NDA Syllabus
Mathematics Syllabus
Trigonometry: Trigonometrical ratios, properties of triangles, Angles and their measures in degrees and in radians, Inverse trigonometric functions, Trigonometric identities Sum and difference formulae, Applications – Height and distance, Multiple and Submultiple angles.
Algebra: Complex numbers – basic properties, modulus, Conversion of a number in decimal system to binary system and viceversa, Arithmetic, argument, cube roots of unity, Geometric and Harmonic progressions, Solution of linear inequations of two variables by graphs, Representation of real numbers on a line, Binary system of numbers, Binomial theorem and its application, Quadratic equations with real coefficients, Permutation and Combination, Logarithms and their applications.
Differential Calculus: Composite functions, one to one, onto and inverse functions, geometrical and physical interpretation of a derivative – applications, increasing and decreasing functions, Continuity of functions – examples, algebraic operations on continuous functions, Application of derivatives in problems of maxima and minima, Concept of a real valued function – domain, range and graph of a function, Notion of limit, Standard limits – examples, geometrical and physical interpretation of a derivative – applications, Derivative of a function at a point, Derivatives of sum, product and quotient of functions, derivative of a function with respect of another function, derivative of a composite function and Second order derivatives.
Vector Algebra: Vectors in two and three dimensions, scalar multiplication of vector, scalar product or dot product of twovectors, Applicationswork done by a force and moment of a force, and in geometrical problems, magnitude and direction of a vector, Unit and null vectors, addition of vectors, Vector product and cross product of two vectors.
Integral Calculus and Differential equations: Integration by substitution and by parts, trigonometric, Definition of order and degree of a differential equation, formation of a differential equation by examples, exponential and hyperbolic functions, solution of first order and first degree differential equations of various types – examples, standard integrals involving algebraic expressions, Evaluation of definite integrals – determination of areas of plane regions bounded by curves – applications, General and particular solution of a differential equation, Integration as inverse of differentiation, Application in problems of growth and decay.
Matrices and Determinants: Types of Matrices, Determinant of a matrix, adjoin and inverse of a square matrix, operations on matrices, Applications – Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method, basic properties of determinant.
Analytical Geometry of two and three dimensions: Distance formula, Equation of a circle in standard and in general form, Ellipse and hyperbola, Angle between two lines, Rectangular Cartesian Coordinate system, Equation of a line in various forms, Standard forms of parabola, Distance of a point from a line, Eccentricity and axis of a conic.
Point in a threedimensional space, distance between two points, Equation of a plane and a line in various forms, Equation of a sphere, Direction Cosines and direction ratios, angle between two lines and angle between two planes.
Statistics: Frequency distribution, Classification of data, cumulative frequency distribution – examples Graphical representation – Histogram, Measures of Central tendency – mean, median and mode, Pie Chart, Frequency Polygon – examples, Variance and standard deviation – determination and comparison, Correlation and regression.
Probability: Outcomes and associated sample space, Binomial distribution, Random experiment, examples of random experiments giving rise to Binominal distribution, events, mutually exclusive and exhaustive events, Bayes’ theorem – simple problems, impossible and certain events, Complementary, elementary and composite events, Union and Intersection of events, Definition of probability – classical and statistical – examples, Conditional probability, Random variable as function on a sample space, Elementary theorems on probability – simple problems, Binomial distribution, examples of random experiments giving rise to Binominal distribution.
Section A – Physics
Motion of objects, Newton’s Laws of Motion, Force and Momentum, Parallelogram of Forces, Stability and Equilibrium of bodies, Gravitation, elementary ideas of work, Velocity and Acceleration, Power and Energy, Sound waves and their properties, Simple musical instruments, Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariner’s Compass; Lightening Conductors, Safety Fuses, Simple Pendulum.
