Cube and Dice MCQ Quiz - Objective Question with Answer for Cube and Dice - Download Free PDF

For this question, the relation is given below -

Logic: If two dice have the same two face values in the given image then the third number is opposite to each other.

In second dice and third dice.

Numbers 4 and 5 are common.

So, the number 2 is the opposite of 6.

Now, check the second pattern:

In first dice and second dice.

If we rotate the second dice in an anti-clockwise direction.

We get,

Logic: If two dice have the same face value in the given image then their clockwise or anticlockwise wise number are known as opposite numbers in dice.

In first dice and second dice. The number '4' is common.

The left letter will be opposite each other writing them clockwise starting from 4.

Hence, the face opposite the 6 is “2”.

Hence, the correct answer is “2”

In first dice and second dice:

Given:

Logic: If two dice have the same face value in the given image then their clockwise or anticlockwise wise number are known as opposite numbers in dice.

In first dice and second dice. The symbol 'l' is common.

The left letter will be opposite each other writing them clockwise starting from I.

Hence, the face opposite the H is “@”.

Hence, the correct answer is “@”

When the box will be constructed, the following symbols will be opposite to each other as shown below:

So, when the box will be constructed, the symbols  will be opposite to each other.

Hence, option 4)  is the correct answer.

When the box will be constructed, the following symbols will be opposite to each other as shown below:

So, when the box will be constructed, the symbols Blue and Orange will be opposite to each other.

Hence, option 3) Blue and Orange is the correct answer.

The opposite faces of the cube are shown below:

On folding the cube, the following faces are opposite to each other:

 is opposite to 

 is opposite to 

 is opposite to 

As we know that, no two opposite surfaces are adjacent to each other.

Option 1:  and  are adjacent to each other​

∴ The cube in option 1 cannot be made on the given unfolded cube in the question figure, as two opposite sides are given adjacent to each other.

Option 2: No opposite surfaces are adjacent to each other.

∴ The cube in option 2 can be made on the given unfolded cube in the question figure.

Option 3: No opposite surfaces are adjacent to each other.

∴ The cube in option 3 can be made on the given unfolded cube in the question figure.

Option 4: No opposite surfaces are adjacent to each other.

∴ The cube in option 4 can be made on the given unfolded cube in the question figure.

Hence, the correct answer is "option 1".

The opposite surface of the open dice/cube can be found by the below methods:-

1. Alternate surfaces are opposite to each other.

2. No two opposite surfaces are touched by side or by corners.

For find the adjacent faces of '4', we need to compare the common surface in the given dices,

Now,

From Dice 2 and Dice 3,

Here, 3, 5, and 6 is the adjacent surfaces of 4.

So, according to the options '6 and 5' will be the adjacent surfaces of 4.

Hence, the correct answer is "Option 4".

Given:

Length of the side of the big cube = 125 cm.

Length of the side of the smaller cube = 25 cm.

Formula:

A cube is a three-dimensional figure with 8 corners, 6 surfaces, and 12 edges (sides).

If a cube is painted on all of its surfaces with the same colour, and then divided into smaller cubes of equal size, then the number of smaller cubes so obtained will be calculated as follows:

• Number of cubes with no face painted = (n - 2)³
• Number of cubes with one face painted = 6(n - 2)²
• Number of cubes with two faces painted = 12(n - 2)
• Number of cubes with three faces painted = 8(Always)

 where n = No. of parts of each side = Length of the side of larger cube ÷ length of the side of the smaller cube

Calculation:

n = 125 ÷ 25 = 5

⇒ n - 2 = 3

Number of smaller cubes having at least two faces painted

= total no. of cubes - (no. of cubes with no face painted + no. of cubes with only one face painted)

= 125 - (3³ + 6 × 3²)

= 125 - (27 + 54)

= 125 - 81

= 44

Hence, 44 is the correct answer.

From the given dice:

L is the common letter in both Dice,

So, 7 is the opposite surface of 8.

and, F and 9 is the opposite surface.

Therefore, among the given options, 8 and L will be the adjacent surface of 'F'.

