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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 2021 · Q63

Medium

There are three points P, Q and R on a straight line such that PQ: QR = 3: 5. If n is the number of possible values of PQ: PR, then what is n equal to?

Answer & explanation

Answer: (b) 2

With PQ = 3 and QR = 5, either Q lies between P and R (PR = 8) or P lies between Q and R (PR = 2); R cannot lie between P and Q because QR is longer than PQ. That gives two ratios, 3 : 8 and 3 : 2.

  1. Take PQ = 3 and QR = 5 units.
  2. Q between P and R: PR = 3 + 5 = 8, so PQ : PR = 3 : 8.
  3. P between Q and R: QR = QP + PR, so PR = 5 − 3 = 2, giving PQ : PR = 3 : 2.
  4. R between P and Q is impossible: then QR (5) would be part of PQ (3).
  5. So there are 2 possible values: n = 2.

Remember · For points on a line, try each point as the middle one and drop the orders that break the given lengths.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2021 · Q68

Easy

A cubical vessel of side 1 m is filled completely with water. How many millilitres of water is contained in it (neglect thickness of the vessel)?

Answer & explanation

Answer: (d) 1000000

A cube of side 1 m holds 1 m³ = 100 × 100 × 100 cm³ = 10 lakh cm³, and each cubic centimetre is one millilitre. So it contains 1000000 mL, i.e. 1000 litres.

  1. Volume = 1 m × 1 m × 1 m = 1 m³.
  2. 1 m³ = 100 cm × 100 cm × 100 cm = 1000000 cm³.
  3. 1 cm³ = 1 mL, so the vessel holds 1000000 mL.
  4. Check: 1 m³ = 1000 litres, and 1 litre = 1000 mL.

Remember · 1 m³ = 1000 L = 10⁶ mL; 1 cm³ = 1 mL.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

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