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NDA Geometry & Mensuration Questions
Practise geometry & mensuration (mathematics) for the National Defence Academy & Naval Academy Examination: 10 multiple-choice questions, each with the correct answer and a worked explanation. Click an option to check it, or “New questions” for another set.
Geometry & Mensuration practice
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Q1.Find the distance between (5, 0) and (13, 15).
Show answer & explanation
Answer: D — 17
Distance = √((Δx)² + (Δy)²) = √(8² + 15²) = 17.
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Q2.Find the volume of a cylinder with radius 14 cm and height 16 cm (take π = 22/7).
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Answer: C — 9,856 cm³
Using πr²h with π = 22/7: 9,856 cm³.
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Q3.Find the distance between (3, 5) and (11, 20).
Show answer & explanation
Answer: A — 17
Distance = √((Δx)² + (Δy)²) = √(8² + 15²) = 17.
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Q4.Find the distance between (1, -1) and (6, 11).
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Answer: B — 13
Distance = √((Δx)² + (Δy)²) = √(5² + 12²) = 13.
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Q5.Find the volume of a cylinder with radius 3.5 cm and height 4 cm (take π = 22/7).
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Answer: A — 154 cm³
Using πr²h with π = 22/7: 154 cm³.
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Q6.Find the area of a right triangle with legs 20 cm and 21 cm.
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Answer: B — 210 cm²
Area = ½ × base × height = ½ × 20 × 21 = 210 cm².
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Q7.Find the distance between (5, -3) and (10, 9).
Show answer & explanation
Answer: D — 13
Distance = √((Δx)² + (Δy)²) = √(5² + 12²) = 13.
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Q8.Find the distance between (5, 5) and (10, 17).
Show answer & explanation
Answer: B — 13
Distance = √((Δx)² + (Δy)²) = √(5² + 12²) = 13.
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Q9.Find the area of a right triangle with legs 8 cm and 15 cm.
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Answer: D — 60 cm²
Area = ½ × base × height = ½ × 8 × 15 = 60 cm².
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Q10.Find the distance between (-5, -2) and (1, 6).
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Answer: C — 10
Distance = √((Δx)² + (Δy)²) = √(6² + 8²) = 10.
How to approach geometry & mensuration questions
Memorise core formulas (circle πr², triangle ½bh, Pythagoras, distance √((x₂−x₁)² + (y₂−y₁)²)). Sketch the figure — most errors come from misreading which length is given.
About NDA
National Defence Academy & Naval Academy Examination — conducted by Union Public Service Commission (UPSC). Entry to the tri-service National Defence Academy after Class 12, with Mathematics and General Ability papers.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
NDA practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Physics | Science | Calculated + question bank |
| Chemistry | Science | Calculated + question bank |
| English Grammar | English | Question bank |