NDA Syllabus: Mathematics and GAT Syllabus

NDA syllabus 2021 comprises of the subjects and topics that the candidates must study to score good marks in the exam. To crack the NDA exam, every aspirant should ensure to prepare for it as per the syllabus prescribed by the authority. NDA is a recruitment exam for selecting the capable candidates for various wings of the Indian Armed Forces. The exam is given by lakhs of candidates every year who aim to pursue an outstanding career in the armed forces.

Given the staggering amount of candidates taking this exam, the competition level naturally becomes high. Therefore, aspirants should leave no stone unturned to qualify all the stages of the exam. The exam will be conducted in two phases- written test and SSB test. To qualify the written test, candidates must prepare as per the NDA Syllabus 2021 decided by the UPSC, the exam conducting body.

NDA Syllabus

The written exam will be composed of two papers namely- Mathematics and General Ability Test. Candidates should clear both the papers to qualify the written exam. NDA syllabus 2021 prescribed for given papers is as follows-

  • Syllabus for Mathematics: The paper-I will carry 300 marks and every question will be of 2.5 marks. Here are the topics to be covered under this section-Algebra, Matrices and Determinants, Trigonometry, Analytical Geometry of 2D and 3D, Differential Calculus, Integral Calculus & Differential Equations, Vector Algebra, Statistics and Probability.
  • Syllabus for General Ability Test: The Paper-II will carry 600 marks and each question will be of 4 marks. Here are the topics to be covered for this paper- English Grammar, Comprehension, General Knowledge pertaining to Environment, Politics, Economics etc. The GAT will be organized in form of two papers, one for English carrying 200 marks and the other for G.K. carrying 400 marks.

Topics to be Prepared under NDA Syllabus

The detailed syllabus for NDA Examination is provided below. Candidates can make a checklist of the topics before starting their preparation and mark the topics completed side by side.

For Mathematics

Algebra: Venn diagrams, De Morgan laws, Concept of set, operations on sets, Cartesian product, relation, equivalence relation, Complex numbers—basic properties, modulus, argument, cube roots of unity,  Binary system of numbers, Permutation and Combination,   Arithmetic, Representation of real numbers on a line, Solution of linear inequations of two variables by graphs,  Conversion of a number in decimal system to binary system and vice-versa, Geometric and Harmonic progressions,  Quadratic equations with real coefficients,  Logarithms and their applications, Binomial theorem and its applications.

Matrices & Determinants: Operations on matrices, Applications-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method , Types of matrices, basic, properties of determinants, Adjoint and inverse of a square matrix, Determinant of a matrix.

Trigonometry: Trigonometrical ratios, Trigonometric identities Sum and difference formulae, Angles and their measures in degrees and in radian, Multiple and Sub-multiple angles, Inverse trigonometric functions, properties of triangles, Applications-Height and distance.

Analytical Geometry of 2D & 3D: Equation of a line in various forms,  Rectangular Cartesian Coordinate system,  Distance formula,  Angle between two lines,  Equation of a circle in standard and in general form,  Standard forms of parabola, ellipse and hyperbola, Equation two points,  Distance of a point from a line,  Eccentricity and axis of a conic, , Angle between two lines and angle between two planes,  Equation of a sphere,  Point in a three dimensional space, distance between two points,  Direction Cosines and direction ratios,  Direction Cosines and direction ratios,  Equation of a plane and a line in various forms.

Differential Calculus: Notion of limit, Standard limits—examples, Concept of a real valued function–domain, range and graph of a function, Composite functions, one to one, onto and inverse functions, Continuity of functions—examples, algebraic operations on continuous functions,   Increasing and decreasing functions,  Application of derivatives in problems of maxima and minima, Derivative of function at a point, Derivatives of sum, product and quotient of functions, derivative of a function with respect to another function, derivative of a composite function,  geometrical and physical interpretation of a derivative—applications,  Second order derivatives.

Integral Calculus & Differential Equations: Standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions, Integration as inverse of differentiation, integration by substitution and by parts, Definition of order and degree of a differential equation, Evaluation of definite integrals—determination of areas of plane regions bounded by curves— applications,  formation of a differential equation by examples, , Application in problems of growth and decay , General and particular solution of a differential equations, solution of first order and first degree differential equations of various types—examples.

Vector Algebra: Unit and null vectors, addition of vectors, scalar multiplication of a vector, Vectors in two and three dimensions, magnitude and direction of a vector,  , Applications—work done by a force and moment of a force and in geometrical problems, scalar product or dot product of two vectors,  Vector product or cross product of two vectors.

Statistics: Classification of data, Graphical representation—Histogram, Pie Chart, frequency polygon—examples, Variance and standard deviation—determination and comparison, Correlation and regression Frequency distribution, cumulative frequency distribution—examples, Measures of Central tendency—Mean, median and mode.

