Problems on Dice MCQ Quiz - Objective Question with Answer for Problems on Dice - Download Free PDF

@ is there in the1^st dice. In order to find the face opposite to @, take 1^st and 3^rd dice. # is common in both the faces. Keeping the face ‘#’ constant, and then rotating in the clockwise direction, we find the faces opposite to each other.

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.

Common trick:- When one digit/letter is common in two positions of dice, then for finding opposite surface we have to write digit/letter in a clockwise direction starting from common surface. In both the orders, the digit is written after the common digit is opposite to each other.

Here from figures 1 and 2, one surface is common. So we can use one common trick.

So, '1' is opposite to '6'.

Hence, '1' is the correct answer.

Given: A solid cube of 4-inch edges has been painted with red, green, and yellow colors such that each color appears on a pair of opposite faces. It has been cut into one-inch cubes.

The number of small one-inch cubes that have only one face painted with red color can be counted as below:

The cube is of 4-inch cubes we have: n → 4 ÷ 1 = 4

Number of 1 faces painted with red cube = (n - 2)2 × number of edges → (4 - 2)2 × 6 ⇒ 24

Hence, "Option 2" is the correct answer.

Shortcut Trick For a cube of side n*n*n painted on all sides which is uniformly cut into smaller cubes of dimension 1*1*1,

Number of cubes with 0 side painted = (n - 2)³

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

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

Number of cubes with 3 sides painted= 8(always)

The number of the rectangles are given:

Thus, the number of rectangles in the given figure are "18".

Hence, the correct answer is "Option 2".

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".

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".

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.

The faces with numbers 3 and 5 are adjacent to the face with number 1 in the first position. The faces with numbers 2 and 6 are adjacent to the face with number 1 in the second position. The only number left is 4.

Given,

A cube is painted Orange on all surfaces and then the cube cuts into 27 small cubes of equal part.

So, it has been cut into: 3 × 3 × 3.

Here, n = 3.

Now, using formula: (n - 2)² × 6

⇒ (n - 2)2 × 6

⇒ (3 - 2)2 × 6

⇒ 12 × 6

⇒ 1 × 6 = 6.

So, total '6' cubes will have only one face painted.

Hence, the correct answer is "6".

The figure given below is:

From figure 2 and 3, we understand that 5 and 4 is not the opposite face of 1 and 2.

The opposite faces are 1 - 2

Hence, the correct answer is "2".

From the given dice:

A is the common letter in both Dice,

Here, H, B, K and T are the adjacent of A.

and, the remaining face will be opposite of A.

Now, checking the options:

Option 1) H and T → False (H is the opposite face of K).

Option 2) H and B → False (H and B is the adjacent of A, not K).

Option 3) B and A → True (B and A will be the adjacent surface of K).

Option 4) A and H → False (A and H is the adjacent of B, not K).

Therefore, 'B and A' the adjacent faces of the face containing 'K'.

Hence, the correct answer is "Option 3".

Concept:

The 3 adjacent faces of the dice which we see will never be the opposite among them.

In figure 1, Adjacent of B is D, F

In figure 2, Adjacent of B is C, D.

In figure 4, Adjacent of B is A, C.

This will never be the opposite of B.

Only remaining alphabet is E, which becomes the opposite of B.

Hence, E is the correct answer.  

For find the opposite surface of 'U', we need to compare the common surface in the given dices,

Now,

From the given Dice,

→ P and S is the common surface in both Dice, 'U' is the opposite surface of 'R'.

Here, 'U' is opposite to the face containing 'R'.

Hence, the correct answer is "R".

For find the adjacent faces of '3', we need to compare the common surface in the given dices,

Now,

From Dice 1 and Dice 3,

2 and 5 is the common surface, so 3 and 7 will be the opposite surfaces.

From Dice 1 and Dice 2,

7 is the opposite surface of 3, so 2,5,4,6 these all are the adjacent surface of 7 and 3.

So, according to the options '6 and 4' will be the adjacent surfaces of 3.

Hence, the correct answer is "Option 3".