NDA SYLLABUS 2019-2020



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NDA Syllabus

  • NDA Syllabus For Paper -I — Mathematics Written Examination (Objective Multiple Choice Type)
  • NDA Syllabus For Paper -II — General Ability Test Written Examination (Objective Multiple Choice Type)

NDA Syllabus For Paper -I — Mathematics

The detailed NDA Syllabus for Maths is tabulated below:

(1) NDA Syllabus For ALGEBRA

  1. The concept of set, operations on sets, Venn diagrams. De Morgan’s laws, Cartesian product, relation, equivalence relation. Representation of real numbers on a line.
  2. Complex numbers -basic properties, modulus, argument, cube roots of unity.
  3. The binary system of numbers. Conversion of a number in decimal system to a binary system and vice-versa.
  4. Arithmetic, Geometric and Harmonic Progressions
  5. 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.


  1. Types of matrices, operations on matrices
  2. The determinant of a matrix, basic properties of determinants
  3. Adjoint and inverse of a square matrix,
  4. Applications -Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method


  1. Angles and their measures in degrees and in radians.
  2. Trigonometrical ratios
  3. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles.
  4. Inverse trigonometric functions.


  1. Rectangular Cartesian Coordinate system
  2. Distance formula, An equation of a line in various forms, An angle between two lines, A distance of a point from a line
  3. An equation of a circle in standard and in general form
  4. Standard forms of parabola, ellipse, and hyperbola, Eccentricity and axis of a conic.
  5. Point in a three-dimensional space, the distance between two points
  6. Direction Cosines and direction ratios, Equation two points. Direction Cosines and direction ratios.
  7. The equation of a plane and a line in various forms. The angle between the two lines and the angle between the two planes. The equation of a sphere.


  1. Notion of limit, Standard limits-examples.
  2. Continuity of functions-examples, algebraic operations on continuous functions.
  3. Derivative of function at a point, geometrical and physical interpretation of a derivative-applications.
  4. Derivatives of the sum, product, and quotient of functions,
  5. Derivative of a function with respect to another function,
  6. Derivative of a composite function. Second order derivatives
  7. Increasing and decreasing functions.
  8. Application of derivatives in problems of maxima and minima.


  1. Integration as inverse of differentiation,
  2. Integration by substitution and by parts,
  3. Standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions.
  4. Evaluation of definite integrals- determination of areas of plane regions bounded by curves-applications.
  5. Definition of order and degree of a differential equation,
  6. Formation of a differential equation by examples.
  7. General and particular solution of differential equations,
  8. Solution of first order and first degree differential equations of various types-examples.
  9. Application in problems of growth and decay



  1. Vectors in two and three dimensions,
  2. Magnitude and direction of a vector
  3. Unit and null vectors,
  4. Addition of vectors,
  5. Scalar multiplication of a vector,
  6. Scalar product or dot product of two vectors
  7. Vector product or cross product of two vectors.
  8. Applications-work done by a force and moment of a force and in geometrical problems


  1. 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.
  2. 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, Baye’s theorem-simple problems. Random variable as function on a sample space. Binomial distribution,examples of random experiments giving rise to Binominal distribution

NDA Syllabus For Paper -II –General Ability Test

NDA Written Exam Paper-II- has two sections the syllabus of which is tabulated below:

(1) NDA Syllabus For English

  1. The question paper in English will be designed to test the candidate’s understanding of English language and its application/usage. The syllabus covers various aspects like:
  2. Grammar and usage,
  3. Vocabulary,
  4. Comprehension and cohesion in extended text to test the candidate’s proficiency in English.

(2) NDA Syllabus For General Knowledge

The question paper on General Knowledge will broadly cover the subjects:

  1. Physics,
  2. Chemistry,
  3. General Science,
  4. Social Studies,
  5. Geography,
  6. Current Events

(3) NDA Syllabus For Physics

  1. Physical Properties and States of Matter, Mass, Weight, Volume, Density, and Specific Gravity,
  2. Principle of Archimedes,
  3. Pressure Barometer
  4. Motion of objects, Velocity and Acceleration, Newton’s Laws of Motion, Force and Momentum, Parallelogram of Forces, Stability and Equilibrium of bodies,
  5. Gravitation,
  6. Elementary ideas of Work, Power and Energy.
  7. Effects of Heat, Measurement of Temperature and Heat, change of State and Latent Heat, Modes of transference of Heat
  8. Sound waves and their properties, Simple musical instruments
  9. Rectilinear propagation of Light, Reflection, and refraction. Spherical mirrors and Lenses, Human Eye.
  10. Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet
  11. 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
  12. 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, Mariner’s Compass; Lightening Conductors, Safety Fuses

(4) NDA Syllabus for Chemistry

  1. Physical and Chemical changes.
  2. Elements, Mixtures and Compounds,
  3. Symbols, Formulae and simple Chemical Equations,
  4. Law of Chemical Combination (excluding problems)
  5. Properties of Air and Water
  6. Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon dioxide,
  7. Oxidation and Reduction
  8. Acids, bases, and salts. Carbon- different forms
  9. Fertilizers-Natural and Artificial
  10. The material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches and Gun-Powder
  11. Elementary ideas about the structure of Atom, Atomic Equivalent and Molecular Weights, Valency

(5) NDA Syllabus For General Science

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

(6) NDA Syllabus For Social Studies

  1. A broad survey of Indian History, with emphasis on Culture and Civilisation
  2. Elementary study of Indian Constitution and Administration
  3. Elementary knowledge of Five Year Plans of India
  4. Panchayati Raj, Co-operatives and Community Development. Bhoodan, Sarvodaya, National Integration and Welfare State, Basic Teachings of Mahatma Gandhi
  5. Forces shaping the modern world; Renaissance, Exploration, and Discovery;
  6. War of American Independence, French Revolution, Industrial Revolution, and Russian Revolution
  7. Impact of Science and Technology on Society
  8. The concept of one World, United Nations, Panchsheel,
  9. Democracy, Socialism and Communism
  10. Role of India in the present world.

(7) NDA Syllabus For Geography

  1. The Earth, its shape and size, Latitudes and Longitudes, Concept of Time, International Date Line, Movements of Earth and their effects, Origin of Earth
  2. Rocks and their classification;
  3. Weathering-Mechanical and Chemical
  4. Earthquakes and Volcanoes
  5. Ocean Currents and Tides
  6. Atmosphere and its composition; Temperature and Atmospheric Pressure, Planetary Winds, Cyclones, and Anti-cyclones; Humidity; Condensation and Precipitation;
  7. Types of Climate,
  8. Major natural resources of the world
  9. Regional Geography of India – Climate, Natural vegetation, Mineral and Power resources; location and distribution of agricultural and Industrial
  10. activities, Important Sea Ports, and major sea, land, and air routes of India, main items of Imports and Exports of India

(8) NDA Syllabus For Current Events

  1. Knowledge of important events that have happened in India in recent years
  2. Current important world events
  3. Prominent personalities-both Indian and International including those connected with cultural activities and sports.
Age Limit, Gender & Marital Status16 ½ to 19 ½ , Unmarried male candidates only
Educational QualificationFor Army:—12th passed or appearing in any stream For Air Force, Navy & Naval Academy:—12th passed or appearing with Physics and Mathematics.
TrainingFor Army/Navy/Air Force-3 Years at National Defence Academy & 1 Year at IMA/AFA/NA For Naval Academy-4 Years B.Tech Course at Naval Academy

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