1. Two positions of a cube are given. Based on them find out which number is found opposite to number 4 in the given cube?
a) 1 b) 2 c) 3 d) 4
Sol: From the given positions it can be concluded that 2 is opposite to 4.
Answer: b
2. In the following figures, four different views of a dice are given. Find the number of dots on the face opposite to the face with one dot.
a) 4 b) 6 c) 5 d) 3
Sol: If in two different positions of a dice, position of one common face is at same place and numbers (or symbols) on other faces are not common then numbers (or symbols) at corresponding faces in two different positions are opposite to each other. Similarly, here in position I and III face with 2 dots is at same place. Hence, face with one dot will be opposite to face with six dots.
Alternate: From dice position I and II, face with 3 dots is opposite to face with 5 dots and from dice position I and III face with 2 dots is opposite to face with 4 dots. Hence, face with 1 dot is opposite to face with 6 dots.
Answer: b
adjacent but they are opposite. Hence, only option (b) is correct.
Answer: b
4. If the given figure is folded, it forms a box. Which among the boxes below will be formed?
Sol: From option (a), 5 and 6 are adjacent but they are opposite to each other. Similarly, in option (b), 2 and 3 are adjacent but they are opposite. And in option (d), 1 and 4 are adjacent but they are opposite. Hence, option (c) is correct.
Answer: c
5. If the given figure is folded and formed into a box, which among the boxes given below can be formed?
Sol: In option (a), 2 and 6 are adjacent but in open figure they are opposite. In option (c), 3 and 5 are adjacent but in open figure they are opposite. In option (d), 1 and 4 are adjacent but in open figure they are opposite. Box in option (b) shows a possible construction.
Answer: b
6.
When the above figure is folded into a cube, which is the only cube that can be produced amongst the following?
but they actually are opposite in open figure.
Cube in option (c) can be constructed using the open figure.
Answer: c
Directions (Qs. 7 to 12): Answer the questions on the basis of the information given below:
A bigger cube of side 5 cm is such that opposite faces of cube has been painted with same color. Three colors viz. green, red and black are used to paint the faces of the cube. Now, cube is cut into smaller cubes, each having side 1 cm. 
7. How many smaller cubes will be formed?
a) 25 b) 125 c) 100 d) 50
Sol: Total smaller cubes = (5)3 = 125
Answer: b
8. How many smaller cubes are there with three faces painted?
a) 1 b) 54 c) 108 d) 8
Sol: Only corner cubes will have all the three faces painted that are 8 in number.
Answer: d
9. How many smaller cubes are there with only one face painted?
a) 72 b) 8 c) 54 d) 108
Sol: Each face contains 9 such cubes and there are 6 faces in a cube. Hence, total 9 × 6 = 54 smaller such cubes are there.
Answer: c
10. How many smaller cubes does not have any face painted?
a) 8 b) 1 c) 27 d) 54
Sol: All internal cubes have no face painted. Hence, there will be 27 such cubes.
Answer: c
11. How many smaller cubes have exactly two faces painted?
a) 36 b) 24 c) 18 d) 8
Sol: Smaller cubes which are situated on the edges of bigger cube has two face painted.
There are 12 edges in a cube and each edge contain 3 such cubes.
Hence, required number of cubes = 12 × 3 = 36
Answer: a
12. How many smaller cubes are there that have exactly two faces painted with same colors?
a) None b) 8 c) 36 d) 1
Sol: There will be no such cube.
Answer: a
13. A big cube of side 3 cm is painted with red colour on all faces and then divided into smaller cubes, each of side 1 cm. How many smaller cubes will have no face painted?
a) None b) 1 c) 8 d) 6
Sol: Only central cube will have no face painted. There will be only one such cube. Hence, option (b) is correct.
Answer: b
14. Two positions of a dice are shown below:
Sol: When the heart shape is at the top. The rhombus would be on the bottom.
Answer: d
15. Two positions of a dice are shown below:
When 2 is at the bottom, which number is at the top?
a) 4 b) 5 c) 3 d) 1
Sol: 1 lies opposite 5; 2 lies opposite 3; 4 lies opposite 6.
Answer: c
16. Two positions of a dice are shown below. When 4 is at the top what number will be at the bottom?
a) 5 b) 1 c) 2 d) 6
Sol: The numbers 2, 4 and 5 cannot be on the opposite face of 6. From the two views of dice, it is clear that 2 is at bottom when 4 is at top.
Answer: c
17. Which number appears on the face opposite to the face with number 4?
Sol: From the two views of dice, it is clear that number ‘1’ lies opposite to number ‘4’.
Answer: a
18. Three positions of a dice are given. Find out which number is found opposite the number 2 in the given cube.
Sol: The numbers 1, 3, 4 and 5 are on the adjacent faces of number 6. Therefore, 2 lies opposite 6.
Answer: a
19. Four positions of a dice are given below:
Identify the number at the bottom when top number is 6:
a) 5 b) 1 c) 3 d) 4
Sol: The numbers 2, 3, 4 and 5 cannot be on the face opposite to 1. Therefore, 6 lies opposite 1.
Answer: b
20. Three positions of a dice are given below. Identify the number on the face opposite to 6.
Sol: The numbers 2, 4, 5 and 6 cannot be on the face opposite to 3.
