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CDS (II) 2020 · 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
31/51/18easy / medium / hard

Topics in this paper

Mathematics · 100 questions

  • Number system6
  • Time, speed and distance6
  • Simple and compound interest4
  • Heights and distances4
  • Trigonometric identities4
  • Mean4
  • Percentage3
  • Profit and loss3
  • Ratio and proportion3
  • Time and work3
  • Quadratic equations3
  • Surds3
  • HCF and LCM2
  • Averages2

Sample question from this paper

HCF and LCM · medium

Three traffic lights change after every 48 s, 72 s and 108 s respectively. If they change together at 8:00:00 a.m., they will next change together at
  1. A. 8:06:00 a.m.
  2. B. 8:07:48 a.m.
  3. C. 8:07:12 a.m.
  4. D. 8:12:00 a.m.
Show answer and solution
Answer: C
The lights coincide after LCM(48,72,108)\text{LCM}(48,72,108) seconds. 48=24⋅348=2^4\cdot3, 72=23⋅3272=2^3\cdot3^2, 108=22⋅33108=2^2\cdot3^3, so LCM =24⋅33=432=2^4\cdot3^3=432 s =7=7 min 1212 s. The trap is adding 432 s as 4 min 32 s or choosing a multiple of 60 s.