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NDA Mock Test
A timed 25-question mock for the National Defence Academy & Naval Academy Examination covering algebra, geometry & mensuration, probability & combinatorics, physics, chemistry, english grammar. Answer, submit and review every question with its explanation; set negative marking to match your exam’s current scheme.
NDA mock test
25 questions · 1 mark each · the timer starts with your first answer and the test submits itself when time runs out.
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Q1.AlgebraSolve: x² − 15x + 54 = 0
Answer: A — 6, 9
Find two roots with sum 15 and product 54: 6 and 9. So x² − 15x + 54 = (x − 6)(x − 9) = 0.
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Q2.Geometry & MensurationFind the volume of a sphere of radius 7 cm (take π = 22/7).
Answer: C — 1,437.33 cm³
Using (4/3)πr³ with π = 22/7: 1,437.33 cm³.
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Q3.Probability & CombinatoricsA card is drawn from a well-shuffled deck of 52. What is the probability that it is a king?
Answer: B — 1/13
There are 4 such cards in 52, so P = 4/52 = 1/13.
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Q4.PhysicsWork done is zero when the force is:
Answer: D — Perpendicular to displacement
W = Fd cos θ; at 90° cos θ = 0.
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Q5.ChemistryThe main component of natural gas is:
Answer: D — Methane
Methane (CH₄).
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Q6.English GrammarChoose the correct option: Hardly had he left ___ it started raining.
Answer: C — when
The correlative pair is “hardly … when” (also “no sooner … than”).
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Q7.AlgebraFind the sum of the first 22 terms of the AP 14, 18, 22, …
Answer: A — 1232
Sₙ = n/2 × [2a + (n − 1)d] = 22/2 × [28 + 84] = 1,232.
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Q8.Geometry & MensurationA right triangle has legs 5 cm and 12 cm. Find the hypotenuse.
Answer: C — 13 cm
By Pythagoras, hypotenuse = √(5² + 12²) = √169 = 13.
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Q9.PhysicsA body starts at 1 m/s and accelerates uniformly at 6 m/s² for 7 s. Find its final velocity.
Answer: B — 43 m/s
v = u + at = 1 + 6×7 = 43 m/s.
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Q10.ChemistryWhat is the mass of 0.5 mol of water (H₂O)? (Molar mass 18 g/mol)
Answer: B — 9 g
Mass = moles × molar mass = 0.5 × 18 g/mol = 9 g.
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Q11.English GrammarChoose the correct option: He prefers tea ___ coffee.
Answer: B — to
“Prefer X to Y” is the correct pattern.
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Q12.AlgebraSolve: x² + 7x − 18 = 0
Answer: B — -9, 2
Find two roots with sum -7 and product -18: -9 and 2. So x² + 7x − 18 = (x + 9)(x − 2) = 0.
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Q13.Geometry & MensurationFind the distance between (-3, -3) and (3, 5).
Answer: C — 10
Distance = √((Δx)² + (Δy)²) = √(6² + 8²) = 10.
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Q14.Probability & CombinatoricsIn how many ways can a committee of 2 be chosen from 12 people?
Answer: D — 66
Order does not matter → combinations: 12C2 = 12! / (2!·10!) = 66.
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Q15.PhysicsThe unit of electrical resistance is the:
Answer: D — Ohm
Resistance is measured in ohms (Ω).
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Q16.ChemistryThe noble gas used in advertising signs that glows red-orange is:
Answer: A — Neon
Neon glows red-orange in discharge tubes.
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Q17.English GrammarChoose the correct option: I would rather you ___ now.
Answer: A — left
“Would rather + subject” is followed by the past tense for present/future meaning: “left”.
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Q18.AlgebraFind the sum of the first 25 terms of the AP 14, 17, 20, …
Answer: B — 1250
Sₙ = n/2 × [2a + (n − 1)d] = 25/2 × [28 + 72] = 1,250.
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Q19.Geometry & MensurationFind the distance between (4, 1) and (10, 9).
Answer: D — 10
Distance = √((Δx)² + (Δy)²) = √(6² + 8²) = 10.
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Q20.Probability & CombinatoricsTwo fair dice are thrown. What is the probability that the sum is 7?
Answer: A — 1/6
6 of the 36 equally likely outcomes give a sum of 7, so P = 6/36 = 1/6.
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Q21.PhysicsA body with initial velocity 3 m/s accelerates at 6 m/s² for 7 s. Find the distance covered.
Answer: B — 168 m
s = ut + ½at² = 3×7 + ½×6×7² = 168 m.
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Q22.Chemistry90 g of NaCl (molar mass 58.5) is dissolved to make 2000 mL of solution. Find the molarity.
Answer: C — 0.769 M
Moles = 90/58.5 = 1.539; molarity = moles ÷ litres = 1.539 ÷ 2 = 0.769 M.
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Q23.English GrammarIdentify the error: “Each of the students have submitted their assignment.”
Answer: B — have submitted
“Each” is singular, so the verb should be “has submitted”.
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Q24.AlgebraFind log 1,000 (base 10).
Answer: D — 3
log_10(1000) asks “10 to what power gives 1000?” → 10^3 = 1000, so the answer is 3.
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Q25.Geometry & MensurationFind the area of a right triangle with legs 20 cm and 21 cm.
Answer: C — 210 cm²
Area = ½ × base × height = ½ × 20 × 21 = 210 cm².
How the mock test works
- The timer starts with your first answer; the test submits itself when time runs out.
- Choose the negative marking that matches your exam (many Indian exams deduct ¼ or ⅓ of a mark — check the official notification).
- After submitting you get your score, accuracy, time taken and a topic-wise breakdown, then every explanation.
- “New mock test” builds another paper — calculation questions get new numbers.
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 |