CDS (II) 2023 · Elementary Mathematics
A full Elementary Mathematics paper in the UPSC CDS pattern: 100 questions in 2 hours, with a third of the question's marks deducted for every wrong answer. Arithmetic, algebra, trigonometry, geometry, mensuration and statistics at Class 10 level, against the clock.
100questions
100marks
2 hoursno calculator
44/40/16easy / medium / hard
Topics in this paper
Mathematics · 100 questions
- Number system7
- Heights and distances6
- Percentage5
- Quadratic equations5
- Trigonometric identities5
- Time and work4
- Profit and loss3
- Time, speed and distance3
- Triangle centres3
- Circles3
- HCF and LCM2
- Average2
- Mixtures2
- Polynomials2
Sample question from this paper
HCF and LCM · medium
The smallest 5-digit number exactly divisible by 18, 27 and 45 is
- A. 10080
- B. 10530
- C. 10260
- D. 10000
Show answer and solution
Answer: C
LCM(18, 27, 45) = 2 · 3³ · 5 = 270. Since 10000 = 270 × 37 + 10, the next multiple is 270 × 38 = 10260. 10080 is divisible by 18 and 45 but not by 27.
LCM(18, 27, 45) = 2 · 3³ · 5 = 270. Since 10000 = 270 × 37 + 10, the next multiple is 270 × 38 = 10260. 10080 is divisible by 18 and 45 but not by 27.