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CDS (II) 2017 · 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
36/48/16easy / medium / hard

Topics in this paper

Mathematics · 100 questions

  • HCF and LCM5
  • Number system5
  • Heights and distances5
  • Triangles5
  • Percentage4
  • Time and work4
  • Time, speed and distance4
  • Trigonometric identities4
  • Circles4
  • Profit and loss3
  • Quadratic equations3
  • Linear equations3
  • Complementary angles3
  • Mean3

Sample question from this paper

HCF and LCM · medium

The greatest number that divides 245 and 1029 leaving remainder 5 in each case is
  1. A. 8
  2. B. 20
  3. C. 16
  4. D. 32
Show answer and solution
Answer: C
The divisor must divide 245−5=240245-5=240 and 1029−5=10241029-5=1024, so it is their HCF. 240=24⋅15240=2^4\cdot15 and 1024=2101024=2^{10}, giving HCF =16=16. It must also exceed 5, which 16 does. Trap: using HCF(245, 1029) directly gives 7, which is wrong.