UPSC Prelims 2016 · CSAT
Question 40: Basic Numeracy
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 :
AnswerUPSC’s answer is (d).
Each of five questions has two choices, so the number of different answer sequences is 2 x 2 x 2 x 2 x 2 = 32. If no two candidates have the same sequence, at most 32 candidates can exist. Remember: n questions with 2 choices give 2^n distinct sequences.
Why each option is right or wrong
- (a) 10 is far too few; 2^5 is 32.
- (b) 18 is not 2^5.
- (c) 26 is not 2^5.
- (d) Right: 2^5 = 32.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2016, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.