In a dice, each face is numbered as follows:
1) 2 is opposite to 6
2) 3 is opposite to 5
3) 4 is opposite to 1
Which of the following is definitely false?
A) 4 is not adjacent to 3 and 5
B) 4 is adjacent to 5
C) 4 is adjacent to 6
D) 4 is adjacent to 3
Dice Opposite Faces Analysis
The problem describes the pairs of opposite faces on a standard six-sided die.
- The face opposite to 2 is 6.
- The face opposite to 3 is 5.
- The face opposite to 4 is 1.
This means the pairs of opposite faces are (2, 6), (3, 5), and (1, 4).
Identifying Adjacent Faces for Number 4
A standard die has 6 faces. The faces adjacent to any given face are all the other faces except the one opposite to it.
For face 4, the opposite face is 1.
Therefore, the faces adjacent to face 4 are all the remaining faces: 2, 3, 5, and 6.
Evaluating the Options
We need to find the statement that is definitely false. Let's examine each option:
- Option A: 4 is not adjacent to 3 and 5
Based on our analysis, 4 *is* adjacent to both 3 and 5. This statement claims the opposite, making it definitely false. - Option B: 4 is adjacent to 5
Since 5 is not opposite to 4 (only 1 is), 5 must be adjacent to 4. This statement is true. - Option C: 4 is adjacent to 6
Since 6 is not opposite to 4 (only 1 is), 6 must be adjacent to 4. This statement is true. - Option D: 4 is adjacent to 3
Since 3 is not opposite to 4 (only 1 is), 3 must be adjacent to 4. This statement is true.
Conclusion on False Statement
The only statement that contradicts the established adjacency rules for face 4 is Option A.
Important Questions from Cube and Dice
A cube of side 4 cm is painted green on all its faces and then divided into smaller cubes of side 2 cm each. How many small cubes have been obtained?
Two adjacent faces of a solid cube are painted with black colour. The faces opposite to the black faces is painted with blue colour while the remaining faces are painted with yellow colour. After painting, this cube has been divided into 125 equal cubes. How many cubes have no faces painted?
A cube, whose two adjacent faces are coloured, is cut into 64 identical small cubes. How many of these small cubes are not coloured at all?
Three different positions of the same dice are shown. Select the number that will be on the face opposite to the face having the number '3'?
Select the dice that can be formed by folding the given sheet along the lines.
