In a dice, each face is numbered as follows: 1) 3 is opposite to 6 2) 4 is opposite to 5 3) 2 is opposite to 1 Which of the following is definitely false?
4 is not adjacent to 3 and 6
Dice Opposite Faces Analysis
The problem describes the opposite face pairings for a specific six-sided die:
- Face 3 is opposite to Face 6 ($3 \leftrightarrow 6$)
- Face 4 is opposite to Face 5 ($4 \leftrightarrow 5$)
- Face 2 is opposite to Face 1 ($2 \leftrightarrow 1$)
Determining Adjacent Faces
For any standard die, a face has 4 adjacent faces and 1 opposite face. We can deduce the adjacent faces from the given opposite pairs:
- Faces adjacent to 3 and 6 are {1, 2, 4, 5}.
- Faces adjacent to 4 and 5 are {1, 2, 3, 6}.
- Faces adjacent to 2 and 1 are {3, 4, 5, 6}.
Evaluating the Statements
We examine each option to find the one that is definitely false:
- Option 1: 4 is not adjacent to 3 and 6
According to our deduction, the faces adjacent to 4 are {1, 2, 3, 6}. This means 4 is adjacent to 3 and 6. Therefore, the statement "4 is not adjacent to 3 and 6" is false. - Option 2: 4 is adjacent to 2
From the list {1, 2, 3, 6}, Face 4 is adjacent to Face 2. This statement is true. - Option 3: 4 is adjacent to 1
From the list {1, 2, 3, 6}, Face 4 is adjacent to Face 1. This statement is true. - Option 4: 5 is adjacent to 3
The faces adjacent to 5 are {1, 2, 3, 6}. Face 5 is adjacent to Face 3. This statement is true.
Conclusion
The statement that contradicts the derived rules of adjacency for the given dice configuration is Option 1. Thus, "4 is not adjacent to 3 and 6" is definitely false.
Important Questions from Cube and Dice
- In a dice, each face is numbered as follows:
1) U is opposite to Z
2) X is opposite to V
3) Y is opposite to W
Which of the following is definitely false?
A) V is not adjacent to Y and W
B) V is adjacent to U
C) W is adjacent to X
D) Y is adjacent to Z A dice is numbered from 1 to 6. Based on the three images of dice, find out which of the following numbers comes in the place of C.
- In a dice, each face is marked as follows:
1) * is adjacent to ^
2)^ is opposite to #
3) @ is opposite to $
4)! is adjacent to ^
Which of the following is definitely true?
A) * is between $ and ^
B) * is adjacent to !
C) ^ is between * and !
D) # is between ^ and @ In a dice, each face is numbered as follows:
1) 4 is opposite to 2
2) 5 is opposite to 3
3) 1 is opposite to 6
Which of the following is definitely false?
A) 1 is not adjacent to 5 and 3
B) 4 is adjacent to 3
C) 4 is adjacent to 5
D) 2 is adjacent to 1
The dice contains A, B, C, D, E, F on the six faces. Which alphabet is opposite to E?
