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CDS (II) 2021 · 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
41/47/12easy / medium / hard

Topics in this paper

Mathematics · 100 questions

  • Trigonometric identities6
  • Number system5
  • Quadratic equations5
  • Heights and distances5
  • Triangles5
  • Circles5
  • HCF and LCM4
  • Percentage4
  • Time, speed and distance4
  • Mean4
  • Profit and loss3
  • Simple and compound interest3
  • Time and work3
  • Averages3

Sample question from this paper

HCF and LCM · medium

The greatest number which divides 458 and 698 leaving remainder 2 in each case is
  1. A. 12
  2. B. 24
  3. C. 48
  4. D. 8
Show answer and solution
Answer: B
The number divides 458−2=456458-2=456 and 698−2=696698-2=696 exactly, so it is gcd⁡(456,696)\gcd(456,696). 696−456=240696-456=240, gcd⁡(456,240)=gcd⁡(240,216)=gcd⁡(216,24)=24\gcd(456,240)=\gcd(240,216)=\gcd(216,24)=24. Taking the gcd of 458 and 698 directly (which is 2) is the trap.