NDA Syllabus 2026: Subject-Wise Maths & GAT + PDF

The nda syllabus is set by the UPSC and split into two written papers — Mathematics (300 marks) and the General Ability Test / GAT (600 marks) — for a total of 900 marks, followed by a 900-mark SSB Interview. Mathematics is drawn from the Class 11 and 12 NCERT/CBSE level, while the GAT tests English plus General Knowledge across Physics, Chemistry, General Science, History, Geography and Current Events. This guide gives you the complete, UPSC-official, subject-wise NDA syllabus with the exam pattern, chapter-wise weightage, a printable one-page chart, stream-specific study plans and a free PDF download.

NDA Syllabus 2026 — Quick Answers:

• Papers: 2 written — Mathematics (300) + GAT (600) = 900 marks.
• GAT split: English 200 marks + General Knowledge 400 marks.
• Highest weightage: GAT (600/900); within GK, Physics leads at ~100 marks.
• Level: Maths = Class 11–12 NCERT; GK Physics/Chemistry = Class 9–10; History/Geography = Class 6–10.
• Negative marking: 1/3 of the marks for every wrong answer in both papers.
• Time to prepare: 4–6 focused months.

This guide is based on the official UPSC NDA & NA Examination notification and has been reviewed for the 2026 exam cycle. Always confirm the topic list against the latest UPSC notification for your attempt.

NDA Exam Overview 2026

The National Defence Academy (NDA) & Naval Academy (NA) Examination is conducted by the Union Public Service Commission (UPSC) twice a year — usually notified in December (NDA I) and May/June (NDA II). It is the gateway for admission to the Army, Navy and Air Force wings of the NDA and the Indian Naval Academy Course (INAC). Unmarried candidates who have passed or are appearing in Class 12 are eligible; a Physics and Mathematics background in Class 12 is mandatory for the Air Force, Navy and the Naval Academy, while the Army wing accepts any stream.

The selection process has three clear stages: (1) the Written Examination (900 marks) covering the nda exam pattern and syllabus explained below, (2) the SSB Interview (900 marks), and (3) the medical examination. Only candidates who clear the written cut-off are called for the SSB. Understanding the full nda syllabus 2026 before you start is the single biggest time-saver, because roughly 60% of the marks come from just the GAT paper.

NDA Exam Pattern and Syllabus at a Glance

Both papers are objective (MCQ) type and are held on the same day — Mathematics in the morning session and the GAT in the afternoon. The question papers are bilingual (English and Hindi), except the English portion of the GAT. Here is the complete nda exam pattern and syllabus in one table.

Marking scheme decoded: In Maths every correct answer earns 2.5 marks and every wrong answer deducts 0.83 marks (one-third). In the GAT, correct answers earn 4 marks and wrong answers deduct 1.33 marks. With a 1/3 negative-marking rule, blind guessing is punished — attempt a question only when you can eliminate at least two options.

NDA Maths Syllabus 2026 (Paper 1 — 300 Marks)

The nda maths syllabus is the highest-scoring section per question and is entirely rooted in the Class 11 and 12 CBSE/NCERT curriculum. There are 120 questions worth 300 marks. Below is the UPSC-official topic list, chapter by chapter, exactly as it appears in the notification.

Algebra

Concept of a set, operations on sets, Venn diagrams. De Morgan laws, Cartesian product, relation, equivalence relation. Representation of real numbers on a line. Complex numbers — basic properties, modulus, argument, cube roots of unity. Binary system of numbers, conversion of a number in decimal to binary and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications.

Matrices and Determinants

Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix. Applications — solution of a system of linear equations in two or three unknowns by Cramer’s rule and by the Matrix Method.

Trigonometry

Angles and their measures in degrees and radians. Trigonometrical ratios. Trigonometric identities, sum and difference formulae. Multiple and sub-multiple angles. Inverse trigonometric functions. Applications — height and distance, properties of triangles.

Analytical Geometry (2D and 3D)

Rectangular Cartesian Coordinate system. Distance formula, equation of a line in various forms, angle between two lines, distance of a point from a line. Equation of a circle in standard and general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in a three-dimensional space, distance between two points. Direction cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

Differential Calculus

Concept of a real-valued function — domain, range and graph. Composite functions, one-to-one, onto and inverse functions. Notion of limit, standard limits. Continuity of functions and algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical interpretation of a derivative — applications. Derivatives of sum, product and quotient of functions, derivative of a function with respect to another function, derivative of a composite function. Second-order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.

Integral Calculus and Differential Equations

Integration as inverse of differentiation, integration by substitution and by parts. Standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals — determination of areas of plane regions bounded by curves — applications. Definition of order and degree of a differential equation, formation of a differential equation. General and particular solution of differential equations, solution of first-order and first-degree differential equations of various types. Application in problems of growth and decay.

