NDA 1 & NDA 2 Mathematics Previous Year Question Papers with Answer Key; Download PDF
NDA Mathematics is the first paper of the National Defence Academy exam conducted by UPSC in NDA 1 and NDA 2. The paper carries 300 marks with 120 objective questions to be solved in two and a half hours, and it is compulsory for candidates opting for the Army, Navy, Air Force or Naval Academy wings. Year wise papers for NDA 2026 and earlier cycles are listed below.
NDA Maths Question Paper and Answer Key PDF
NDA Mathematics Exam Pattern 2026
NDA 2026 Mathematics paper follows a fixed pattern that UPSC has kept steady for years. Reading the exam pattern before solving the first past paper is important because the 2.5 mark question weight and the sharp 0.83 mark penalty shape the entire attempt strategy.
| Feature | Details |
|---|---|
| Mode of Exam | Offline, pen and paper with an OMR sheet |
| Paper Name | Paper I – Mathematics |
| Type of Questions | Objective multiple choice, four options each |
| Total Questions | 120 |
| Total Marks | 300 |
| Marks per Correct Answer | 2.5 marks |
| Negative Marking | 0.83 mark (1/3 of 2.5) for every wrong answer |
| Duration | 2 hours 30 minutes (150 minutes) |
| Language of Paper | English and Hindi (bilingual) |
| Level of Questions | 10+2 (Class 11 and Class 12) |
Important Chapters in NDA Mathematics
NDA 2026 Mathematics paper spreads 120 questions across eight main chapters of the Class 11 and 12 syllabus. Not all chapters carry equal weight, and candidates who plan their revision around the top three chapters usually gain 50 to 60 marks even before touching the rest.
| Chapter | Questions | Weightage | Key Topics |
|---|---|---|---|
| Algebra | 20 to 25 | ~18% | Sets, Complex Numbers, Quadratic Equations, Binomial Theorem, Sequences |
| Calculus (Differential + Integral) | 20 to 25 | ~18% | Limits, Continuity, Differentiation, Integration, Applications of Derivatives |
| Trigonometry | 20 to 25 | ~18% | Identities, Inverse Trigonometric Functions, Heights and Distances |
| Analytical Geometry (2D & 3D) | 15 to 20 | ~14% | Straight Lines, Circles, Conics, Point and Plane in Space |
| Probability and Statistics | 10 to 15 | ~10% | Mean, Median, SD, Probability Distributions, Bayes Theorem |
| Matrices and Determinants | 8 to 10 | ~7% | Types, Properties, Adjoint, Inverse, System of Equations |
| Vector Algebra | 5 to 8 | ~5% | Dot Product, Cross Product, Applications in Geometry |
| Differential Equations | 5 to 8 | ~5% | Order, Degree, Formation and General Solution |
Algebra, Calculus and Trigonometry together account for close to 55 percent of the paper. Analytical Geometry and Probability follow closely, while Vector Algebra and Differential Equations are the shortest sections but still fully scoring since the questions are direct.
NDA Mathematics Books and Preparation Resources
NDA 2026 Mathematics preparation works best when candidates use the right mix of concept books, practice books, and past papers. Piling on too many books slows revision down. The list below covers the resources that most toppers stick to, grouped by what each one is meant for.
Concept Building
- NCERT Mathematics for Class 11 and Class 12 (both parts) - the base for every chapter.
- Mathematics for NDA and NA by R S Aggarwal - clear theory with worked examples.
Practice and Problem Solving
- NDA Pathfinder by Arihant - topic wise question banks with solutions.
- Study Package Mathematics for NDA/NA by Arihant - for extra problems on tough chapters.
- Objective Mathematics by R D Sharma - for candidates who want deeper practice in Calculus and Algebra.
Past Papers and Mock Tests
- NDA Mathematics previous year papers compiled year wise along with study material, ideally for the last six to eight cycles.
- Weekly full length mock tests matched to the 120 question, 150 minute format.
- Chapter tests for high weightage sections like Calculus and Trigonometry.
NDA Mathematics Recommended Attempt Strategy
A well planned attempt strategy in NDA Mathematics can add 40 to 50 marks without any extra study. The idea is to keep the flow of the paper moving forward and never let a single tough question eat into the time of five easier ones. The steps below are the order most toppers follow inside the exam hall.
1. Open the paper and quickly go through all 120 questions in the first 10 minutes. Mark the ones that look direct with a small tick.
2. Start the first pass with Trigonometry, Matrices and Determinants, and Straight Lines. These give quick marks and warm up the mind.
3. Move to Algebra, Complex Numbers, and Probability in the second pass. Most sums are one or two step.
4. Attempt Calculus and Analytical Geometry (3D) in the third pass. These are calculation heavy but scoring if concepts are strong.
5. Leave the shortest chapters (Vector Algebra, Differential Equations) for the last 15 minutes. The questions are direct and can be solved fast.
6. Never spend more than two minutes on a single question in the first round. If a sum is not clicking, skip and come back.
7. Guess only when two options can be safely ruled out. Blind guessing hurts because the penalty per wrong answer is nearly one full mark.
NDA Mathematics is a paper where preparation pays back in a straight line. Every extra hour spent on Calculus and Trigonometry, every mistake caught in a paper, and every mock test scored on time shows up in the final marks. Regular practice with NDA Mathematics previous year papers and full length mock tests builds the twin habits UPSC looks for accuracy and speed. Candidates who follow this loop for three months usually see their score climb from around 120 to well past 200, which is enough to clear the paper safely and open the door to the SSB interview.
| Relevant Links | ||
|---|---|---|
| NDA Eligibility | NDA Admit Card | NDA Result |
| NDA Application Process | NDA Answer Key | NDA Salary |
NDA Mathematics Previous Year Question Papers FAQs
Ques: Is the NDA Mathematics paper the same for Army, Navy and Air Force candidates?
Ans: Yes. UPSC sets one common Mathematics paper for all NDA candidates on the same day. The academy allotment later depends on the candidate's preference, rank, and the vacancies in each service.
Ques: What is the minimum qualifying mark in NDA Mathematics?
Ans: UPSC does not fix the qualifying mark in advance. It is decided after each exam based on paper difficulty and vacancies. In recent cycles the sectional cutoff has ranged between 25 and 30 percent of the paper's 300 marks.
Ques: Can a 10+2 appearing student take the NDA Mathematics paper?
Ans: Yes. Candidates appearing in Class 12 can apply. Mathematics as a subject in Class 12 is compulsory for the Air Force, Navy and Naval Academy wings, but not for the Army wing.
Ques: How is NDA Mathematics different from JEE Main Mathematics?
Ans: NDA questions are shorter, more direct, and closer to NCERT level. JEE Main questions test deeper concept application and often carry longer calculations. A student preparing for JEE Main will find NDA Mathematics easier, but the negative marking in NDA is sharper per question.
Ques: Are calculators or log tables allowed in NDA Mathematics?
Ans: No. Calculators, log tables, and any electronic device are strictly banned. All calculations must be done on the rough space inside the question booklet.
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