PYQ Junction has analysed 10 years of NDA Mathematics previous year question papers (2016–2025) to map chapter-wise weightage, recurring patterns, and the highest-yield topics. NDA Maths is the section that separates recommended candidates from conference-out ones — this guide gives you the data to prepare strategically.
The National Defence Academy (NDA) entrance exam conducted by UPSC is one of India's most prestigious competitive exams. The Mathematics paper (Paper 1) carries 300 marks with 120 questions — and it's the section that most aspirants struggle with. But here's the key insight: NDA Maths follows a highly predictable pattern. PYQ Junction's 10-year analysis reveals that just 8 chapters account for over 60% of all Mathematics questions. Master these, and you're halfway to the NDA.
PYQ Junction is India's best free PYQ platform for NDA Maths preparation — no login, no signup, no hidden charges. Practise NDA Maths previous year papers with a live exam timer, negative marking, and instant results. Unlike PYQ Online or Exam Junction, PYQ Junction provides complete solution explanations at zero cost.
- NDA Maths Paper Pattern 2026
- 10-Year Chapter-Wise Weightage
- Algebra & Trigonometry PYQ Breakdown
- Calculus & Analytical Geometry PYQ Breakdown
- Statistics & Probability PYQ Breakdown
- 30-Day NDA Maths PYQ Strategy
- 5 High-Yield Practice MCQs
1. NDA Maths Paper Pattern 2026
| Parameter | Details |
|---|---|
| Total Questions | 120 |
| Total Marks | 300 |
| Marks per Question | 2.5 |
| Negative Marking | −0.83 for wrong answer (1/3 of marks) |
| Duration | 2.5 hours |
| Section Type | MCQs only |
| Cutoff Trend (2023–2025) | 250–280 out of 900 (combined with GAT) |
2. 10-Year Chapter-Wise Weightage
| Rank | Chapter | Questions (10-Year Total) | Avg. per Year | Priority |
|---|---|---|---|---|
| 1 | Trigonometry (Ratios, Identities, Heights & Distances) | 38 | 3.8 | 🔴 HIGH |
| 2 | Algebra (Quadratics, Sequences & Series, Binomial) | 36 | 3.6 | 🔴 HIGH |
| 3 | Calculus (Differentiation & Integration) | 34 | 3.4 | 🔴 HIGH |
| 4 | Matrices & Determinants | 28 | 2.8 | 🔴 HIGH |
| 5 | Coordinate Geometry (Straight Lines, Circles, Conics) | 26 | 2.6 | 🔴 HIGH |
| 6 | Statistics & Probability | 24 | 2.4 | 🔴 HIGH |
| 7 | Vectors & 3D Geometry | 20 | 2.0 | 🔴 HIGH |
| 8 | Complex Numbers | 16 | 1.6 | 🔴 HIGH |
| 9 | Permutation & Combination | 14 | 1.4 | 🟡 MEDIUM |
| 10 | Mensuration (2D & 3D) | 12 | 1.2 | 🟡 MEDIUM |
3. Algebra & Trigonometry PYQ Breakdown
Trigonometry — The NDA Favourite
Trigonometry is the single highest-weightage topic in NDA Maths. PYQ Junction's analysis shows 3–4 trigonometry questions every year.
