700 से 1000 तक के पूर्णांकों को सूचीबद्ध किया गया है । इनमें से कितने पूर्णांकों में, अंकों का योगफल 10 है ?
Read this question in English
Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10?
(a) 6 · (b) 7 · (c) 8 · (d) 9
उत्तर और व्याख्या · explanation in English
Answer: (d) 9
Fix the hundreds digit and count the ways the last two digits can make up the rest: sums of 3, 2 and 1 give 4, 3 and 2 numbers. 1000 does not qualify, so the total is 9.
- 7ab: a + b = 3 → 703, 712, 721, 730 (4 numbers).
- 8ab: a + b = 2 → 802, 811, 820 (3 numbers).
- 9ab: a + b = 1 → 901, 910 (2 numbers).
- 1000 has digit sum 1, so it does not count. Total = 4 + 3 + 2 = 9.
Remember · Two digits adding to k (k ≤ 9) can be chosen in k + 1 ways.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·