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Claim Free Beta AccessThe NDA Mathematics paper consists of 120 multiple-choice questions carrying 300 marks, with Algebra, Calculus, and Matrices & Determinants contributing over 65% of the total weightage. Mastering high-yield chapters and regular mock practice are essential for clearing the sectional cut-off and securing a recommendation.
What is the Exam?
The National Defence Academy (NDA) Examination is a prestigious national-level defense entrance test conducted twice a year by the Union Public Service Commission (UPSC). It serves as the gateway for young aspirants seeking entry into the Army, Navy, and Air Force wings of the NDA, as well as the Indian Naval Academy Course (INAC).
At ExamBhai, we understand that cracking the NDA exam requires more than just hard work; it demands a strategic understanding of the syllabus and meticulous tracking of chapter-wise weightage. The written examination comprises two papers: Mathematics and the General Ability Test (GAT). Among these, the Mathematics paper acts as a critical filter. Candidates must clear the individual sectional cut-off in Mathematics to have their GAT paper evaluated. Our expert mentors have designed this guide to provide a deep, analytical breakdown of the NDA mathematics syllabus chapter wise weightage, helping you channel your preparation toward maximum score efficiency.
Key Highlights 2026
To stay ahead of the competition, every serious aspirant must keep track of the critical administrative and structural parameters governing the examination. Below is the quick reference table highlighting the key details for the upcoming cycles:
| Parameter | Details |
|---|---|
| Exam Name | National Defence Academy and Naval Academy Examination (NDA & NA) |
| Conducting Body | Union Public Service Commission (UPSC) |
| Frequency | Twice a year (NDA I and NDA II) |
| Stages of Selection | Written Examination (Mathematics & GAT) followed by SSB Interview |
| Total Marks for Math | 300 Marks |
| Number of Questions | 120 Objective-type questions |
| Marking Scheme | +2.5 marks for correct answers, -0.83 marks for incorrect answers |
| Official Website | upsc.gov.in |
Syllabus 2026
The NDA Mathematics syllabus spans across several core branches of senior secondary mathematics. Understanding the thematic distribution allows aspirants to prioritize high-scoring topics. Below is the detailed chapter-wise weightage analysis based on historical trends:
| Chapter / Topic | Approximate Number of Questions | Approximate Marks | Core Focus Areas |
|---|---|---|---|
| Algebra | 30 - 35 | 75 - 87.5 | Sets, Relations, Functions, Complex Numbers, Quadratic Equations, (AP), (GP), (HP), Permutations & Combinations, Binomial Theorem |
| Matrices and Determinants | 25 - 30 | 62.5 - 75 | Types of matrices, operations, determinant properties, inverse, system of linear equations |
| Trigonometry | 20 - 25 | 50 - 62.5 | Ratios, multiple and sub-multiple angles, inverse trigonometric functions, properties of triangles |
| Calculus | 25 - 30 | 62.5 - 75 | Limits, continuity, differentiability, derivatives, applications of derivatives, integration, differential equations |
| Vector Algebra & 3D Geometry | 15 - 20 | 37.5 - 50 | Vectors in two and three dimensions, dot and cross products, lines and planes in 3D space |
| Analytical Geometry (2D) | 10 - 15 | 25 - 37.5 | Straight lines, circles, parabola, ellipse, hyperbola |
| Statistics and Probability | 10 - 12 | 25 - 30 | Frequency distributions, measures of central tendency, probability axioms, conditional probability |
When studying Algebra, focus heavily on quadratic equations and properties of roots, ensuring you can evaluate expressions like (x^2+px+q=0) swiftly. Similarly, in Calculus, mastering integration techniques for definite integrals like (\int_{0}^{\pi/2} \sin^n x , dx) can save crucial minutes during the actual test.
Exam Pattern
The structure of the NDA Mathematics paper is designed to test both computational speed and conceptual clarity within a strict time limit.
- Duration: 2.5 hours (150 minutes)
- Total Questions: 120 questions
- Maximum Marks: 300 marks
- Marking Scheme: Each correct answer fetches 2.5 marks. A penalty of 0.33 of the marks assigned to that question (i.e., -0.83 marks) is deducted for every incorrect response.
- Medium of Exam: Bilingual (English and Hindi)
Because time management is the biggest bottleneck, candidates must build a robust strategy. To evaluate your speed against fellow aspirants across the country, we strongly recommend you practice free mock tests for Defence on ExamBhai on a weekly basis.
