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A dice is numbered from 1 to 6 in different ways. If 1 is adjacent to 2, 4 and 6, then which of the following statements is necessarily true?
  • a)
    2 must be opposite to 6
  • b)
    1 must be adjacent to 3
  • c)
    3 must be adjacent to 5
  • d)
    3 must be opposite to 5
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A dice is numbered from 1 to 6 in different ways. If 1 is adjacent to ...
1 adjacent to 2, 4, 6 means opposite of 1 will be either 3 or 5

Therefore, 3 and 5 are definitely adjacents.
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Community Answer
A dice is numbered from 1 to 6 in different ways. If 1 is adjacent to ...
Introduction:
In this given problem, we have a dice numbered from 1 to 6 in different ways. We are given that 1 is adjacent to 2, 4, and 6. We need to determine which of the given statements is necessarily true based on this information.

Explanation:
Let's analyze each statement one by one.

Statement a) 2 must be opposite to 6:
This statement is not necessarily true. The dice can be arranged in such a way that 2 is adjacent to 3, 4, and 6. In this case, 2 would not be opposite to 6.

Statement b) 1 must be adjacent to 3:
This statement is not necessarily true either. Based on the given information, 1 is adjacent to 2, 4, and 6, but it does not necessarily mean that 1 must be adjacent to 3. The dice can be arranged in a way that 1 is adjacent to 2, 4, and 6, but not adjacent to 3.

Statement c) 3 must be adjacent to 5:
This statement is necessarily true. Since 1 is adjacent to 2, 4, and 6, and 2 is adjacent to 3, it follows that 1 is indirectly adjacent to 3. Similarly, since 1 is adjacent to 2, 4, and 6, and 4 is adjacent to 5, it follows that 1 is indirectly adjacent to 5. Therefore, since 1 is indirectly adjacent to both 3 and 5, it implies that 3 and 5 must be adjacent to each other.

Statement d) 3 must be opposite to 5:
This statement is not necessarily true. The dice can be arranged in such a way that 3 is adjacent to 1, 2, and 4, but not adjacent to 5. In this case, 3 would not be opposite to 5.

Conclusion:
After analyzing each statement, we can conclude that statement c) "3 must be adjacent to 5" is necessarily true based on the given information.
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A dice is numbered from 1 to 6 in different ways. If 1 is adjacent to 2, 4 and 6, then which of the following statements is necessarily true?a)2 must be opposite to 6b)1 must be adjacent to 3c)3 must be adjacent to 5d)3 must be opposite to 5Correct answer is option 'C'. Can you explain this answer?
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A dice is numbered from 1 to 6 in different ways. If 1 is adjacent to 2, 4 and 6, then which of the following statements is necessarily true?a)2 must be opposite to 6b)1 must be adjacent to 3c)3 must be adjacent to 5d)3 must be opposite to 5Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A dice is numbered from 1 to 6 in different ways. If 1 is adjacent to 2, 4 and 6, then which of the following statements is necessarily true?a)2 must be opposite to 6b)1 must be adjacent to 3c)3 must be adjacent to 5d)3 must be opposite to 5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A dice is numbered from 1 to 6 in different ways. If 1 is adjacent to 2, 4 and 6, then which of the following statements is necessarily true?a)2 must be opposite to 6b)1 must be adjacent to 3c)3 must be adjacent to 5d)3 must be opposite to 5Correct answer is option 'C'. Can you explain this answer?.
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