Hence, the correct answer is "Option 1".

Logic : (Cube of 1st number + Cube of 3rd number) / 2 = 2nd number

Given :

• (3, 14, 1)

⇒\({(3)^3 + (1)^3 \over 2}\) = 14

⇒\({27 + 1 \over 2}\) = 14

⇒\({28 \over 2}\) = 14

⇒14 = 14 (LHS = RHS)

• (4, 36, 2)​

⇒\({(4)^3 + (2)^3 \over 2}\) = 36

⇒\({64 + 8 \over 2}\) = 36

⇒\({72 \over 2}\) = 36

⇒36 = 36 (LHS = RHS)

So,

• Option - (1) : (8, 12, 2)​

⇒\({(8)^3 + (2)^3 \over 2}\) = 12

⇒\({512 + 8 \over 2}\) = 12

⇒\({520 \over 2}\) = 12

⇒260 ≠ 12 (LHS ≠ RHS)

• Option - (2) : (5, 81, 4)

⇒\({(5)^3 + (4)^3 \over 2}\) = 81

⇒\({125 + 64 \over 2}\) = 81

⇒\({189 \over 2}\) = 81

⇒94.5 ≠ 81 (LHS ≠ RHS)

• Option - (3) : (7, 40, 3)

⇒\({(7)^3 + (3)^3 \over 2}\) = 40

⇒\({343 + 27 \over 2}\) = 40

⇒\({370 \over 2}\) = 40

⇒185 ≠ 40 (LHS ≠ RHS)

• Option - (4) : (8, 260, 2)

⇒\({(8)^3 + (2)^3 \over 2}\) = 260

⇒\({512 + 8 \over 2}\) = 260

⇒\({520 \over 2}\) = 260

⇒260 = 260 (LHS = RHS)

Hence, "Option - (4)" is the correct answer.

In first dice and second dice:

Given:

Logic: If two dice have the same face value in the given image then their clockwise or anticlockwise wise number are known as opposite numbers in dice.

In first dice and second dice. The symbol 'l' is common.

The left letter will be opposite each other writing them clockwise starting from I.

Hence, the face opposite the H is “@”.

Hence, the correct answer is “@”

• A cube of side 80 cm is painted yellow on all the faces and then cut into smaller cubes of sides 8 cm each.

• The number of smaller cube having all the three faces painted.

All corner cubes are painted on three sides there are 8 corners in cubes.

So, cubes with paint on 3 sides = 8

Hence, "8" is the correct answer.

Additional Information

If a cube has been painted red, blue, and black on pairs of opposite faces and divide it into X parts.

1) Total number of cubes = X³

2) Cubes that have three faces painted = 8 (Because there are only 8 corners in the cube)

3) Cubes which has only two faces painted = (X - 2) × No of Edges (12)

4) Cubes that have only one face painted = (X - 2)² × 6

5) Cubes that have no face painted = (X - 2)³

For this question, the relation is given below -

Logic: If two dice have the same two face values in the given image then the third number is opposite to each other.

In first dice and second dice.

Symbols 'Y' and 'Z' are common.

So, the symbol '&' is the opposite of $.

Hence, the correct answer is “&”

Common number in both the positions = 2

Start with common number 2 moving clockwise.

Opposite letters:

2 ⇒ 6

3 ⇒ 4

1 ⇒ 5

Hence, "1" is the opposite of 5.

A cube of side 18 cm is painted yellow on all the faces and then cut into smaller cubes of sides 3 cm each.

Cube is divided into 18/3 = 6 equal parts, hence n = 6.

Number of cubes with 2 sides painted = 12 (n - 2)

= 12 (6 - 2)

= 12 × 4

= 48 

Hence, '48' is the correct answer. 

A cube of side 12 cm is painted green on all the faces and then cut into smaller cubes of sides 2 cm each.

Cube is divided into 12/2 = 6 equal parts, hence n = 6.

Number of cubes with 1 sides painted = 6(n - 2)²

= 6 (6 - 2)²

= 6 × 4²

= 6 × 16

= 96

Hence, '96' is the correct answer.