Consider a set of 11 numbers: 1. Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers ≥ − 5. 2. Value-II = Minimum value of the product of the numbers of the set when they are consecutive non-negative integers. Which one of the following is correct?

Let's solve for Value-I first. The question asks for the minimum average of 11 consecutive integers $\\ge -5$. To get the minimum average, we must pick the smallest possible numbers allowed. So, we start the sequence at exactly -5. \nThe sequence is: $-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5$. \nInstead of summing these up, we apply the 'Mean = Middle Term' logic found in PYQs [20], [54]. The middle term of this symmetric sequence (spanning from -5 to 5) is clearly **0**. So, Value-I is 0.\n\nNow for Value-II. We need the minimum product of 11 consecutive *non-negative* integers. We must recall the 'Precise Definition of Number Sets' [41], [45]: non-negative integers start from 0 (i.e., 0, 1, 2...). \nTo minimize the product, we pick the smallest numbers starting from 0. The sequence is $0, 1, 2, ..., 10$. \nUsing the 'Zero Property' [25], since 0 is present in the set, the product is $0 \\times 1 \\times ... = 0$. So, Value-II is 0.\n\nComparing them: Value-I (0) = Value-II (0). Therefore, they are equal.