A dice has its faces marked by digits 1, 2, 5, 6, 8 and 9. Three positions of the dice are given below. One of the faces in the second image of the dice is masked by '#'.<br>Which of the following statements is/are true?<br>I) The product of the values of '#' and the side opposite to it is 54.<br>II) The sum of the values of '#' and the side opposite to '6' is a prime number.<br>III) The square root of the sum of all the sides adjacent to '#' gives a rational number.
- A. Only II ✓
- B. Only III
- C. Both I and II
- D. Both II and III
Correct Answer: A. Only II
Explanation
From the figures, 9 is opposite 5, 8 is opposite 1, and 6 is opposite 2. In the second dice position (8 on top, 2 in front), the right face '#' must be 9. The side opposite 6 is 2. Therefore, 9 + 2 = 11, which is a prime number, making statement II true.
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