2006 General Studies, all questions
UPSC Prelims 2006 · General Studies
Question 92: Basic Numeracy
In a question paper, there are four multiple-choice questions. Each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?
a19
b120
c624
d1024
AnswerThe answer is (c).
Each of the four questions has 5 choices, so the answer sheet can be filled in 5 x 5 x 5 x 5 = 625 ways. Exactly one of these is the all-correct sheet. So the number of ways in which not all four are correct is 625 - 1 = 624.
Why each option is right or wrong
- (a) 19 is not close to the count of 625 - 1.
- (b) 120 is 5 factorial, not the count asked for.
- (c) Correct: 5 to the power 4 minus 1 = 624.
- (d) 1024 is 4 to the power 5, which swaps the numbers.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2006, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.