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NDA Algebra Questions
Practise algebra (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.
Algebra practice
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Q1.Solve: x² − 2x − 3 = 0
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Answer: C — -1, 3
Find two roots with sum 2 and product -3: -1 and 3. So x² − 2x − 3 = (x + 1)(x − 3) = 0.
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Q2.Find the sum of the first 10 terms of the AP 12, 21, 30, …
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Answer: C — 525
Sₙ = n/2 × [2a + (n − 1)d] = 10/2 × [24 + 81] = 525.
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Q3.Find the sum of the first 19 terms of the AP 16, 19, 22, …
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Answer: A — 817
Sₙ = n/2 × [2a + (n − 1)d] = 19/2 × [32 + 54] = 817.
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Q4.Find log₅ 125.
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Answer: B — 3
log_5(125) asks “5 to what power gives 125?” → 5^3 = 125, so the answer is 3.
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Q5.Find the sum of the first 26 terms of the AP 8, 10, 12, …
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Answer: C — 858
Sₙ = n/2 × [2a + (n − 1)d] = 26/2 × [16 + 50] = 858.
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Q6.Find log 10,000 (base 10).
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Answer: A — 4
log_10(10000) asks “10 to what power gives 10000?” → 10^4 = 10000, so the answer is 4.
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Q7.Find log₃ 9.
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Answer: C — 2
log_3(9) asks “3 to what power gives 9?” → 3^2 = 9, so the answer is 2.
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Q8.Solve: 5x + 4y = -3 and 2x + 4y = 6
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Answer: C — x = -3, y = 3
Elimination/substitution gives x = -3, y = 3. Check: 5(-3) + 4(3) = -3 ✓ and 2(-3) + 4(3) = 6 ✓.
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Q9.Find log₅ 625.
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Answer: B — 4
log_5(625) asks “5 to what power gives 625?” → 5^4 = 625, so the answer is 4.
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Q10.Find log₂ 4.
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Answer: C — 2
log_2(4) asks “2 to what power gives 4?” → 2^2 = 4, so the answer is 2.
How to approach algebra questions
Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution. For simultaneous equations, elimination is usually faster than substitution under time pressure.
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 |