion: The face opposite to 2 is 5. Reason: On this die, opposite faces have numbers whose sum is 7.
15A cube of side 4 cm is painted on all its faces and then cut into small cubes of side 1 cm each. How many small cubes will have exactly two painted faces?