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- Question 1 of 20
##### 1. Question

**Directions**(Qs 1 – 4) : Read the information given below to answer the questions that follow.- A cube has six sides, each of which has a different colour : black, blue, brown, green, red and white.
- The red side is opposite the black.
- The green side is between the red and the black.
- The blue side is adjacent to the white.
- The brown side is adjacent to the blue.
- The red side is the bottom face.

The four colours adjacent to green are :

##### Hint

When the cube is unfolded, it will look like as

The four colours adjacent to green are black, brown, red and white. - Question 2 of 20
##### 2. Question

**Directions**(Qs 1 – 4) : Read the information given below to answer the questions that follow.- A cube has six sides, each of which has a different colour : black, blue, brown, green, red and white.
- The red side is opposite the black.
- The green side is between the red and the black.
- The blue side is adjacent to the white.
- The brown side is adjacent to the blue.
- The red side is the bottom face.

Which of the following can be deduced from the statements 1, 2 and 6 ?

##### Hint

The red side is opposite to the black. Therefore, if red is at the bottom, black will be at the top.

- Question 3 of 20
##### 3. Question

**Directions**(Qs 1 – 4) : Read the information given below to answer the questions that follow.- A cube has six sides, each of which has a different colour : black, blue, brown, green, red and white.
- The red side is opposite the black.
- The green side is between the red and the black.
- The blue side is adjacent to the white.
- The brown side is adjacent to the blue.
- The red side is the bottom face.

Which of the following statements given above adds no information?

##### Hint

6 does not add to the information provided by 1 – 5.

- Question 4 of 20
##### 4. Question

**Directions**(Qs 1 – 4) : Read the information given below to answer the questions that follow.- The red side is opposite the black.
- The green side is between the red and the black.
- The blue side is adjacent to the white.
- The brown side is adjacent to the blue.
- The red side is the bottom face.

If the red side is exchanged for the green side and the blue is swapped for black, then which of the following is false ?

##### Hint

Adjacent to white, we have brown.

- Question 5 of 20
##### 5. Question

**Directions**(Qs. 5 – 9) : Following questions are based on the figures given below which represent different positions of the same dice.

Which number lies at the bottom face of the dice (i)?##### Hint

Since 1, 3, 5 and 6 are adjacent to 2. Therefore, 4 lies opposite 2 i.e. at the bottom face of dice (i).

- Question 6 of 20
##### 6. Question

**Directions**(Qs. 5 – 9) : Following questions are based on the figures given below which represent different positions of the same dice.

Which number lies at the bottom face of the dice (iii)?##### Hint

Since 2, 3, 6 and 4 are adjacent to 1. Therefore, 5 lies opposite 1. Hence, 1 lies at the bottom face of dice (iii).

- Question 7 of 20
##### 7. Question

**Directions**(Qs. 5 – 9) : Following questions are based on the figures given below which represent different positions of the same dice.

Which number lies opposite 6?##### Hint

Since 1, 4, 2 and 5 are adjacent to 6. Therefore, 3 lies opposite 6.

- Question 8 of 20
##### 8. Question

**Directions**(Qs. 5 – 9) : Following questions are based on the figures given below which represent different positions of the same dice.

Which of the following combinations shows the numbers at the adjacent surfaces of the number 4?##### Hint

Hence, 1, 5, 3 and 6 are adjacent to 4. - Question 9 of 20
##### 9. Question

**Directions**(Qs. 5 – 9) : Following questions are based on the figures given below which represent different positions of the same dice.

Which of the following numbers does not appear on any one of the adjacent surfaces of the number 3?##### Hint

From the figure in previous solution, 6 is not adjacent to 3.

- Question 10 of 20
##### 10. Question

Two positions of a dice are shown, when 4 is at the bottom, what number will be on the top?

##### Hint

From the two figures it is clear that the numbers 2, 3, 5 and 6 cannot appear opposite 1. So, 4 appears opposite 1. Therefore, when 4 is at the bottom, 1 will be on the top.