The numbers 1, 3, 4 and 6 cannot be on the face opposite to 5.
Therefore, 2 lies opposite 5. Clearly, 4 lies opposite 6.
Answer: b
OPEN DICE
1. Which of the following cube in the answer figure cannot be made based on the unfolded cube in the question figure?
Answer: D
2. Which of the following cube in the answer figure cannot be made based on the unfolded cube in the question figure?
Answer: B
3. Form the given options, which answer figure can be formed by folding the given in the question?
Answer: A
4. Which of the following cube in the answer figure cannot be made based on the unfolded cube in the question figure?
Answer: B
5. Which of the following cube in the answer figure cannot be made based on the unfolded cube in the question figure ?
Answer: B
6. Which of the following cube in the answer figure cannot be made based on the unfolded cube in the question figure?
Answer: A
7. Which of the following cube in the answer figure cannot be made based on the unfolded cube in the question figure?
Answer: C
8. Which of the following cube in the answer figure cannot be made based on the unfolded cube in the question figure?
Answer: D
9. Which of the following cube in the answer figure cannot be made based on the unfolded cube in the question figure? SSC CGL - 2018
Answer: A
10. Which of the following cube in the answer figure cannot be made based on the unfolded cube in the question figure? SSC CGL - 2019
Answer: A
Some more...
1. From the four positions of a dice given below, find the colour which is opposite to pink.
A) Green B) Blue C) Red D) Pink
Explanation: The colours adjacent to pink are Blue, Red, Yellow & Orange. Hence, Green will be opposite to pink. Ans: A
2. In the diagrams below, faces of dice are shown from two different directions, which number of dots will be opposite to 4 dots?
A) 2 B) 3 C) 1 D) 5
Explanation: It is clear from the two views of the same dice that from first figure to second figure. The dice has been rotated downward. Hence, number 2 lies opposite the 4. Ans: A
3. Which face is opposite to face with alphabet B. If four positions are given as below as?
A) A B) C C) B D) E
Explanation: From fig (i), (ii) & (iv) we can conclude that F, D, C & A lie adjacent to B. Hence, E must lie opposite to B. Ans: D
4. Two positions of a dice are shown when 4 is at the bottom, what number will be on the top?
A) 2 B) 1 C) 6 D) 5
Explanation: It can be observed from the figure, if 2, 3, 5 & 6 are adjacent to 1. Then the number opposite 1 should be 4. Hence the
correct answer is option B. Ans: B
5. Here 4 positions of a cube are shown which sign will be oppoisite to ‘#”?
A) ∧ B) # C) ! D) ?
Explanation: In the above given information @, *, ! are adjacent to ‘∧’ & ‘?’ is adjacent to ‘#’. Hence ‘∧’ is opposite to ‘#’ Ans: A
6. Three positions of a dice are given below what will come opposite to the face containing ‘white”?
A) Pink B) Brown C) Purple D) Orange
Explanation: The adjacent phases of white are orange, brown, blue & pink. Hence, purple is the opposite face of white. Ans: C
7. Which of the following dice can be formed by folding the following shape.
Explanation: Opposite faces:- b ↔ d f ↔ c a ↔ e
Hence, option C is correct. Ans: C
8. Which of the following dice can be formed by folding the given figure?
Explanation: Opposite faces: a ↔ e
d ↔ b
c ↔ f
Hence, Option B is correct Answer. Ans: B
9. Which of the following dice ‘cannot be’ formed by folding the given figure?
Explanation : Opposite faces:
1 ↔ 3 4 ↔ 6 2 ↔ 5
Hene Option ‘A’ is cannot be formed Ans: A
10. Which number lie opposite to the face having numbers ‘I’ when the given figure is folded to form a cube?
A) V B) IV C) II D) VI
Explanation: Opposite faces:
VI ↔ III IV ↔ V I ↔ II
Hence, option ‘C’ is correct Ans: C
11. What number will be opposite to 6?
A) 2 B) 1 C) 3 D) 4
Explanation:It is a standard dice as sum of numbers of opposite faces will equal to ‘7’ Hence, Option B is correct.
Ans: B
12. What number will be opposite to ‘3’?
A) 4 B) 5 C) 6 D) 2
Explanation: It is a standard dice as sum of the numbers of opposite faces will be equal to ‘7’ Hence, option ‘A’ is correct
Opposite faces
6 ↔ 1
5 ↔ 2
4 ↔ 3 Ans: A
13. What will be the number at the bottom, if 4 is at the top, the two positions of the dice being as given below.
A) 3 B) 5 C) 6 D) 2
Explanation: 2 → 4, 1
2 → 6, 3
(rotated clockwise direction)
Ans: C
14. Two positions of a dice are shown below (a) and (b) when 5 is at the top which number will be at the bottom?
A) 2 B) 3 C) 4 D) 1
Explanation: As we can observe the positions of 4, 6 are same in both the figures. So 1, 5 will be opposite faces. Hence, Option D is correct. Ans: D
15. Study the two different positions of a cube given below with numbers from 1 to 6 marked on its faces. Find out which number is contained on the face opposite to that containing number ‘2
A) 3 B) 1 C) 4 D) 6