Probability: Union and Intersection of events, Complementary, elementary and composite events, Definition of probability—classical and statistical— examples, Elementary theorems on probability—simple problems, Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events, Conditional probability, Bayes’ theorem—simple problems, Random variable as function on a sample space,  examples of random experiments giving rise to Binominal distribution, Binomial distribution.

For General Aptitude Test (GAT)

NDA syllabus 2021 for GAT is as follows-

English: Grammar & Usage, Jumble Words, Rearrangement of sentences, Vocabulary, Antonym and Synonym, Comprehension, Passage Reading, Fill in the blanks etc.

General Knowledge: The G.K part will broadly cover the topics Physics, Chemistry, General Science, Social Studies, Geography and Current Events. Here are the core concepts to be prepared under NDA syllabus 2021-

Physics: Density and Specific Gravity, Physical Properties and States of Matter, Mass, Weight, Volume, Principle of Archimedes, Pressure Barometer,   Motion of objects, Velocity and Acceleration, Newton’s Laws of Motion, Force and Momentum, Stability and Equilibrium of bodies, Gravitation, elementary ideas of work, Power and Energy,  Effects of Heat, Parallelogram of Forces, Sound waves and their properties, Simple musical instruments, Measurement of Temperature and Heat, change of State and Latent Heat, Modes of transference of Heat.

Spherical mirrors and Lenses, Human Eye, Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet, conductors and Non-conductors, Simple Electrical Circuits, Heating, Lighting and Magnetic effects of Current, Measurement of Electrical Power, Primary and Secondary Cells, Use of X-Rays, Rectilinear propagation of Light, Reflection and refraction,  General Principles in the working of the following:  Simple Pendulum, Simple Pulleys, Static and Current Electricity,  Ohm’s Law, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, , Lightening Conductors, Safety Fuses , Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariner’s Compass.

Chemistry: Elements, Mixtures and Compounds, Physical and Chemical changes,  Symbols, Formulae and simple Chemical Equations, Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon dioxide, Oxidation and Reduction, Carbon— different forms,   Law of Chemical Combination (excluding problems),  Properties of Air and Water,  Acids, bases and salts,  Fertilizers—Natural and Artificial. Material used in the preparation of substances like Soap, Glass, Ink, Paper,  Atomic Equivalent and Molecular Weights, Valency,  Cement, Paints, Safety Matches and Gun-Powder , Elementary ideas about the structure of Atom.

General Science: Basis of Life—Cells, Protoplasms and Tissues, Difference between the living and non-living,  Growth and Reproduction in Plants and Animals,  Common Epidemics, their causes and prevention,  Food—Source of Energy for man , Eclipses, Achievements of Eminent Scientists, Elementary knowledge of Human Body and its important organs, Constituents of food, Balanced Diet, The Solar System—Meteors and Comets.

Social Studies:  Elementary study of Indian Constitution and Administration, , Role of India in the present world, Elementary knowledge of Five Year Plans of India, Panchayati Raj, Impact of Science and Technology on Society, Co-operatives and Community Development, A broad survey of Indian History, with emphasis on Culture and Civilization, Freedom Movement in India, Bhoodan, Sarvodaya, National Integration and Welfare State,  Forces shaping the modern world,  Renaissance, Exploration and Discovery,  War of American Independence,  French Revolution, Basic Teachings of Mahatma Gandhi, Industrial Revolution and Russian Revolution, Concept of one World, United Nations, Panchsheel, Democracy, Socialism and Communism.

Geography: The 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.

Current Events: Knowledge National/International affairs, environment related issues, political issues, sports related news etc.

How to Prepare for the NDA Exam

Given below are some preparation tips for the candidates that will help them crack the exam-

  • Make a checklist of the topics to be studied.
  • Then prepare a time table based on the time left for studies. The time table should be practical enough to be easily followed.
  • Study daily as per your learning capacity. Try to devote minimum 3-6 hours daily for preparation.
  • Make short notes while studying.
  • Develop a habit of reading newspaper regularly.
  • Revise the topics studied on a daily basis.
  • Strictly study as per the NDA syllabus 2021 mentioned above.
  • Solve previous year papers to improve your performance and efficiency.

Recommended Books

Candidates can note down the names of some popular NDA Preparation books as mentioned below-

  • NCERTs for class 10th, 11th and 12th.
  • Objective English by Hari Mohan Prasad.
  • Objective English by R.S. Aggarwal.
  • Objective G.K & Current affairs by Disha Publication.
  • Lucent’s G.K.
  • NDA & NA mathematics by Manjul Tyagi
  • Mathematics for NDA & NA by R.S. Aggarwal
  • Indian Polity by Laxmikant.
  • Pathfinder for NDA & NA by Arihant Publication.

Exam Pattern

Candidates can note down the exam pattern to plan their exam preparation strategy properly. Aligning the syllabus with the exam pattern will surely yield better result. The exam pattern for the National Defence Academy Examination is as follows-

Subject Code Duration Maximum Marks
Mathematics 01 2 Hours 30 Minutes 300
General Ability Test 02 2 Hours 30 Minutes 600
Total 900
SSB Test/Interview 900

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