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:
Answer & explanation
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). ·