Simple Pulleys, Physical Properties and States of Matter, Mass, Weight, Volume, Density and Specific Gravity , Principle of Archimedes, Pressure Barometer, Effects of Heat, change of State and Latent Heat, Modes of transference of Heat, Rectilinear propagation of Light, Reflection and refraction’s. Spherical mirrors and Lenses . Human Eye , Static and Current Electricity, Measurement of temperature and heat, conductors and Nonconductors, Ohm’s Law, Simple Electrical Circuits, Heating, Lighting and Magnetic effects of Current, Measurement of Electrical Power, Primary and Secondary Cells, Use of XRays.
Section B – Chemistry
Preparation and Properties of Hydrogen, Oxygen, Nitrogen and CarbonDioxide, Oxidation and Reduction, Material used in the preparation of substances like soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and GunPowder, Carbon – different forms, Physical and Chemical changes. Symbols, Formulas and simple Chemical Equations, Law of Chemical Combination (excluding problems). Properties of Air and Water, Acids, bases and salts, Elements, Mixtures and Compounds, Fertilizers – Natural and Artificial, Elementary ideas about the Structure of Atom, Atomic, Equivalent and Molecular Weights, Valency.
Section C – General Science
Basis of Life – Cells, Protoplasms and Tissues, Constituents of food, Balanced Diet, Achievements of Eminent Scientists, Difference between the living and nonliving, Elementary knowledge of human Body and its important organs, Food – Source of Energy for man, Growth and Reproduction in Plants and Animals, Common Epidemics, their causes and prevention, The Solar System – Meteors and Comets, Eclipses.
Section D – History
Freedom Movement in India, Bhoodan, Sarvodaya, National Integration and Welfare State, Basic Teachings of Mahatma Gandhi, A broad survey of Indian History, with emphasis on Culture and Civilisation, Elementary knowledge of Five Year Plans of India, Elementary study of Indian Constitution and Administration, Panchayati Raj, 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, Cooperatives and Community Development, Role of India in the present world.
Section E – Geography
Origin of Earth, Weathering – Mechanical and Chemical, Earthquakes and volcanoes, Atmosphere and its composition, Temperature and Atmospheric Pressure, Rocks and their classification, Planetary Winds, cyclones and Anticyclones, Humidity, Condensation and Precipitation, Major Natural regions of the World, Important Sea ports and main sea, land and air routes of India. Main items of Imports and Exports of India, Types of Climate, The Earth, its shape and size, Lattitudes 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.
NDA Syllabus and Exam Pattern 2021
National Defence Academy (NDA) is the Joint Services academy of the Indian Armed Forces. The Union Public Service Commission (UPSC) conducts the National Defence Academy (NDA) Exam every year. NDA is a nationallevel exam conducted twice a year. This is one of the most soughtafter defence jobs in India to join the Defence Forces as an Officer by the male candidates. The selection into NDA is on the basis of the written test followed by the Personality Test. NDA written examination is divided into two papers namely Mathematics and General Ability Test (GAT).
NDA Syllabus 2021: Overview
Check the important points of the NDA Syllabus and Exam Pattern in the table below.
Name of the Exam 
National Defence Academy (NDA) 
Conducting Body 
Union Public Service Commission, UPSC. 
Frequency Of Exam 
Twice in a Year 
Selection Process 
1. Written Test consisting of Objective Type Questions 2. Intelligence & Personality Test (SSB) 
Mode of exam 
Offline 
Papers in NDA Exam 
1. Mathematics 2. General Ability Test 
Marks Segregation 
1. Mathematics: 300 Marks 2. GAT: 600 Marks 
Total No. of Questions 
1. Mathematics: 120 2. GAT: 150 
Negative Marking 
1. Mathematics: 0.83 2. GAT: 1.33 marks 
Exam Duration 
2.5 Hours For Each Paper (5 hours total) 
Language of Question Paper 
English & Hindi English Language paper has to be attempted in English. 
NDA Exam Pattern 2021
Before getting into the NDA Syllabus let us have a look at the NDA Exam Pattern. The mathematics paper have 120 questions of 300 marks and GAT will have English and GK Papers of 200 & 400 marks respectively.
NDA Mathematics Exam Pattern
Paper I Mathematics 

