एक प्रश्न-पत्र में पांच प्रश्नों पर प्रयास किए जाने हैं और प्रत्येक प्रश्न के उत्तर के दो विकल्प हैं – सही (T) अथवा गलत (F)। यह दिया गया है कि किन्हीं भी दो परीक्षार्थियों ने पाँचों प्रश्नों के उत्तर एकसमान अनुक्रम में नहीं दिए हैं। ऐसा होने के लिए परीक्षार्थियों की अधिकतम संख्या कितनी है ?
Read this question in English
In a question paper there are five questions to be attempted and answer to each question has two choices – True (T) or False (F). It is given that no two candidates have given the answers to the five questions in an identical sequence. For this to happen the maximum number of candidates is:
(a) 10 · (b) 18 · (c) 26 · (d) 32
उत्तर और व्याख्या · explanation in English
Answer: (d) 32
Each question can be answered in 2 ways, so there are 2⁵ = 32 different answer sequences. If no two candidates repeat a sequence, at most 32 candidates are possible.
- Each of the 5 questions has 2 possible answers.
- Distinct sequences = 2 × 2 × 2 × 2 × 2 = 2⁵ = 32.
- No two candidates share a sequence, so the maximum is 32.
Remember · Independent choices multiply: k options at each of n places give kⁿ sequences.
Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·