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UPSC NDA (National Defence Academy & Naval Academy Examination)

UPSC NDA is a national-level defence entrance examination conducted by the Union Public Service Commission (UPSC) for admission to the Army, Navy, and Air Force wings of the National Defence Academy (NDA) and Naval Academy (NA). The exam tests candidates on Mathematics and General Ability, followed by SSB Interview for final selection.

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Official 2025 syllabus extracted from https://upsc.gov.in/sites/default/files/Notific-NDA-NA-I-2025-Engl-11122024F.pdf

Paper-I: Mathematics

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 between decimal and binary system

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 applications

Logarithms and their applications

Algebra

Types of matrices, operations on matrices

Determinant of a matrix

Basic properties of determinants

Adjoint and inverse of a square matrix

Solution of system of linear equations by Cramer's rule and Matrix Method

Matrices and Determinants

Angles and their measures in degrees and radians

Trigonometric ratios

Trigonometric identities, sum and difference formulae

Multiple and sub-multiple angles

Inverse trigonometric functions

Heights and distances

Properties of triangles

Trigonometry

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 between two planes

Equation of a sphere

Analytical Geometry of Two and Three Dimensions

Real valued function: domain, range, graph

Composite, one-to-one, onto and inverse functions

Notion of limit, standard limits

Continuity of functions, algebraic operations on continuous functions

Derivative of function at a point, geometrical and physical interpretation

Derivatives of sum, product and quotient of functions

Derivative of composite functions

Second order derivatives

Increasing and decreasing functions

Maxima and minima

Differential Calculus

Integration as inverse of differentiation

Integration by substitution and by parts

Standard integrals involving algebraic, trigonometric, exponential and hyperbolic functions

Evaluation of definite integrals

Areas of plane regions bounded by curves

Order and degree of a differential equation

Formation of differential equations

General and particular solutions of differential equations

Solution of first order and first degree differential equations

Applications in growth and decay problems

Integral Calculus and Differential Equations

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 of two vectors

Vector (cross) product of two vectors

Applications: work done by a force, moment of a force, geometrical problems

Vector Algebra

Classification of data

Frequency distribution and cumulative frequency distribution

Graphical representation: histogram, pie chart, frequency polygon

Measures of central tendency: mean, median, mode

Variance and standard deviation

Correlation and regression

Random experiment, outcomes, sample space

Events: mutually exclusive, exhaustive, impossible, certain

Union and intersection of events

Complementary, elementary and composite events

Classical and statistical definition of probability

Elementary theorems on probability

Conditional probability

Bayes' theorem

Random variable on a sample space

Binomial distribution

Statistics and Probability

Paper-II: General Ability Test — English

Grammar and usage

Vocabulary

Comprehension

Cohesion in extended text

English

Paper-II: General Ability Test — General Knowledge

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 transfer of heat

Sound waves and properties

Simple musical instruments

Rectilinear propagation of light, reflection and refraction

Spherical mirrors and lenses

Human eye

Natural and artificial magnets, properties

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

Working of simple pendulum, pulleys, siphon, levers, balloon, pumps, hydrometer, pressure cooker, thermos flask, gramophone, telegraph, telephone, periscope, telescope, microscope, mariner compass, lightning conductors, safety fuses

Physics

Physical and chemical changes

Elements, mixtures and compounds

Symbols, formulae and simple chemical equations

Law of chemical combination

Properties of air and water

Preparation and properties of hydrogen, oxygen, nitrogen, carbon dioxide

Oxidation and reduction

Acids, bases and salts

Carbon and its different forms

Fertilizers: natural and artificial

Material used in preparation of soap, glass, ink, paper, cement, paints, safety matches, gun-powder

Structure of atom

Atomic equivalent and molecular weights

Valency

Chemistry

Difference between living and non-living

Basis of life: cells, protoplasms, tissues

Growth and reproduction in plants and animals

Human body and its important organs

Common epidemics, causes and prevention

Food as source of energy, constituents of food, balanced diet

Solar system, meteors, comets, eclipses

Achievements of eminent scientists

General Science

Broad survey of Indian history with emphasis on culture and civilization

Freedom movement in India

Indian Constitution and administration

Five Year Plans of India

Panchayati Raj, cooperatives and community development

Bhoodan, Sarvodaya, National Integration and Welfare State

Basic teachings of Mahatma Gandhi

Renaissance, Exploration and Discovery

War of American Independence

French Revolution, Industrial Revolution, 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

History, Freedom Movement etc.

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 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

UPSC NDA (National Defence Academy & Naval Academy Examination) — Discussion

UPSC NDA (National Defence Academy & Naval Academy Examination) — Group Discussion