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NDA Practice Questions
Original practice questions for the National Defence Academy & Naval Academy Examination (Union Public Service Commission (UPSC)), mixed across 6 topics with instant answers and explanations. Practise by topic below or take the timed mock test.
NDA mixed practice
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Q1.AlgebraFind log₃ 243.
Show answer & explanation
Answer: D — 5
log_3(243) asks “3 to what power gives 243?” → 3^5 = 243, so the answer is 5.
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Q2.Geometry & MensurationA right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
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Answer: A — 15 cm
By Pythagoras, hypotenuse = √(9² + 12²) = √225 = 15.
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Q3.Probability & CombinatoricsIn how many ways can the letters of the word GARDEN be arranged?
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Answer: D — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q4.PhysicsThe frequency of a wave is measured in:
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Answer: D — Hertz
1 hertz = 1 cycle per second.
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Q5.ChemistryThe main component of natural gas is:
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Answer: D — Methane
Methane (CH₄).
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Q6.English GrammarChoose the correct option: The committee ___ divided in their opinions.
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Answer: B — were
When members of a collective noun act individually (divided opinions), a plural verb is used: “were”.
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Q7.AlgebraFind the sum of the first 24 terms of the AP 10, 15, 20, …
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Answer: D — 1620
Sₙ = n/2 × [2a + (n − 1)d] = 24/2 × [20 + 115] = 1,620.
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Q8.Geometry & MensurationFind the volume of a cylinder with radius 14 cm and height 20 cm (take π = 22/7).
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Answer: D — 12,320 cm³
Using πr²h with π = 22/7: 12,320 cm³.
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Q9.Probability & CombinatoricsIn how many ways can a committee of 2 be chosen from 8 people?
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Answer: A — 28
Order does not matter → combinations: 8C2 = 8! / (2!·6!) = 28.
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Q10.PhysicsFind the power dissipated when 3 A flows through a 25 Ω resistor.
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Answer: A — 225 W
P = I²R = 3² × 25 = 225 W.
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.
Practise by topic
- Algebra questions — Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution.
- Geometry & Mensuration questions — Memorise core formulas (circle πr², triangle ½bh, Pythagoras, distance √((x₂−x₁)² + (y₂−y₁)²)).
- Probability & Combinatorics questions — Probability = favourable ÷ total outcomes.
- Physics questions — Write the formula before substituting and keep SI units throughout.
- Chemistry questions — Moles = mass ÷ molar mass; molarity = moles ÷ litres.
- English Grammar questions — Find the subject first and make the verb agree with it, ignoring phrases in between.
- NDA mock test — 25 timed questions with negative marking.
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 |