The National Defence Academy (NDA) examination, conducted by the Union Public Service Commission (UPSC), is a gateway to a prestigious career in the Indian Armed Forces. Understanding the UPSC NDA syllabus is the first step in preparing effectively. This article provides a detailed, subject-wise breakdown of the syllabus for the UPSC NDA 2025 exam, ensuring aspirants have all the essential information to excel.
UPSC NDA Syllabus 2025 Overview
The UPSC NDA syllabus 2025 is divided into two papers: Mathematics and General Ability Test (GAT). While Mathematics tests candidates’ numerical and problem-solving skills, the GAT evaluates their grasp of English, General Knowledge (GK), and Science. Each section has specific topics and subtopics that candidates must master.
NDA Exam 2025 Marking Scheme
Following table consists of details about the marking scheme of the exam. There are a total of two papers carrying 900 marks.
| Subject | Duration | Maximum Marks | Type | Medium |
| Mathematics | 2.5 hours | 300 | MCQs | English & Hindi |
| GAT | 2.5 | 600 | MCQs | English & Hindi |
UPSC NDA Subject Wise Syllabus 2025
Understanding the syllabus is the first step in the direction of comprehensive preparation. It ensures you are on the right path and are well equipped to deal with the exam diligently.
There are two papers in the exam schedule. Mathematics paper is conducted in the morning which is worth 300 marks.
UPSC NDA Syllabus 2025 MATHEMATICS |
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| Algebra | Concept of 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 decimal to binary and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequalities 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 Matrix Method. |
| Trigonometry | Angles and their measures in degrees and radians. Trigonometric ratios. Trigonometric identities. Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications—Height and distance, properties of triangles. |
| Analytical Geometry | 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 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 of a function. Composite functions, one-to-one, onto, and inverse functions. Notion of limit, standard limits—examples. Continuity of functions—examples, 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 by examples. General and particular solutions of differential equations, solution of first-order and first-degree differential equations of various types—examples. Applications 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 product or dot product of two vectors. Vector product or 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—examples. Graphical representation—Histogram, Pie Chart, frequency polygon—examples. Measures of Central Tendency—Mean, median, and mode. Variance and standard deviation—determination and comparison. 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—examples. Elementary theorems on probability—simple problems. Conditional probability, Bayes’ theorem—simple problems. Random variable as a function on a sample space. Binomial distribution, examples of random experiments giving rise to Binomial distribution. |
UPSC NDA Syllabus 2025 for GENERAL ABILITY TEST
GAT paper is conducted in the evening which is of total 600 marks.
UPSC NDA GENERAL ABILITY TEST Syllabus 2025 |
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UPSC NDA Syllabus 2025 For English |
The question paper in English will test the candidate’s understanding of English and workmanlike use of words. The syllabus covers various aspects like grammar and usage, vocabulary, comprehension, and cohesion in extended text to test the candidate’s proficiency in English. | ||||
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UPSC NDA Syllabus 2025 Physics |
Physical properties and states of matter, mass, weight, volume, density, 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, elementary ideas of work, power and energy. Effects of heat, measurement of temperature and heat, change of state and latent heat, modes of heat transfer. 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 in the working of the following: simple pendulum, simple pulleys, siphon, levers, balloon, pumps, hydrometer, pressure cooker, thermos flask, gramophone, telegraphs, telephone, periscope, telescope, microscope, mariner’s compass, lightning conductors, safety fuses. | ||||
UPSC NDA Syllabus 2025 Chemistry |
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 gunpowder. Elementary ideas about the structure of atom, atomic equivalent and molecular weights, valency. | ||||
UPSC NDA Syllabus 2025 General Science |
Difference between the living and non-living. Basis of life—cells, protoplasms, 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. | ||||
UPSC NDA Syllabus 2025 History, Freedom Movement |
A broad survey of Indian history, with emphasis on culture and civilization. Freedom movement in India. Elementary study of Indian Constitution and administration. Elementary knowledge of 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. | ||||
UPSC NDA Syllabus 2025 Geography |
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. | ||||
UPSC NDA Syllabus 2025 Current Events |
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. | ||||
UPSC NDA Syllabus 2025 Personality Test
The 3rd stage of examination consists of a Personality test or SSB Interview. The notification provides for the following instructions to prepare for the same.
Personality Test |
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| The SSB procedure consists of two stage Selection processes – stage I and stage II. Only those candidates who clear stage I are permitted to appear for stage II. | |
| Stage I | Officer Intelligence Rating (OIR) tests and Picture Perception and Description Test (PP&DT). The candidates will be shortlisted based on combination of performance in OIR Test and PP&DT. |
| Stage II | Comprises Interview, Group Testing Officer Tasks, Psychology Tests and the Conference. These tests are conducted over 4 days. The details of these tests are given on the website www.joinindianarmy.nic.in. |
| The personality of a candidate is assessed by three different assessors viz. The Interviewing Officer (IO), Group Testing Officer (GTO) and the Psychologist. There are no separate weightage for each test. The marks are allotted by assessors only after taking into consideration the performance of the candidate holistically in all the tests. In addition, marks for Conference are also allotted based on the initial performance of the Candidate in the three techniques and decision of the Board. All these have equal weightage. The various tests of IO, GTO and Psych are designed to bring out the presence/absence of Officer Like Qualities and their trainability in a candidate. Accordingly candidates are Recommended or Not Recommended at the SSB. | |
UPSC NDA Syllabus and Recommended Books
The table below summarizes the key subjects in the NDA exam and the books recommended for preparation:
| Subject | Topics Covered | Recommended Books |
| Mathematics | Algebra, Trigonometry, Calculus, Probability | NCERT Mathematics (Class 11 & 12), RS Aggarwal |
| English | Grammar, Vocabulary, Comprehension | Wren & Martin English Grammar, Word Power Made Easy
by Norman Lewis |
| General Knowledge | History, Geography, Science, Current Affairs | NCERT History & Geography (Class 6-10), Lucent’s GK |
| Physics | Mechanics, Thermodynamics, Optics | NCERT Physics (Class 11 & 12), HC Verma’s Concepts of
Physics |
| Chemistry | Organic, Inorganic, Physical Chemistry | NCERT Chemistry (Class 11 & 12), Modern’s ABC of
Chemistry |
| Current Affairs | National and International News, Events | Daily Newspapers (The Hindu/Indian Express), Monthly
Current Affairs Magazines |
Other Articles |
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UPSC NDA Syllabus 2025 FAQs
Q1: What topics are covered in the NDA Maths syllabus?
The UPSC NDA Maths syllabus includes algebra, trigonometry, calculus, statistics, probability, and vector algebra, among other topics.
Q2: What are the key areas in the NDA Physics syllabus?
The Physics syllabus covers laws of motion, optics, thermodynamics, and basics of electricity and magnetism.
Q3: How much weightage does the General Knowledge section hold?
The General Knowledge section is part of the GAT paper and holds significant weightage. It covers history, geography, current affairs, and general science.
Q4: Is the syllabus for UPSC NDA 2025 different from previous years?
The syllabus remains consistent, with minor updates. Always refer to the latest notification for updates.
Q5: How can I improve my proficiency in English for the NDA exam?
Focus on grammar, vocabulary, and comprehension skills. Practice reading diverse materials and solve sample English question papers to improve accuracy and speed.