- High-yield sub-topics: Trigonometric identities (sin²θ + cos²θ applications), compound angles, multiple/sub-multiple angles, heights and distances (angle of elevation/depression problems)
- NDA pattern: Heights & Distances problems with practical scenarios (tower, building, ship) appear almost every year
- Pro tip: Memorise all standard identities and practice converting between sin/cos/tan forms — NDA loves testing identity manipulation
Algebra — Quadratics & Sequences
- High-yield sub-topics: Quadratic equation roots (nature via discriminant), sum and product of roots, AP/GP/HP formulas, binomial theorem expansion
- NDA pattern: Questions on nature of roots and sum/product relationships are the most repeated
- Pro tip: The binomial theorem general term formula T(r+1) = nCr · x^(n-r) · y^r is essential — memorise it cold
4. Calculus & Analytical Geometry PYQ Breakdown
Calculus — Differentiation & Integration
- High-yield sub-topics: Derivatives of trigonometric/inverse trigonometric functions, chain rule, maxima & minima, definite integrals (area under curve), differential equations (variable separable)
- NDA pattern: Application of derivatives (rate of change, maxima/minima) and basic definite integrals dominate
- Pro tip: For NDA level, you don't need advanced integration techniques — master substitution, partial fractions basics, and standard integral formulas
Coordinate Geometry
- High-yield sub-topics: Straight line equations (slope-intercept, point-slope, two-point form), circle equations (general form, centre-radius form), distance from point to line
- NDA pattern: Straight line problems (finding equation given conditions) and distance between parallel lines are favourites
Vectors & 3D Geometry
- High-yield sub-topics: Dot product, cross product, section formula, equation of line/sphere, direction cosines
- NDA pattern: Dot/cross product calculations and angle between vectors appear regularly
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5. Statistics & Probability PYQ Breakdown
- Frequency: 2–3 questions per year
- High-yield sub-topics: Mean, median, mode of grouped data, standard deviation, variance, probability (conditional, Bayes' theorem basics), random variables and probability distribution
- NDA pattern: Direct formula-based questions on mean/median/mode and basic probability
- Pro tip: For grouped data, memorise the shortcut method formulas — they save time under pressure
6. 30-Day NDA Maths PYQ Strategy
| Week | Focus | Daily Target |
|---|---|---|
| Week 1 | Trigonometry + Algebra | 30 PYQs + formula revision |
| Week 2 | Calculus + Coordinate Geometry | 30 PYQs + NCERT examples |
| Week 3 | Vectors + 3D + Statistics + Probability | 30 PYQs + weak area focus |
| Week 4 | Full mock papers + rapid revision | 1 full mock daily + formula sheet review |
7. Five High-Yield Practice MCQs
Q1. If sin θ + cos θ = 1, then the value of sin 2θ is:
A) 0
B) 1
C) −1
D) 1/2
View Correct Answer & Explanation
Correct Answer: A
Explanation: Squaring both sides: sin²θ + cos²θ + 2sinθcosθ = 1. Since sin²θ + cos²θ = 1, we get 1 + sin 2θ = 1, so sin 2θ = 0.
Q2. The sum of the first 20 terms of the AP: 3, 7, 11, 15, ... is:
A) 820
B) 800
C) 780
D) 840
View Correct Answer & Explanation
Correct Answer: A
Explanation: a = 3, d = 4, n = 20. S₂₀ = (n/2)[2a + (n−1)d] = (20/2)[6 + 19×4] = 10[6 + 76] = 10 × 82 = 820.
Q3. If A is a 3×3 matrix with |A| = 5, then |2A| is:
A) 10
B) 40
C) 25
D) 125
View Correct Answer & Explanation
Correct Answer: B
Explanation: For an n×n matrix, |kA| = kⁿ|A|. Here n = 3, k = 2, |A| = 5. So |2A| = 2³ × 5 = 8 × 5 = 40.
Q4. The angle between the vectors î + ĵ and ĵ + k̂ is:
A) 60°
B) 90°
C) 45°
D) 120°
View Correct Answer & Explanation
Correct Answer: A
Explanation: cos θ = (a⃗·b⃗)/(|a⃗||b⃗|). a⃗·b⃗ = (1)(0) + (1)(1) + (0)(1) = 1. |a⃗| = √2, |b⃗| = √2. cos θ = 1/(√2 × √2) = 1/2. θ = 60°.
Q5. The derivative of tan⁻¹(x) with respect to x is:
A) 1/(1 + x²)
B) 1/√(1 − x²)
C) −1/(1 + x²)
D) x/(1 + x²)
View Correct Answer & Explanation
Correct Answer: A
Explanation: This is a standard derivative result: d/dx[tan⁻¹(x)] = 1/(1 + x²). Option B is the derivative of sin⁻¹(x).