Vector Algebra

Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, addition of vectors, scalar multiplication of a vector, scalar (dot) product and vector (cross) product of two vectors. Applications — work done by a force and moment of a force, and in geometrical problems.

Statistics and Probability

Statistics — classification of data, frequency distribution, cumulative frequency distribution. Graphical representation — histogram, pie chart, frequency polygon. Measures of central tendency — mean, median and mode. Variance and standard deviation, correlation and regression. Probability — random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary and composite events. Definition of probability — classical and statistical. Conditional probability, Bayes’ theorem, Binomial distribution, random variable as function on a sample space, expectation.

NDA Maths Chapter-Wise Weightage & Expected Questions

Based on previous-year-question trends across recent NDA papers, here is the approximate distribution of 120 Maths questions. Use it to decide where your revision hours go.

The takeaway: Algebra, Trigonometry, Calculus and Analytical Geometry together account for roughly 70% of the paper. If you master these four blocks first, you secure the bulk of the 300 marks before touching the smaller chapters.

NDA GAT Syllabus 2026 (Paper 2 — 600 Marks)

The nda gat syllabus is the deciding paper because it carries 600 of the 900 written marks. It is split into Part A — English (200 marks) and Part B — General Knowledge (400 marks), with 150 questions in total.

Part A — English (200 Marks, 50 Questions)

The English section tests the candidate’s understanding of English and the workmanlike use of words. The syllabus covers grammar and usage, vocabulary, comprehension and cohesion in extended text. Question types include:

• Spotting errors and sentence improvement
• Synonyms and antonyms
• Ordering of words in a sentence / para jumbles
• Selecting the correct word (fill in the blanks)
• Comprehension passages
• Idioms and phrases

English is a pure scoring section with no formulas — daily reading and 30 minutes of vocabulary practice can push you past 150 of 200 marks.

Part B — General Knowledge (400 Marks, 100 Questions)

Part B is a broad general-knowledge paper covering six areas: Physics, Chemistry, General Science, History & Freedom Movement, Geography and Current Events. The UPSC allots a fixed weightage to each — memorise this because it tells you exactly where the 400 marks sit.

Subject-Wise GK Syllabus Breakdown

Here is the official topic list for each of the six GAT-GK sections, so you can map your revision precisely.

Section A — Physics (100 Marks)

Physical properties and states of matter, mass, weight, volume, density and specific gravity. Principle of Archimedes, pressure barometer. Motion of objects, velocity and acceleration, Newton’s laws of motion, force and momentum, parallelogram of forces, stability and equilibrium of bodies, gravitation, work, power and energy. Effects of heat, measurement of temperature and heat, change of state and latent heat, modes of transference of heat. Sound waves and their properties, simple musical instruments. Rectilinear propagation of light, reflection and refraction, spherical mirrors and lenses, human eye. Natural and artificial magnets, properties of a magnet, Earth as a magnet. Static and current electricity, conductors and non-conductors, Ohm’s law, simple electrical circuits, heating, lighting and magnetic effects of current, measurement of electrical power, primary and secondary cells, use of X-rays. General principles of the working of Simple Pendulum, Simple Pulleys, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariner’s Compass, Lightning Conductors and Safety Fuses.

Section B — Chemistry (60 Marks)

Physical and chemical changes. Elements, mixtures and compounds, symbols, formulae and simple chemical equations, Law of Chemical Combination (excluding problems). Properties of air and water. Preparation and properties of Hydrogen, Oxygen, Nitrogen and Carbon dioxide, Oxidation and Reduction. Acids, bases and salts. Carbon — different forms. Fertilizers — natural and artificial. Material used in the preparation of substances like soap, glass, ink, paper, cement, paints, safety matches and gun-powder. Elementary ideas about the structure of atom, atomic, equivalent and molecular weights, valency.

Section C — General Science (40 Marks)

Difference between the living and non-living. Basis of Life — cells, protoplasm and tissues. Growth and reproduction in plants and animals. Elementary knowledge of the human body and its important organs. Common epidemics, their causes and prevention. Food — source of energy for man, constituents of food, balanced diet. The Solar System — meteors and comets, eclipses. Achievements of eminent scientists.

Section D — History and Freedom Movement (80 Marks)

A broad survey of Indian History, with emphasis on culture and civilisation. Freedom Movement in India. Elementary study of the Indian Constitution and Administration. Elementary knowledge of the Five-Year Plans of India. Panchayati Raj, Co-operatives and Community Development. Bhoodan, Sarvodaya, National Integration and Welfare State, Basic Teachings of Mahatma Gandhi. Forces shaping the modern world — Renaissance, Exploration and Discovery, War of American Independence, French Revolution, Industrial Revolution and Russian Revolution. Impact of Science and Technology on Society. Concept of one World, United Nations, Panchsheel, Democracy, Socialism and Communism. Role of India in the present world.

