Rotated positions of a single solid are shown below. The various faces of the solid are marked with different symbols like dots, cross and line. Answer the three items (14-16) that follow the given figures.
What is the symbol on the face opposite to that containing two dots?
Correct Answer :
Four dots
Solution :
The correct option is Four dots.
To find the symbol on the face opposite to the one containing two dots, we can identify all the faces that are adjacent to the face with two dots by analyzing the given rotated positions of the cube:
1. From Figure (I): The face with two dots (on the right) is adjacent to the face with the line (on the top) and the face with a single dot (on the front).
2. From Figure (II): The face with two dots (on the front) is adjacent to the face with the line (on the top) and the face with three dots (on the right).
3. From Figure (IV): The face with two dots (on the front) is adjacent to the face with the cross (on the top) and the face with a single dot (on the right).
Combining these observations, the face with two dots is adjacent to the following four distinct faces:
- The face with a single dot
- The face with three dots
- The face with the line
- The face with the cross
Since any face of a cube has exactly four adjacent faces and one opposite face, the face opposite to the two dots must be the remaining symbol on the cube, which is the face containing four dots (visible on the right face of Figure (III)).
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