UPSC Prelims 2022 · CSAT
Question 76: Basic Numeracy
One non-zero digit, one vowel and one consonant from English alphabet (in capital) are to be used in forming passwords, such that each password has to start with a vowel and end with a consonant. How many such passwords can be generated?
AnswerUPSC’s answer is (c).
A password has three characters: one non-zero digit, one vowel and one consonant. It must start with a vowel and end with a consonant, so the digit goes in the middle. The choices are 5 vowels × 9 digits (1 to 9) × 21 consonants = 945. English has 5 vowels and 21 consonants, and zero is excluded from the digits.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) 105 = 5 × 21 leaves out the choice of digit.
- (b) 525 does not match the choices of 5, 9 and 21.
- (c) Correct: 5 × 9 × 21 = 945.
- (d) 1050 = 5 × 10 × 21 wrongly counts 0 as a digit option.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.