NDA Syllabus 2025, Download GAT & Math Syllabus PDF

Topics

Sub-topics

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 a decimal system to a binary system and vice-versa.
• Arithmetic, geometric and harmonic progressions.
• Quadratic equations with real coefficients.
• The solution of linear inequations of two variables by graphs.
• Permutation and combination.
• Binomial theorem and its applications.
• Logarithms and their applications.

Matrices & Determinants

• Types of matrices
• Operations on matrices
• Determinant of a matrix
• Basic properties of determinants
• Adjoint and inverse of a square matrix
• Applications of matrices
  1. Solution of a system of linear equations in two or three unknowns using Cramer's rule
  2. Solution of a system of linear equations in two or three unknowns using Matrix Method

Trigonometry

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

Analytical Geometry of 2 & 3 Dimensions

• Rectangular Cartesian Coordinate system
• Distance formula
• Equation of a line in various forms
• The angle between two lines
• The 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
• A point in three-dimensional space and the distance between two points
• Direction cosines and direction ratios
• Equation of a plane and a line in various forms
• The angle between two lines and the angle between two planes
• Equation of a sphere

Differential Calculus

• Concept of a real-valued function including domain, range, and graph of a function.
• Composite functions and their properties including one-to-one, onto, and inverse functions.
• Understanding of the notion of limit and examples of standard limits.
• Continuity of functions and examples, including algebraic operations on continuous functions.
• Derivative of a function at a point, with geometrical and physical interpretation, and applications.
• Derivatives of sum, product, and quotient of functions, a derivative of a function with respect to another function, a derivative of a composite function, and second-order derivatives.
• Understanding increasing and decreasing functions.
• Application of derivatives in problems of maxima and minima.

Integral Calculus & Differential Equations

• Integration as the inverse of differentiation.
• Methods of integration: 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 of integrals.
• Definition of order and degree of a differential equation.
• Formation of a differential equation by examples.
• General and particular solutions of differential equations.
• Solutions of the first-order and first-degree differential equations of various types.
• 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 in work done by a force and moment of a force and in geometrical problems

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

Topics

Mark Distribution

Algebra

40-45

Matrices and Determinants

10-15

Trigonometry

20-25

Analytical Geometry

30-35

Differential Calculus

25-30

Integral Calculus

20-25

Vector Algebra

15-20

Syllabus

Topics

English

Grammar & usage

Comprehension & cohesion

Spotting errors

Para Jumbling

Fill in the blanks

Synonyms & Antonyms

Vocabulary

Cloze Test

Idioms & Proverbs

Completion of Sentence & Para

Sentence Correction & Improvement

Topic

Sub-topics

Physics

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, 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 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

Mariners Compass

Lightning Conductors

Safety Fuses

Topic

Sub-topics

Chemistry

Preparation and Properties of Hydrogen, Oxygen, Nitrogen, and Carbon Dioxide, Oxidation and Reduction.

Acids, bases and salts.

Carbon— different forms.

Fertilizers—Natural and Artificial.

The 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.

Physical and Chemical Changes.

Elements.

Mixtures and Compounds.

Symbols, Formulae and simple Chemical Equation.

Law of Chemical Combination (excluding problems).

Properties of Air and Water.

Topic

Sub-topics

General Science

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.

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.

Sub-topics

Forces shaping the modern world: The 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.

A broad survey of Indian History, with emphasis on Culture and Civilisation.

Basic Teachings of Mahatma Gandhi.

Freedom Movement in India.

Elementary study of the 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.

Sub-topics

Latitudes and Longitudes.

The Earth, its shape and size.

Ocean Currents and Tides.

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.

Earth’s Functioning - Ocean Currents, Tides, Atmosphere and its composition, Temperature and Atmospheric Pressure, Planetary Winds, Cyclones and Anticyclones, Humidity, Condensation and Precipitation.

Types of Climates.

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.

Topics

Sub-topics

Current Affairs

Important events in India in recent years

Prominent personalities

Current important world events

Topic-wise Weightage for English and General Awareness

Sections

Topics and Subjects

Mark Distribution

English

Grammar and Usage

25-30

Vocabulary

20-25

Comprehension

40-50

Cohesion and Coherence

10-15

General Awareness

Physics

25-30

Chemistry

15-20

General Science

25-30

History and Geography

20-25

Current Events

30-40

NDA Exam Syllabus for Personality Test

Stages

Tests

Types of tests

Stage 1

Screening Test

• Verbal and non-verbal tests.
• PPDT

Stage 2

Psychological Test

• Thematic Apperception Test (TAT)
• Word Association Test (WAT)
• Situation Reaction Test (SRT)
• Self-Description Test (SD)

Group Testing Officer Tasks

• Group Discussion(GD)
• Group Planning Exercise(GPE)
• Progressive Group Task(PGT)
• Half Group Task(HGT)
• Individual Obstacles Task(IOT)
• Command Task
• Snake Race/Group Obstacle Race
• Individual lecture
• Final Group Task(FGT)

Paper

Subject

Maximum Marks

Duration

Marking per Question

Negative marking per Question

Paper 1

Mathematics

300

150 minutes

2.5

1/3 of the marks allotted for the question

Paper 2

General Ability Test

600

150 minutes

4