- Question 11 of 20
##### 11. Question

What should be the number opposite 3?

##### Hint

From the three given figures, it is clear that the 1, 2, 5 and 4 appear adjacent to 3, so none of these can appear opposite 3. Therefore, 6 appears opposite 3.

- Question 12 of 20
##### 12. Question

On the basis of two positions of dice, find what number will be on the opposite face of number 5 ?

##### Hint

Common number i.e. 3 to both the dice is placed on the central position of the figure. Now place the numbers in the anti-clock wise direction in block I, II, III and IV respectively. Remaining number i.e. 2 will come in the block V. Hence number 4 is opposite to number 5.

- Question 13 of 20
##### 13. Question

**Directions**(Qs.13–14): Three positions of the same dice are given below. Find which number will come in place of the Question mark ‘?’.

##### Hint

Hence, the numbers that are adjacent to 1 are 5, 2, 6 and 3.

∴ 3 will come in place of ‘?’. - Question 14 of 20
##### 14. Question

**Directions**(Qs.13–14): Three positions of the same dice are given below. Which number lies at the bottom face of the dice (iii)?

##### Hint

From (i) and (ii): 3, 4, 5 and 1 are adjacent to 2.

From (ii) and (iii): 2, 5, 6, and 3 are adjacent to 1

Hence, number 4 lies at the bottom face of number 1. - Question 15 of 20
##### 15. Question

Select from the alternative, the box that can be formed by folding the sheet shown in figure given below:

(A) (B) (C) (D)##### Hint

When the sheet shown in fig. is folded to from a cube, then the face bearing the dot lies opposite to the shaded face, the face bearing a circle (With ‘+’ sign inside it) lies opposite to a blank face and the remaining two blank faces lie opposite to each other. Clearly, the cubes shown in figures (B) and (D) cannot be formed since they have the shaded face adjacent to the face bearing a dot and the cube shown in fig. (C) cannot be formed since it shown all the three blank face adjacent to each other. Hence, only the cube shown in fig.(A) can be formed.

- Question 16 of 20
##### 16. Question

Select from the alternative, the box that can be formed by folding the sheet shown in figure given below:

(A) (B) (C) (D)##### Hint

When the sheet shown in fig. is folded to form a cube , then ‘F’ appears opposite ‘C’ and ‘A’ appears opposite ‘D’. Therefore, the cube in fig. (A) which shows ‘F’ adjacent to ‘B’, the cube in fig.(C) which shows ‘E’ adjacent to ‘C’ and the cube in fig. (D) which shows ‘A’ adjacent to ‘D’ cannot be formed.

- Question 17 of 20
##### 17. Question

How many dots are their on the dice face opposite the one with three dots ?

##### Hint

From figure (i) (ii) and (iv), we conclude that 6, 4, 1 and 2 dots appear adjacent to 3 dots. Clearly, there will be 5 dots on the face opposite the face with 3 dots.

- Question 18 of 20
##### 18. Question

When the following figure is folded form a cube, how many dots would lie opposite the face bearing five dots ?

##### Hint

When this figure is folded to form a cube then the face bearing three dots will lie opposite the face bearing five dots.

- Question 19 of 20
##### 19. Question

Which number is on the opposite face of 4, if the four different positions of a dice are as shown in the figures given below.

##### Hint

From figure (i) (ii) and (iv), we conclude that 6, 5, 2 and 3 appear adjacent to 4. Clearly, 1 will be opposite the face of 4.

- Question 20 of 20
##### 20. Question

Count the number of cubes in the given figure

##### Hint

Clearly, in the figure there are –1 column containing

3 cubes, 2 columns containing 2 cubes each and 3 columns containing 1 cube each.

Number of cubes in columns of 3 cubes = 1 × 3 = 3;

Number of cubes in columns of 2 cubes = 2 × 2 = 4;

Number of cubes in columns of 1 cubes = 3 × 1 = 3;

Therefore, total number of cubes = 3 + 4 + 3 = 10.