Section E — Geography (80 Marks)

The Earth, its shape and size. Latitudes and Longitudes, Concept of time. International Date Line. Movements of Earth and their effects. Origin of Earth, Rocks and their classification, Weathering — mechanical and chemical, Earthquakes and Volcanoes. Ocean Currents and Tides. Atmosphere and its composition, Temperature and Atmospheric Pressure, Planetary Winds, cyclones and anti-cyclones, Humidity, Condensation and Precipitation, Types of Climate, Major Natural Regions of the World. Regional Geography of India — climate, natural vegetation, mineral and power resources, location and distribution of agricultural and industrial activities. Important Sea ports and main sea, land and air routes of India. Main items of imports and exports of India.

Section F — Current Events (40 Marks)

Knowledge of important events that have happened in India in recent years. Current important world events. Prominent personalities — both Indian and international — including those connected with cultural activities and sports. Because this section changes every cycle, a dedicated monthly current-affairs source is essential. A structured magazine such as the Vision IAS Current Affairs Magazine (January 2026) compresses a whole month of national and international events into an exam-ready format that works just as well for NDA GK as it does for UPSC.

High-Yield Topics: Maximum Marks, Least Effort

Not every chapter deserves equal time. Here is the smart-prioritisation map that most top pages skip — the topics that give the highest return per hour of study.

Strategic sequence: lock down English (200 marks) and the Physics + History + Geography trio (180 marks) first — that is 380 GAT marks from low-volatility, high-certainty topics before you even touch current affairs.

Is the NDA Syllabus Based on Class 11 and 12 NCERT?

Yes — largely. The Mathematics paper is drawn almost entirely from the Class 11 and 12 NCERT/CBSE mathematics curriculum; a student comfortable with school-board maths already knows 90% of the topics. The GAT Physics and Chemistry portions sit at the Class 9–10 NCERT level, while General Science, History and Geography span Class 6–10 NCERT social-science and science books. This is why NCERT textbooks are the recommended foundation: the NDA does not test beyond school level, it tests school-level concepts thoroughly and at speed. The difference between NDA and a board exam is the negative marking and the time pressure — 120 maths questions in 150 minutes demands roughly 75 seconds per question.

Stream-Specific Study Plans (PCM, Arts/Commerce, Hindi-Medium)

Most guides give one generic plan. Your stream changes your strategy dramatically — here is a realistic breakdown.

Note for Arts and Commerce aspirants: you can apply for NDA. Candidates who did not study Physics and Mathematics in Class 12 are eligible only for the Army wing of the NDA; the Navy, Air Force and Naval Academy require Physics and Mathematics at the 10+2 level. Hindi-medium students face no disadvantage in eligibility — the entire question paper except GAT-English is bilingual, and dedicated Hindi study material covers the GK load comfortably.

NDA Preparation Strategy: 4–6 Month Study Plan

A focused aspirant can complete the full nda syllabus in four to six months. Here is a month-by-month timeline that balances both papers.

Daily routine: 3–4 hours of Maths, 2 hours of GAT-GK, 1 hour of English and current affairs. Reserve every Sunday for a full-length timed mock and a detailed error analysis. Track your accuracy — because of negative marking, a student attempting 90 maths questions at 85% accuracy scores far better than one attempting all 120 at 65% accuracy.

Best Books for NDA 2026 Preparation

The right booklist keeps you inside the syllabus and out of over-preparation. These are the standard, topper-recommended resources mapped to each section.

Because NDA GK overlaps heavily with civil-services General Studies, well-structured UPSC-oriented notes are an efficient shortcut for the History, Polity and Geography load. Polity is one of the most predictable scoring areas — a compact set like the Vajiram Polity Notes covers the Indian Constitution and administration topics the GAT repeatedly asks. For the economy-linked and Five-Year-Plan questions, concise Vision IAS Economics Notes give you exam-ready coverage without wading through a full textbook. Keep NCERT as your spine and use these notes to consolidate revision.

NDA Syllabus Subject-Wise PDF Download

To make revision portable, keep a one-page nda syllabus subject-wise PDF pinned to your study desk. The printable chart should list, on a single sheet: the exam pattern table, the eight Maths chapters, the six GAT-GK sections with their marks, and the high-yield topic map from this guide. You can generate your nda syllabus pdf download by using your browser’s Print > Save-as-PDF option on this page, which preserves every table above in a clean, offline format. Always cross-check the topic list against the latest UPSC NDA notification before your exam cycle, as the Commission occasionally rewords sections.

