NDA Syllabus: Maths & GAT (Physics, Chemistry, English, GK) — UPSC NDA

From the official Union Public Service Commission (UPSC) documents · last checked 18 October 2026

UPSC NDA 2026 Paper I: Mathematics (Code 01, 300 marks) syllabus

Mathematics - 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 from the decimal system to the binary system 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

Mathematics - 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

Mathematics - Trigonometry

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

Mathematics - Analytical Geometry of Two and Three Dimensions

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 in 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

Mathematics - Differential Calculus

Concept of a real-valued function: domain, range and graph of a function
Composite functions; one-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 meaning 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

Mathematics - Integral Calculus and Differential Equations

Integration as the inverse of differentiation
Integration by substitution and by parts
Standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions
Evaluation of definite integrals; finding 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 solution of a differential equation
Solution of first order and first degree differential equations of various types (examples)
Application in problems of growth and decay

Mathematics - 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, moment of a force, and geometrical problems

Mathematics - Statistics and Probability

Statistics: classification of data; frequency distribution; cumulative frequency distribution (examples)
Statistics: graphical representation - histogram, pie chart, frequency polygon (examples)
Statistics: measures of central tendency - mean, median and mode
Statistics: variance and standard deviation - finding and comparing them
Statistics: correlation and regression
Probability: random experiment, outcomes and associated sample space
Probability: events; mutually exclusive and exhaustive events; impossible and certain events
Probability: union and intersection of events
Probability: complementary, elementary and composite events
Probability: definition of probability - classical and statistical (examples)
Probability: elementary theorems on probability (simple problems)
Probability: conditional probability; Bayes' theorem (simple problems)
Probability: random variable as a function on a sample space
Probability: binomial distribution; examples of random experiments that give a binomial distribution

UPSC NDA 2026 Paper II: General Ability Test (Code 02, 600 marks) syllabus

Part A - English (200 marks)

Tests your understanding of English and practical, correct use of words (described officially as 'workmanlike use of words')
Grammar and usage
Vocabulary
Comprehension
Cohesion in extended text

Part B - General Knowledge (400 marks): how it is set

Broadly covers Physics, Chemistry, General Science, Social Studies, Geography and Current Events
Approximate weightage of Part B marks: Section A Physics 25%, Section B Chemistry 15%, Section C General Science 10%, Section D History and Freedom Movement 20%, Section E Geography 20%, Section F Current Events 10%
The topics listed are not complete. Questions on similar topics that are not named may also be asked. Answers should show knowledge and intelligent understanding of the subject

Part B - Section A: Physics (about 25%)

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
Elementary ideas of work, power and energy
Effects of heat; measurement of temperature and heat
Change of state and latent heat
Modes of transfer of heat
Sound waves and their properties; simple musical instruments
Rectilinear propagation of light (light travels in straight lines); reflection and refraction
Spherical mirrors and lenses; the human eye
Natural and artificial magnets; properties of a magnet; the 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: 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

Part B - Section B: Chemistry (about 15%)

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 - its different forms
Fertilizers - natural and artificial
Materials used in making substances like soap, glass, ink, paper, cement, paints, safety matches and gunpowder
Elementary ideas about the structure of the atom
Atomic, equivalent and molecular weights
Valency

Part B - Section C: General Science (about 10%)

Difference between the living and the 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

Part B - Section D: History, Freedom Movement etc. (about 20%)

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

Part B - Section E: Geography (about 20%)

The Earth, its shape and size
Latitudes and longitudes; concept of time; International Date Line
Movements of the Earth and their effects
Origin of the 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 of India; 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

Part B - Section F: Current Events (about 10%)

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 2026 SSB Interview (Intelligence and Personality Test, 900 marks) syllabus

Stage I

Officer Intelligence Rating (OIR) tests
Picture Perception and Description Test (PP&DT)
Shortlisting is based on combined performance in both

Stage II (over 4 days)

Interview
Group Testing Officer tasks
Psychology tests
Conference
The tests look for Officer Like Qualities and whether the candidate can be trained

Air Force candidates only

Computerised Pilot Selection System (CPSS) for the flying branch. It is given only once; the first grade counts at every later Air Force Selection Board

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