Total Marks 
300 Marks 
Total No. of Questions 
120 
Marks awarded for Correct answer 
2.5 marks 
Marks deducted for the wrong answer 
0.83 
Exam Duration 
2.5 Hours 
General Ability Test Exam Pattern
PaperII General Ability Test 

Total Marks 
600 marks 
Total No. of Questions 
150 
No. of questions in English Section 
50 
No. Of questions in General knowledge Section 
100 
Maximum Marks for English 
200 marks 
Maximum Marks for G.K. 
400 marks 
Marks for Correct Answer 
4 marks in both sections 
Marks for Incorrect Answer 
1.33 marks in both sections 
Exam Duration 
2.5 Hours 
NDA Exam Pattern for SSB Interview
After clearing the written exam of NDA, candidates have to appear for the SSB Interview rounds. The pattern of NDA Interview is as mentioned below:
NDA – SSB Interview Pattern  
Stage 1  Screening Test 
1. Verbal and nonverbal tests. 2. PPDT 
Stage 2  Psychological Test 
1. Thematic Apperception Test (TAT) 2. Word Association Test (WAT) 3. Situation Reaction Test (SRT) 4. Self Description Test (SD) 
Group Testing Officers Test 
1. GD 2. GPE 3. PGT 4. HGT 5. IoT 6. Command Task 7. Snake race/Group Obstacle Race 8. Individual lecture 9. FGT 

Personal Interview & conference  – 
NDA Syllabus 2021
After getting to know the NDA Exam Pattern it is important for the candidates to know the Syllabus of NDA Exam. The NDA Syllabus is discussed below.
NDA Mathematics Syllabus
The chapters covered for NDA Maths Syllabus are given in the table below.
Mathematics 

Topic 
Topicwise Syllabus 
Algebra 
Sets, Venn diagrams, De Morgan laws, Cartesian product, relation, equivalence relation. Real numbers, Complex numbers, Modulus, Cube roots, Conversion of a number in Binary system to Decimals, and viceversa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations, Linear inequations, Permutation and Combination, Binomial theorem, and Logarithms. 
Calculus 
Concept of a realvalued function, domain, range, and graph of a function. Composite functions, onetoone, onto, and inverse functions. The notion of limit, Standard limits, Continuity of functions, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivativeapplication. Derivatives of sum, product, and quotient of functions, a derivative of a function concerning another function, the derivative of a composite function. Secondorder derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima 
Matrices and Determinants 
Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix, ApplicationsSolution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method. 
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.Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of differential equations, solution of the first order, and firstdegree differential equations of various types—examples. Application in problems of growth and decay. 
Trigonometry 
Angles and their measures in degrees and radians. Trigonometric ratios. Trigonometric identities Sum and difference formulae. Multiple and Submultiple angles. Inverse trigonometric functions. ApplicationsHeight and distance, properties of triangles. 
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 done by a force and moment of a force and in geometrical problems. 
Analytical Geometry Of Two and Three Dimension 
Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. The angle between two lines. Distance of a point from a line. Equation of a circle in standard and a general form. Standard forms of parabola, ellipse, and hyperbola. Eccentricity and axis of a conic. Point in a threedimensional space, the distance between two points. Direction Cosines and direction ratios. Equation 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. 
Statistics and Probability 
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. 
The topicwise question distribution in Maths
Topic 
Questions 
Calculus 
2025 
Quadratic equation 
2015 
Matrices & Determinants 
30 
Probability 
10 
Trigonometry 
30 
Complex number 
1015 
NDA General Ability Test Syllabus
The General ability test comprises two papers English and General Knowledge. The English paper consists of 200 Marks while the General Knowledge is of 400 Marks.
English
The question paper in English will be designed to test the candidate’s understanding of English. The syllabus covers various aspects like as given below:
Topic 
No. of Questions 
No. of Marks 
Spotting Errors 
5 
20 
Comprehension 
6 
24 
Selecting Words 
10 
40 
Ordering of Words in a Sentence 
9 
36 
Sentence Improvement 
10 
40 
Antonyms 
5 
20 
Synonyms 
5 
20 
Total 
50 
200 
General Knowledge
Check the topicwise number of questions and marks distribution in the table below.
Topic 
No. of Questions 
No. of Marks 
Physics 
23 
92 
Chemistry 
16 
64 
General Science 
11 
44 
History & Freedom Movement 
16 
64 
Geography 
17 
68 
Current Events 
17 
68 
Total 
100 
400 
Physics
NDA Syllabus For Physics  


Chemistry
NDA Syllabus For Chemistry  


General Science
NDA Syllabus For General Science  


History, Freedom Movement
NDA Syllabus For History  


Geography
NDA Syllabus For Geography  


Current Events
NDA Syllabus For Current Events 

Knowledge of Important events that have happened in India in recent yearsProminent personalities of both Indian and International level, Cultural activities and sports activities, Current important world events. 