What Comes After the Written Syllabus: SSB Interview

Clearing the 900-mark written exam is only half the battle. Candidates above the cut-off are called for the SSB Interview, also worth 900 marks, conducted over 4–5 days by a Services Selection Board. It has two stages:

• Stage 1 (Screening): Officer Intelligence Rating (OIR) tests and the Picture Perception & Description Test (PP&DT). Only those who clear Stage 1 continue.
• Stage 2: Psychology tests (TAT, WAT, SRT, Self-Description), Group Testing Officer tasks (Group Discussion, GPE, PGT, HGT, Individual Obstacles, Command Task, Lecturette) and the Personal Interview, followed by the Conference.

After the SSB, selected candidates undergo a medical examination by a board of service doctors. The final merit list combines your written (900) and SSB (900) marks out of 1800 — so a balanced performance in both, not just the written syllabus, secures your seat at the Academy.

Common Mistakes NDA Aspirants Make

• Ignoring negative marking: attempting every question blindly can pull a strong candidate below the cut-off.
• Neglecting English: 200 easy marks are routinely under-prepared because aspirants over-focus on Maths.
• Skipping current affairs: the 40 Current Events marks are lost by candidates who only study static GK.
• Not practising bilingually (Hindi medium): reading maths only in English slows you down on exam day when the Hindi paper reads differently.
• Under-timing revision: without weekly full-length mocks, students never build the 75-seconds-per-question speed the paper demands.

Frequently Asked Questions

What is the syllabus of the NDA exam?

The NDA syllabus has two written papers — Mathematics (300 marks) covering Algebra, Matrices, Trigonometry, Analytical Geometry, Differential and Integral Calculus, Vector Algebra and Statistics & Probability, and the General Ability Test / GAT (600 marks) covering English plus General Knowledge in Physics, Chemistry, General Science, History, Geography and Current Events. The total written exam is 900 marks, followed by a 900-mark SSB Interview.

How many subjects are there in the NDA exam?

The NDA written exam has two papers. Paper 1 is Mathematics. Paper 2 (GAT) is divided into English and General Knowledge, where GK further covers six subjects — Physics, Chemistry, General Science, History, Geography and Current Events. So there is one dedicated Maths paper plus seven broad subject areas within the GAT.

Is the NDA syllabus based on Class 11 and 12 NCERT?

Yes. The Mathematics paper is drawn from the Class 11 and 12 NCERT/CBSE curriculum, while the GAT Physics and Chemistry are at the Class 9–10 NCERT level and General Science, History and Geography span Class 6–10 NCERT books. NCERT textbooks are the recommended foundation for the entire nda syllabus.

Which subject has the highest weightage in NDA?

The General Ability Test (GAT) carries the highest weightage at 600 of the 900 written marks. Within the GAT-GK section, Physics has the largest share at about 100 marks, followed by History and Geography at 80 marks each. Mathematics as a single paper is worth 300 marks.

What is the exam pattern and marking scheme of NDA?

The NDA written exam has two objective papers held the same day: Mathematics (120 questions, 300 marks, +2.5 per correct answer) and the GAT (150 questions, 600 marks, +4 per correct answer). Both apply 1/3 negative marking — 0.83 marks deducted per wrong answer in Maths and 1.33 in the GAT. Each paper runs 2.5 hours, and the written total of 900 marks is followed by a 900-mark SSB Interview.

Which are the best books for NDA preparation?

Start with NCERT Class 11–12 Maths and Class 6–10 Science and Social Science as your core, then add Mathematics for NDA & NA by RS Aggarwal, Wren & Martin and Word Power Made Easy for English, and Lucent’s General Knowledge and General Science for the GAT. For the polity, economy and current-affairs load that overlaps with UPSC, structured notes such as the Vajiram Polity Notes and Vision IAS Economics Notes are efficient revision aids.

How many months are needed to complete the NDA syllabus?

A focused aspirant can complete the full NDA syllabus in four to six months — roughly two months for foundation (NCERT concepts), two months for core building and current affairs, and one to two months for previous-year papers, mock tests and revision, studying about 6–7 focused hours a day.

Recommended Study Material

Vision IAS Current Affairs Magazine January 2026 | English Medium Edition

★★★★☆ (66)

₹299

View Product →

Vajiram Polity Notes GS Edition 2025-2026 Booklet Set of 2

★★★★☆ (268)

₹788

View Product →

Vision IAS Economics Notes Booklet Set 2025 – 2026 English GS for UPSC CSE

★★★★☆ (276)

₹1188

View Product →