Consider a set of 11 numbers:
- Value-I: Minimum value of the average of the numbers of the set when they are consecutive integers ≥ −5.
- 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?
Answer & explanation
Answer: (c) Value-I = Value-II
The lowest allowed set, −5 to 5, is balanced around 0, so its average is 0. The product of 0, 1, …, 10 is 0, the smallest possible for non-negative integers. Both values are 0.
- Value-I: the lowest possible set is −5, −4, …, 4, 5. Its average is 0; any later set has a larger average. So Value-I = 0.
- Value-II: the set 0, 1, …, 10 has product 0; any set starting above 0 has a positive product. So Value-II = 0.
- Value-I = Value-II.
Remember · Consecutive integers balanced around 0 average 0; a product of non-negative numbers is smallest (0) when it includes 0.
Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·