Eligibility Criteria
Before committing to a rigorous preparation schedule, candidates must verify their eligibility as prescribed by the governing authority. According to the guidelines published on the official portal upsc.gov.in, the criteria include:
- Nationality: Must be an Indian citizen, a subject of Bhutan or Nepal, or a Tibetan refugee who came over to India before January 1, 1962.
- Age Limit: Only unmarried male and female candidates born between specific dates notified in the official notification are eligible. Typically, candidates must be between 16.5 and 19.5 years of age.
- Educational Qualification:
- For Army Wing: 12th Class pass of the 10+2 pattern of school education or equivalent examination conducted by a State Education Board or a University.
- For Air Force and Naval Wings and cadet entry scheme of the Indian Naval Academy: 12th Class pass with Physics, Chemistry, and Mathematics of the 10+2 pattern or equivalent.
Application Process
The application process for the NDA examination is conducted online through the official UPSC portal. Here is a step-by-step overview of how to apply:
- One-Time Registration (OTR): Visit the official website upsc.gov.in or upsconline.nic.in and complete the OTR profile by entering basic personal and educational details.
- Form Submission: Log in using your OTR credentials, select the NDA examination notification, and fill out Part I and Part II of the application form.
- Fee Payment: Pay the requisite application fee of INR 100 (SC/ST candidates, sons of serving/retired JCOs, NCOs, and Other Ranks are typically exempted from the fee).
- Center Selection and Final Submission: Choose your preferred examination center city, verify all entered details, and submit the application. Take a printout of the final confirmation page for future reference.
Preparation Strategy
Achieving a high score in the NDA Mathematics paper requires disciplined execution and smart resource utilization. Here are the core pillars of an effective preparation strategy:
- Focus on High-Weightage Chapters: Dedicate at least 60% of your study timeline to Algebra, Matrices & Determinants, and Calculus, as these consistently yield the highest number of questions.
- Formula Retention: Maintain a dedicated formula notebook for Trigonometry, 3D Geometry, and Coordinate Geometry. Regular revision prevents silly calculation errors.
- Previous Years' Analysis: Solve at least the last 5 to 7 years of UPSC NDA past papers to identify recurring question patterns and conceptual templates.
- Timed Sectional Practice: Since you have only 125 seconds per question on average, speed is paramount. Use structured platforms to practice free mock tests for Defence on ExamBhai to build exam-day stamina.
- Error Analysis: After every mock test, carefully review unattempted or incorrect questions to eliminate conceptual gaps.
To enhance your daily practice regimen, you can also explore our dedicated modules and practice free mock tests for Defence on ExamBhai which mirror the exact difficulty level set by the commission.
Cut-Off Trends
Understanding past cut-off trends helps aspirants set a clear target score. The UPSC releases two tiers of cut-offs: the sectional cut-off (minimum qualifying marks required in Mathematics, usually 25% which is 75 marks out of 300) and the final written total cut-off.
According to official data archived on upsc.gov.in, the historical trends show that:
- The minimum qualifying percentage for the Mathematics paper has consistently remained around 25% of the total 300 marks.
- However, to be safe and clear the overall written stage comfortably, candidates generally aim for a score between 140 and 170 marks in Mathematics alone.
- Final recommendation cut-offs fluctuate based on the total vacancies and the combined score of the written exam and the SSB interview.
Frequently Asked Questions
What is the total weightage of Calculus in the NDA mathematics paper?
Calculus generally contributes around 25 to 30 questions in the NDA mathematics paper, translating to approximately 62.5 to 75 marks. Key sub-topics include limits, derivatives, definite and indefinite integration, and differential equations.
Is negative marking applicable in the NDA Mathematics exam?
Yes, negative marking is applicable. For every incorrect answer, 0.33 of the marks assigned to that question—which equals 0.83 marks—will be deducted from your total score.
Can commerce or arts students without Mathematics in Class 12 apply for NDA?
Yes, commerce and arts students can apply for the Army wing of the NDA, provided they have passed the 12th standard examination. However, Mathematics in Class 12 is mandatory for candidates applying to the Air Force and Naval wings.
What is the minimum qualifying mark required in the NDA math paper?
Candidates must secure a minimum qualifying percentage (historically 25%, which is 75 out of 300 marks) in the Mathematics paper to clear the sectional cut-off and ensure the evaluation of their GAT paper.
How many questions are asked in the NDA Mathematics exam?
The NDA Mathematics paper consists of exactly 120 objective-type multiple-choice questions, each carrying 2.5 marks, making the maximum possible score 300 marks.
Are calculators allowed inside the NDA examination hall?
No, electronic devices such as calculators, log tables, cellular phones, smartwatches, and any other computing gadgets are strictly prohibited inside the NDA examination hall.
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