11 संख्याओं के एक समुच्चय पर विचार कीजिए :
- मात्रा-I: समुच्चय की संख्याओं के औसत का न्यूनतम मान जब वे क्रमागत पूर्णांक ≥ – 5 हैं ।
- मात्रा-II: समुच्चय की संख्याओं के गुणनफल का न्यूनतम मान जब वे क्रमागत ऋणेतर पूर्णांक हैं ।
निम्नलिखित में से कौन-सा एक सही है ?
Read this question in English
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?
(a) Value-I < Value-II · (b) Value-II < Value-I · (c) Value-I = Value-II · (d) Cannot be determined due to insufficient data
उत्तर और व्याख्या · explanation in English
Answer: (c) मात्रा-I = मात्रा-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). ·