Detailed Syllabus Of NDA ( National Defence Academy)

Detailed Syllabus Of NDA

NDA (National Defence Academy) is the Joint Services Academy of Indian Armed Forces. UPSC conducts a national level exam called NDA Exam, held 2 times in a year. This exam is conducted for those candidates who want to join Indian Defence Forces. Gurukul Vidya Institute helps for those candidates who want to join NDA , Indian Army by providing best NDA Coaching in Chandigarh .We have complete information about NDA Syllabus 2017 that will be elaborated further.

NDA Exam has of two main sections: Mathematics & General Ability. Detailed syllabus of each of these sections is specified below for clear and deep understanding of candidates.

NDA Syllabus 2022:

  1. Mathematics
    In NDA Exam Mathematics carries 300 marks and allotted two and a half hours to attempt this exam. Students are advised to practice carefully each and every sector of this exam.


Sections Concepts
  • Arithmetic, Geometric and Harmonic progressions
  • Complex Numbers – basic properties, modules, arguments, cube roots of unity
  • Binomial Theorem and its applications
  • Representation of real numbers on a line
  • Quadratic equations with real coefficients
  • Permutation and Combination
  • Conversion of numbers in decimal system and vice-versa
  • Solution of Linear equations in two variables by graphs
  • Binary system of numbers
Matrices & Determinants
  • Types of matrices
  • Operations on matrices
  • Determinant of a matrix
  • Applications – Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.
  • Basic properties of determinants
  • Adjoint and inverse of a square matrix
  • Trigonometrical ratios, Inverse trigonometric functions, properties of triangles
  • Derivative of function at a point, Derivatives of sum and Product and quotient of functions
  • Trigonometric identities
  • Sum and difference formulae
  • Angles and their measures in degrees and in radians
  • Applications – Height and distance, Multiple and Sub multiple angles.
Differential Calculus
  • Concept of a real valued function – domain,range and graph of a function
  • Composite functions
  • Derivative of a function with respect of another function
  • Derivative of a composite function
  • Application of derivatives in problems of maxima and minima.
  • Second order derivatives
  • Increasing and decreasing functions
Integral Calculus & Differential Equations
  • Integration by substitution and by parts, trigonometric, exponential and hyperbolic functions
  • Definition of order and degree of a differential equation and formation of a differential equation by examples
  • Solution of first order and first degree differential equations of various types.
  • General and particular solution of a differential equation
  • Evaluation of definite integrals – determination of areas of plane regions bounded by curves – applications ,Integration as inverse of differentiation, standard integrals involving algebraic expressions,
  • Application in problems of growth and decay.
Analytical Geometry of 2D & 3D
  • Rectangular Cartesian Coordinate system
  • Distance formula
  • Equation of a circle in standard and in general form
  • Equation of a line in various forms
  • Standard forms of Ellipse ,hyperbola and parabola
  • Angle between two lines
  • Distance of a point from a line
  • Eccentricity and axis of a conic
Vector Algebra
  • Vectors in two and three dimensions
  • Scalar multiplication of vector
  • Unit and null vectors
  • Addition of vectors
  • Magnitude and direction of a vector
  • Scalar product or dot product of two-vectors
  • Applications-work done by a force and moment of a force, and in geometrical problems
  • Vector product and cross product of two vectors.
  • Frequency distribution
  • Measures of Central tendency – mean, median and mode
  • Graphical representation – Histogram, Pie Chart, Frequency Polygon – examples, Classification of data, cumulative frequency distribution – examples, Correlation and regression ,Variance and standard deviation – determination and comparison.
  • Random experiment
  • Events, Mutually exclusive and exhaustive events, Impossible and certain events
  • Union & Intersection of events
  • Outcomes and associated sample space
  • Complementary, Elementary and Composite events
  • Conditional probability
  • Bayes’ theorem – simple problems, Random variable as function on a sample space
  • Binomial distribution, random experiments giving rise to Binomial distribution.


Confused? Know everything about NDA Exam Pattern.

NDA Syllabus 2022: General Ability
General Ability section covers wide syllabus of English and General Knowledge. Total time given is two and a half hours and carries 300 marks.

Part A: English
English syllabus of NDA Exam covers topics such as vocabulary, grammar & usage and cohesion in extended text to test candidate’s proficiency in English. To know more about the format of this particular section, refer to NDA Exam papers.

Part B: General Knowledge
General Knowledge covers sections like Physics, Chemistry, Social Studies, Geography and Current Events.

Subjects Syllabus Covered
  • Material used in the preparation of substances like soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and Gunpowder
  • Law of Chemical Combination (excluding problems).
  • Elements, Symbols, Formulas Mixtures and Compounds, and simple Chemical Equations
  • Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon-Di-oxide, Oxidation and Reduction, Carbon – different forms
  • Properties of Air and Water
  • Acids, bases and salts
  • Physical and Chemical changes.
  • Fertilizers – Natural and Artificial
  • Elementary ideas about the Structure of Atom, Atomic, Equivalent and Molecular Weights, Valency.
  • Physical Properties and States of Matter, Volume, Density, Mass, Weight and Specific Gravity, Pressure Barometer, Principle of Archimedes.
  • Newton’s Laws, Motion of objects, Velocity and Acceleration, Force and Momentum, Power and Energy Stability ,Parallelogram of Forces, elementary ideas of work, and Equilibrium of bodies, Gravitation.
  • Measurement of temperature and heat, Effects of Heat, Change of State and Latent Heat, Modes of transference of Heat. Simple musical instruments , Sound waves and their properties,.
  • Reflection and refraction. Spherical mirrors rectilinear propagation of Light and Lenses. Human Eye.
  • Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet.
  • Ohm’s Law, conductors and Non-conductors, Simple Electrical Circuits, Static and Current Electricity, Heating, Lighting and Magnetic effects of Current, Measurement of Electrical Power, Primary and Secondary Cells, Use of X-Rays.
  • 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
General Science
  • Basis of Life – Cells, Protoplasm and Tissues
  • Elementary knowledge of human Body and it’s important organs
  • Food – Source of Energy for man, Constituents of food, Balanced Diet
  • Achievements of Eminent Scientists
  • Difference between the living and nonliving
  • Growth and Reproduction in Plants and Animals
  • Common Epidemics, their causes and prevention
  • The Solar System – Meteors and Comets, Eclipses
  • Origin of Earth, Rocks and their classification
  • Weathering – Mechanical and Chemical, Earthquakes and volcanoes, Atmosphere and its composition
  • Temperature and Atmospheric Pressure, Planetary Winds, cyclones and Anticyclones
  • Humidity; Condensation and Precipitation
  • Types of Climate.
  • Major Natural regions of the World, Important Seaports and main sea, land and air routes of India. Main items of Imports and Exports of India
  • The Earth, its shape and size. Latitudes and Longitudes, Concept of time, International Date Line, Movements of Earth and their effects, Ocean Currents and Tides,
  • Regional Geography of India – Climate, Natural vegetation. Mineral and Power resources; location and distribution of agricultural and industrial activities.
  • 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 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.
Current Events Current important world events, Knowledge of Important events that have happened in India in the recent years, prominent personalities – both Indian and International including those connected with cultural activities and sports.

You must learn the exact weight-age of each of these sections by looking into previous NDA Exam papers to understand on how to prepare effectively. Keep up with tips to prepare NDA Entrance Exam.