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CSAT · 20 questions

Geometry & mensuration

Every UPSC CSAT question on this topic, 2016–2026, newest first. Tap an option to check yourself; the answer and explanation open below it.

Geometry & mensuration questions per year: 2016: 6, 2017: 1, 2018: 3, 2019: 0, 2020: 3, 2021: 2, 2022: 2, 2023: 2, 2024: 1, 2025: 0, 2026: 0 Asked in 8 of 11 years · most in 2016 (6)

UPSC syllabus: “Basic numeracy (numbers and their relations, orders of magnitude, etc.) (Class X level), Data interpretation (charts, graphs, tables, data sufficiency etc. — Class X level);” See the full syllabus →

CSAT 2020 · Q38

Easy

Let x, y be the volumes; m, n be the masses of two metallic cubes P and Q respectively. Each side of Q is two times that of P and mass of Q is two times that of P. Let u = m/x and v = n/y. Which one of the following is correct?

Answer & explanation

Answer: (a) u = 4v

Doubling the side multiplies a cube's volume by 2³ = 8, while the mass only doubles. So Q's mass per unit volume is 2/8 = 1/4 of P's, i.e. u = 4v.

  1. Side of Q = 2 × side of P, so y = 2³ x = 8x.
  2. n = 2m.
  3. v = n/y = 2m/8x = (1/4)(m/x) = u/4.
  4. So u = 4v.

Remember · Scaling a length by k scales volume by k³; compare ratios by writing each in terms of the smaller object.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2020 · Q73

Easy

Consider the following statements:

  1. 1.The minimum number of points of intersection of a square and a circle is 2.
  2. 2.The maximum number of points of intersection of a square and a circle is 8.

Which of the above statements is/are correct?

Answer & explanation

Answer: (b) 2 only

A circle and a square need not meet at all — a small circle can sit inside the square without touching it — so the minimum is 0, not 2. Each side is a straight segment that can cut a circle at most twice, so four sides give at most 8 points, and 8 is actually reachable.

  1. A small circle inside the square, or one far away from it, meets the square in 0 points — so the minimum is 0.
  2. A straight line meets a circle in at most 2 points; the square has 4 sides, so at most 4 × 2 = 8 points.
  3. 8 is reached by a circle with the square's centre whose radius is more than half the side but less than half the diagonal: it crosses each side twice.
  • ✗ 1. The minimum is 0 — the circle can lie wholly inside or wholly outside the square without touching it.
  • ✓ 2. Four sides × at most 2 crossings each = 8, and a suitably sized concentric circle achieves it.

Remember · For 'minimum' claims, look for the case where the figures do not touch at all; for 'maximum', count lines × 2 for a circle.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2020 · Q78

Easy

If 1 litre of water weighs 1 kg, then how many cubic millimetres of water will weigh 0.1 gm?

Answer & explanation

Answer: (c) 100

1 litre = 1 kg means 1 gram of water occupies 1 cm³. Since 1 cm³ = 10 × 10 × 10 = 1000 mm³, 0·1 g occupies 100 mm³.

  1. 1 litre = 1000 cm³ weighs 1 kg = 1000 g, so 1 g of water = 1 cm³.
  2. 1 cm³ = 10 mm × 10 mm × 10 mm = 1000 mm³.
  3. 0·1 g = 0·1 cm³ = 100 mm³.

Remember · Water: 1 g = 1 cm³ = 1 mL; and 1 cm³ = 1000 mm³.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

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