Correct Option (3)
To determine the correct relationship between Value-I and Value-II, each value is calculated as follows:
Value-I: Minimum average of 11 consecutive integers, each ≥ -5.
- To achieve the minimum average, the set of integers must commence with the smallest permissible value, which is -5.
- The 11 consecutive integers are: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.
- The sum of these integers is: (-5) + (-4) + (-3) + (-2) + (-1) + 0 + 1 + 2 + 3 + 4 + 5.
- This sum simplifies to 0, as the positive and negative integer pairs cancel each other out.
- The average is the sum divided by the number of integers: 0 / 11 = 0.
- Therefore, Value-I = 0.
Value-II: Minimum product of 11 consecutive non-negative integers.
- Non-negative integers include 0.
- To achieve the minimum product for a set of integers, the inclusion of 0 is essential, as any product involving 0 will result in 0.
- The 11 consecutive non-negative integers starting from 0 are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
- The product of these integers is: 0 × 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10.
- This product is 0.
- Therefore, Value-II = 0.
Comparing the calculated values, Value-I = 0 and Value-II = 0. Hence, Value-I = Value-II.
Incorrect Options:
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Options 1 (Value-I < Value-II) and 2 (Value-II < Value-I) are incorrect because both Value-I and Value-II are determined to be 0, establishing their equality.
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Option 4 (Cannot be determined due to insufficient data) is incorrect as the problem provides all necessary conditions to precisely calculate both values.
