UPSC CSE Prelims 2018
The 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 questions that follow based on the given figures.
 |  |  |  |
| (I) | (II) | (III) | (IV) |
What is the symbol on the face opposite to that containing the cross?
EXPLANATION
Correct Option (3)
To determine the symbol opposite the cross (×), we analyze the adjacencies presented in the given figures:
- From figures (I), (II), and (III), it is observed that the single dot (·), two dots (··), three dots (···), and four dots (::) are all adjacent to the line (–).
- Since a face can only have one opposite, this adjacency pattern implies that the cross (×) must be on the face opposite to the line (–), as it is the only remaining symbol not adjacent to the line.
- Therefore, the symbol on the face opposite to the cross (×) is the line (–).
Incorrect Options:
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Option 1 (Single dot): Based on the analysis of the figures, the single dot (·) is determined to be opposite to the three dots (···). It is also observed to be adjacent to the cross (×) in figures (II) and (IV). Thus, it cannot be opposite to the cross (×).
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Option 2 (Two dots): Analysis of figures (I), (II), and (IV) reveals that the two dots (··) are adjacent to the line (–), single dot (·), three dots (···), and cross (×). This establishes that the two dots (··) are opposite to the four dots (::), not the cross (×).
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Option 4 (Four dots): As derived from the figures, the four dots (::) are opposite to the two dots (··). Consequently, they cannot be opposite to the cross (×).
