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CDS (II) 2022 · 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
35/53/12easy / medium / hard

Topics in this paper

Mathematics · 100 questions

  • Heights and distances6
  • Triangles5
  • Circles5
  • Quadratic equations4
  • Trigonometric identities4
  • Percentage3
  • Averages3
  • Indices3
  • LCM2
  • Number system2
  • Profit and loss2
  • Simple interest2
  • Ratio2
  • Time and work2

Sample question from this paper

LCM · medium

The greatest 3-digit number divisible by each of 18, 24 and 36 is
  1. A. 864
  2. B. 972
  3. C. 990
  4. D. 936
Show answer and solution
Answer: D
LCM(18,24,36)=72\text{LCM}(18,24,36)=72. Since 999=72×13+63999=72\times13+63, the greatest 3-digit multiple is 72×13=93672\times13=936. Subtracting only the remainder of one divisor, or using 36 as the LCM, gives 972, which is not divisible by 24.