The NDA mathematics chapter-wise PYQ (Previous Year Questions) collection is the most critical resource for aspirants, as UPSC consistently repeats core concepts across topics like Algebra, Trigonometry, and Calculus. Analyzing these trends allows candidates to prioritize high-weightage chapters, optimize their study time, and master the specific question-solving speed required.
What is the Exam?
The National Defence Academy (NDA) examination is a prestigious, highly competitive national-level entrance exam conducted by the Union Public Service Commission (UPSC). It serves as the gateway for young aspirants to join the Indian Army, Navy, and Air Force. The selection process involves a rigorous written examination followed by the Services Selection Board (SSB) interview process, designed to assess a candidate's intellectual capacity, leadership potential, and psychological suitability for military service.
Key Highlights 2026
- Exam Conducting Body: Union Public Service Commission (UPSC)
- Exam Level: National
- Frequency: Twice a year (NDA I and NDA II)
- Mode of Exam: Offline (Pen and Paper based)
- Mathematics Paper Duration: 2.5 hours (150 minutes)
- Total Marks (Mathematics): 300 marks
- Total Questions: 120 objective-type questions
- Negative Marking: One-third (1/3rd) of the marks assigned to the question are deducted for each wrong answer.
Syllabus 2026
The Mathematics syllabus is vast and requires a systematic approach. Below is the breakdown of the core topics as per the official UPSC curriculum.
| Unit | Topics Covered |
|---|---|
| Algebra | Sets, Relations, Functions, Complex Numbers, Quadratic Equations, Sequences, Logarithms |
| Matrices & Determinants | Operations on matrices, inverse, determinants, solutions of linear equations |
| Trigonometry | Angles, Trigonometric ratios, Identities, Inverse trigonometric functions |
| Analytical Geometry | 2D (Lines, Circles) and 3D (Planes, Spheres) geometry |
| Differential Calculus | Functions, Limits, Continuity, Differentiation, Applications of derivatives |
| Integral Calculus & DE | Integration, Definite integrals, Area under curves, Differential Equations |
| Vector Algebra | Scalar/Vector products, magnitude, applications |
| Statistics & Probability | Frequency distribution, mean, median, mode, Probability basics |
Exam Pattern
The Mathematics paper is a separate section in the GAT (General Ability Test) paper structure. Because of the negative marking, strategic selection of questions is vital. When you practice free mock tests for Defence on Exam Bhai, you simulate the real-time pressure that tests your ability to skip time-consuming questions.
| Paper | Subject | Total Marks | Duration |
|---|---|---|---|
| Paper I | Mathematics | 300 | 2.5 Hours |
| Paper II | GAT | 600 | 2.5 Hours |
Eligibility Criteria
As stipulated by the UPSC official portal, candidates must meet specific requirements:
- Nationality: Citizen of India, subject of Nepal/Bhutan, or Tibetan refugee.
- Age: Must be unmarried and between the age of 16.5 to 19.5 years.
- Educational Qualification:
- For Army: 12th pass under 10+2 pattern.
- For Air Force/Navy: 12th pass with Physics, Chemistry, and Mathematics.
Application Process
- Notification: Visit upsc.gov.in to download the official notification.
- Registration: Fill out Part I and Part II of the online form.
- Exam Center: Select your preferred exam city.
- Fee Payment: Pay the required examination fee (exempted for SC/ST and wards of JCOs/NCOs).
- Admit Card: Download the admit card from the UPSC website 3 weeks before the exam.
Preparation Strategy
At Exam Bhai, we emphasize that success in NDA Math isn't about solving every question—it’s about choosing the right ones.
1. Master the PYQs
Treat chapter-wise PYQs as your primary textbook. Many students make the mistake of jumping into advanced books before understanding the pattern of questions asked by the UPSC. Start by categorizing questions based on the weightage provided in our syllabus table.
2. Strategic Time Management
With 120 questions in 150 minutes, you have roughly 75 seconds per question. Use this time to access curated NDA study materials to practice speed drills.
3. Focus on High-Yield Topics
Probability, Statistics, and Matrices often provide the highest Return on Investment (ROI). These topics are formula-driven and take less time than complex calculus problems. You should analyze your performance with detailed analytics after every mock session to see if your accuracy in these high-yield areas is improving.
Cut-Off Trends
Based on historical data from the UPSC official website, the qualifying marks for the written examination typically hover between 25% and 30% per subject. However, to secure a recommendation in the final merit list, candidates should aim for at least 40% to 50% in the mathematics section. Always monitor the official UPSC cut-off trends to understand the evolving difficulty levels.
Frequently Asked Questions
Q1: Is it mandatory to clear the cutoff for each subject separately?
Yes, UPSC mandates that candidates secure at least the minimum qualifying marks in both Mathematics and the General Ability Test (GAT) to qualify for the SSB interview.
Q2: Are NDA math questions repetitive?
While the exact numbers change, the underlying concepts and the methodology of framing questions remain highly consistent. This is why practicing chapter-wise PYQs for the last 10 years is essential.
Q3: Which books are best for NDA Math besides PYQs?
Apart from PYQs, NCERT Mathematics textbooks (Class 11 and 12) are the gold standard for building conceptual foundations. R.S. Aggarwal is a popular supplementary resource.
Q4: How do I handle negative marking in Mathematics?
Accuracy is more important than volume. If you are unsure of the answer, skip it. With 120 questions available, you do not need to attempt all of them to cross the cutoff.
Q5: Is Calculus very difficult for NDA?
Calculus covers roughly 25-30% of the paper. While it can be challenging, focusing on the basics of derivatives, limits, and integration using standard formulas is sufficient for most exam questions.
Q6: Can I use a calculator in the NDA exam?
No, the use of calculators or any electronic device is strictly prohibited inside the examination hall. You must develop strong mental calculation skills.
Crush Your Defence Exam
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