UPSC NDA 1 Syllabus 2025 | Paper 1 & 2 Exam Pattern, Subject-wise Syllabus, Weightage

• Written Exam consisting of Objective Type Questions
• Intelligence & Personality Test (SSB)

• Mathematics: 300 Marks
• GAT: 600 Marks

• Mathematics: 120
• GAT: 150

(English Language paper has to be attempted in English)

Online Registration Start Date

Online registration Last Date

Papers

Maximum marks

Total

900

Topics

Subtopics of UPSC NDA Maths Syllabus

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 a number in decimal system to binary system and vice versa.
• Arithmetic, Geometric and Harmonic Progressions.
• Quadratic equations with real coefficients.
• Solution of linear equations of two variables by graphs.
• Permutation and Combination.
• Binomial theorem and its applications.
• Logarithmic 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 in radians.
• Trigonometric ratios – Sine, Cosine, Tangent, Cotangent, Secant and Cosecant.
• Trigonometric identities formulae (Sum and Difference).
• Use of trigonometric tables.
• Multiple and Sub multiple angles
• Inverse trigonometric Functions
• Applications Height and distances, properties of triangles.

Analytical Geometry of Two and Three Dimensions

• Rectangular Cartesian Coordinate system.
• Distance formula.
• Equation of a line in various forms.
• The angle between two lines.
• Distance of a point from a line.
• Equation of a circle in standard and in a 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 two points.
• Direction Cosines and direction ratios.
• Equation of a plane and a line in various forms.
• The angle between two lines and angle between two planes.
• Equation of a Sphere

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 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.
• A general and particular solution of a differential equation, solution of the first order and first-degree differential equations of various types – examples.
• Application in problems of growth and decay.

• 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 and cross product of two vectors.
• Applications—work done by a force and moment of a force and in geometrical problems.

• 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 function on a sample space.
• Binomial distribution, examples of random experiments giving rise to Binomials distribution.

• Parts of speech: Noun, Pronoun, Adjective, Verb, Adverb, Conjunction, Preposition, Interjection
• Subject-verb agreement
• Tenses: Present, Past, Future
• Active and passive voice
• Coherence and unity: Theme, Idea, Paragraph, Sentence Structure
• Vocabulary: Synonyms, Antonyms, One-word substitution, Idioms and Phrases, Words often confused

• Comprehension of a given passage
• Drawing of inferences
• Use of vocabulary: Synonyms, Antonyms, One-word substitution, Idioms and Phrases, Words often confused

Expression

• Simple sentence structure
• Punctuation: Comma, Full stop, Question Mark, Exclamation Mark, Apostrophe
• Conjunctions: Coordinating, Subordinating
• Adverbs and Prepositions
• Direct and indirect speech
• Comparison: Degrees of comparison
• Articles: Definite and Indefinite Articles
• Verbs: Auxiliary, Modal, Regular and Irregular verbs
• Sentence correction: Spotting Errors, Sentence Improvement

NDA Syllabus for Physics

• Physical Properties and States of Matter
• Modes of transference of Heat
• Mass, Weight, Volume, Sound waves and their properties
• Simple musical instruments
• Rectilinear propagation of Light
• Density and Specific Gravity
• Reflection and refraction
• Principle of Archimedes
• Spherical mirrors and Lenses
• Pressure Barometer
• Human Eye
• Motion of objects
• Natural and Artificial Magnets
• Velocity and Acceleration
• Properties of a Magnet
• Newton’s Laws of Motion
• Earth as a Magnet
• Force and Momentum
• Static and Current Electricity
• Parallelogram of Forces
• Conductors and Non-conductors
• Stability and Equilibrium of bodies
• Ohm’s Law
• Gravitation
• Simple Electrical Circuits
• Elementary ideas of work
• Heating, Lighting, and Magnetic effects of Current
• Power and Energy
• Measurement of Electrical Power
• Effects of Heat
• Primary and Secondary Cells
• Measurement of Temperature and Heat
• Use of X-Rays
• General Principles in 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, Safety Fuses.

UPSC NDA 1 Syllabus for Chemistry

• Physical and Chemical changes. Elements, Mixtures and Compounds, Symbols, Formulae and simple Chemical Equations, Law of Chemical Combination (excluding problems).
• Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon Dioxide, Oxidation and Reduction.
• Acids, bases and salts.
• Carbon— different forms
• Physical and Chemical Changes
• Fertilizers—Natural and Artificial
• Elements
• Material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and Gunpowder
• Mixtures and Compounds
• Elementary ideas about the structure of Atom
• Symbols, Formulae, and simple Chemical Equation
• Atomic Equivalent and Molecular Weights
• Law of Chemical Combination (excluding problems)
• Valency
• Properties of Air and Water

UPSC NDA Syllabus for General Science

• Common Epidemics, their causes, and prevention
• Difference between the living and non-living
• Food—Source of Energy for man
• Basis of Life—Cells, Protoplasms, and Tissues
• Constituents of food
• Growth and Reproduction in Plants and Animals
• Balanced Diet
• Elementary knowledge of the Human Body and its important organs
• The Solar System—Meteors and Comets, Eclipses. Achievements of Eminent Scientists

UPSC NDA Syllabus for History, Freedom Movement

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

UPSC NDA Syllabus for Geography

• The Earth, its shape and size
• Ocean Currents and Tides Atmosphere and its composition
• Latitudes and Longitudes
• Temperature and Atmospheric Pressure, Planetary Winds, Cyclones, and Anticyclones; Humidity; Condensation and Precipitation
• Concept of time
• Types of Climate
• International Date Line
• Major Natural Regions of the World
• Movements of Earth and their effects
• Regional Geography of India
• Climate, Natural vegetation. Mineral and Power resources;
• Location and distribution of agricultural and Industrial activities
• Origin of Earth. Rocks and their classification
• Important Sea ports and main sea, land, and air routes of India
• Weathering—Mechanical and Chemical, Earthquakes and Volcanoes
• Main items of Imports and Exports of India

UPSC NDA Syllabus for Current Events

Cultural activities and sports activities Knowledge of Important events that have happened in India in recent years. Current important world events. Prominent personalities of both Indian and International level

NDA Paper

Marks Incorrect answer

Topic

Questions

Subjects 

Name and Author of the Book

• Mathematics for NDA and NA: National Defence Academy and Naval Academy by RS Aggarwal
• Quantitative aptitude for competitive examinations by RS Aggarwal
• NCERT Class 11 and 12th Maths Books

• History Of Modern India (History) by Bipan Chandra
• Science and Technology in India (Science and Technology) by Kalpana Rajaram: Spectrum
• Objective General English for Competitive Exams by S P Bakshi
• Manorama Yearbook by Mammen Mathew
• Lucent’s GK