National Defence Academy(NDA & NA) Syllabus

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NDA Syllabus 2019 – Union Public Service Commission (UPSC) prescribes the syllabus of NDA 2019 along with the notification. NDA exam is bifurcated into two papers – Mathematics and General Ability Test (GAT). The list of topics from which questions will be asked in the examination is provided in NDA syllabus 2019. The difficulty level of questions asked in Mathematics will be similar to that of class 12 level. NDA syllabus 2019 of General Ability Test comprises topics to assess candidates’ proficiency of English language and knowledge of subjects including Physics, Chemistry, General Science, Social Studies, Geography and Current Events. NDA is likely to be held by UPSC in September 2019.

NDA Syllabus 2019 for Mathematics

Paper 1 of NDA 2019 consists of topics pertaining to Mathematics. The syllabus of NDA 2019 Paper 1 has been provided below.

Topics Sub-Topics
Algebra 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 17 equations with real coefficients.

A solution of linear inequations of two variables by graphs.

Permutation and Combination.

Binomial theorem and its applications.

Logarithms and their applications.

Concept of set

Operations on sets

Venn diagrams.

De Morgan laws, Cartesian product, relation, equivalence relation.

Matrices and Determinant 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.

Trigonometrical ratios.

Trigonometric identities Sum and difference formulae.

Multiple and Sub-multiple angles. Inverse trigonometric functions.

Applications-Height and distance, properties of triangles.

Analytical Geometry of two and three dimensions Rectangular Cartesian Coordinate system. Distance formula.

Distance formula.

The equation of a line in various forms.

The angle between two lines.

The distance of a point from a line.

The equation of a circle in standard and in general form. Standard forms of

Standard forms of a parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in a

Eccentricity and axis of a conic. Point in a three-dimensional space, the distance between two points.

Direction Cosines and direction ratios.

Equation two points. Direction Cosines and direction ratios.

Direction Cosines and direction ratios.

Equation two points. Direction Cosines and direction ratios. The equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

Direction Cosines and direction ratios. The equation of a plane and a line in various forms. The angle between two lines and angle between two planes. The equation of a sphere.

The equation of a plane and a line in various forms. The angle between two lines and angle between two planes. The equation of a sphere.

The angle between two lines and angle between two planes. The equation of a sphere.

Differential Calculus The concept of a real-valued function–domain, range and graph of a function.

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

The notion of limit, Standard limits—examples.

Continuity of functions—examples, algebraic operations on continuous functions.

Derivative of the function at a point, geometrical and physical interpretation of a derivative—applications.

Derivatives of the sum, product, and quotient of functions, the 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.

18 Definition of order and degree of a differential equation, formation of a differential equation by examples.

General and particular solution of differential equations, the solution of first order and first-degree differential equations of various types—examples.

Application in problems of growth and decay.

Vector Algebra Vectors in two and three dimensions, magnitude and direction of a vector.

Unit and null vectors, the 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 was 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, Graphical representation Histogram, Pie Chart, frequency polygon, 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 Binominal distribution.


NDA Syllabus 2019 for General Ability Test

The General Ability Test (GAT) is the second paper required for the written exam of NDA 2019. GAT paper is bifurcated into two parts – Part A: English and Part B: General Knowledge. English section (Part A) test candidates’ proficiency in English. NDA 2019 syllabus covers grammar and its usage, vocabulary, comprehension and cohesion, etc. The paper on General Knowledge (Part B) covers subjects including Physics, Chemistry, General Science, Social Studies, Geography and Current Events. Each of these subjects has been divided into sections. Questions asked in Part B will evaluate candidates’ knowledge, understanding and expertise in each of the subjects. Check below for the complete NDA syllabus 2019 of Paper 2: General Ability Test.

Sections Topics Sub-Topics
Section A 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, change of State and Latent 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 – Simple Pendulum, Simple Pulleys, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariner’s Compass; Lightening Conductors, Safety Fuses
Section B 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 preparation of substances such as Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches and Gun-Powder
  • Elementary ideas about the structure of Atom, Atomic Equivalent and Molecular Weights, Valency
Section C General Science
  • Difference between living and non-living
  • The basis of Life – Cells, Protoplasms, and Tissues
  • Growth and Reproduction in Plants and Animals
  • Elementary knowledge of Human Body and its important organs
  • Common Epidemics, their causes and prevention
  • Food – Source of energy for man
  • Constituents of food and Balanced Diet
  • Solar System – Meteors, Comets, and Eclipses
  • Achievements of Eminent Scientists
Section D History, Freedom Movement etc.
  • A broad survey of Indian History with emphasis on Culture and Civilisation
  • 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 modern world; Renaissance, Exploration and Discovery; War of American Independence
  • French Revolution, Industrial Revolution and Russian Revolution
  • The impact of Science and Technology on Society
  • The concept of one World, United Nations, Panchsheel, Democracy, Socialism, and Communism
  • Role of India in the present world
Section E Geography
  • 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
Section F Current Events
  • Knowledge of important events in India in recent years
  • Current important world events
  • Prominent personalities – Indian and International including those connected with cultural activities and sports

NDA 2019 Exam Pattern

Candidates must be well-informed regarding the exam pattern of NDA. As per NDA exam pattern 2019, the written exam will be held for 900 marks. Of the total marks, the Mathematics paper will comprise 300 marks while GAT paper will be conducted for 900 marks. Both the papers will be conducted for 2 hours 30 minutes each. After the completion of the written test, candidates qualifying the exam stage will be called for SSB Interview. The Interview stage will comprise a total 900 marks. The complete exam pattern of the written exam has been provided in the table below.

NDA Exam Pattern 2019 – Written examination



Maximum Marks


2.5 hours


General Ability Test

2.5 hours


Total Marks


Best Books to prepare for NDA

Some of the best books for preparation of NDA exam had been given below for the convenience of candidates. The list of books below are provided as per subject it covers for the exam. However, candidates who are searching for books that cover both papers of the exam can refer to Arihant’s “Pathfinder for NDA & NA – National Defense Academy and Naval Academy”. The paper-wise best books for the preparation of NDA 2019 are as follows.








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