NDA 2021 Syllabus
The NDA syllabus has 2 sections i.e. Mathematics and General Ability. The detailed syllabus for both the sections are given below:
Mathematics:
The Highlight of Mathematics syllabus:
Algebra Matrices and Determinants | Trigonometry | Analytical Geometry of Two and Three Dimensions |
Differential Calculus | Integral Calculus | Differential Equations |
Vector Algebra | Statistics | Probability |
Details present in mathematics syllabus of NDA:
1. ALGEBRA:
Concept of set, operations on sets, Venn diagrams. De Morgan laws. Cartesian product, relation, equivalence relation. Representation of real numbers on a line. Maple 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 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.
2. MATRICES AND DETERMINANTS:
Types of matrices, operations on matrices. The 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.
3. TRIGONOMETRY:
Angles and their measures in degrees and in radians. Trigonometrically ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications – Height and distance, properties of triangles.
4. ANALYTICAL GEOMETRY OF TWO AND THREE DIMENSIONS:
Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. The angle between the two lines. The distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse, and hyperbola. Eccentricity and axis of a conic. The point in a three-dimensional space, distance between two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. The angle between the two lines and the angle between the two planes. Equation of a sphere.
5. DIFFERENTIAL CALCULUS:
Concept of a real-valued function – domain, range, and graph of a function. Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits – examples. Continuity of functions – examples, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivative – applications. Derivatives of sum, product and quotient of functions, the derivative of a function with respect to another function, the derivative of a composite function. Second-order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.
6. 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 first-degree differential equations of various types – examples. Application in problems of growth and decay.
7. 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 did by a force and moment of a force and in geometrical problems.
8. STATISTICS AND PROBABILITY:
Statistics: Classification of data, Frequency distribution, And 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. 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.
General Ability:
The general ability section consists of 7 subjects that are Physics, Chemistry, General Science, History, Geography, English, Current events. The detailed syllabus is mentioned below:
1. Physics:
Physics Syllabus highlight:
Physical Properties and States of Matter | Force and Momentum | Reflection and refraction |
Density and Specific Gravity | Stability and Equilibrium of bodies | Spherical mirrors and Lenses |
Principle of Archimedes | Gravitation | Human Eye |
Pressure Barometer | Power and Energy | Properties of a Magnet |
Motion of objects | Effects of Heat | Static and Current Electricity |
Velocity and Acceleration | Sound waves and their properties | Ohm’s Law |
Newton’s Laws of Motion | Rectilinear propagation of Light | Simple Electrical Circuits |
Heating, Lighting and Magnetic effects of Current | Measurement of Electrical Power | Use of X-Rays |
Details in Physics level:
Physical Properties and States of Matter, Mass, Weight, Volume, Density, and Specific Gravity, Principle of Archimedes, Pressure Barometer. The 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 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.
2. Chemistry:
Chemistry syllabus Highlight:
Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon Dioxide, Oxidation and Reduction. Acids, bases, and salts | Atomic Equivalent and Molecular Weights | Symbols, Formulae and simple Chemical Equation |
Different forms of carbon | Valency | Law of Chemical Combination |
Fertilizers—Natural and Artificial | Elements | Mixtures and Compounds |
Structure of Atom | Physical and Chemical Changes | Properties of Air and Water |
Details in Chemistry syllabus:
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 the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and Gun-Powder. Elementary ideas about the Structure of Atom, Atomic, Equivalent and Molecular Weights, Valency.
3. General Science:
General Science Highlight:
Common Epidemics, their causes, and prevention | Difference between the living and non-living |
Food—Source of Energy for man | Basis of Life—Cells, Protoplasms, and Tissues |
Constituents of food | Growth and Reproduction in Plants and Animals |
Balanced Diet | Elementary knowledge of Human Body and its important organs |
The Solar System | Achievements of Eminent Scientists |
Details in General Science Syllabus:
Difference between living and non- living. Basis of Life – Cells, Protoplasms, and Tissues. Growth and Reproduction in Plants and Animals. Elementary knowledge of the Human Body and its important organs. Common Epidemics, their causes, and prevention. Food – Source of Energy for man. Constituents of food, Balanced Diet. The Solar System – Meteors and Comets, Eclipses. Achievements of Eminent Scientists.
4. History:
Exploration and Discovery: War of American Independence, French Revolution, Industrial Revolution, and Russian Revolution | Freedom Movement in India |
United Nations, Panchsheel, Democracy, Socialism, and Communism | Elementary study of Indian Constitution and Administration |
Role of India in the present world | Panchayati Raj |
Basic Teachings of Mahatma Gandhi | Co-operatives and Community Development |
A broad survey of Indian History, with emphasis on Culture and Civilisation | Bhoodan, Sarvodaya, National Integration and Welfare State |
Details in History syllabus:
A broad survey of Indian History, with emphasis on Culture and Civilizations. 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, the Industrial Revolution, and the 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.
5. Geography:
The syllabus of geography contents the topic like-
The Earth, its shape and size | Temperature and Atmospheric Pressure, Planetary Winds, Cyclones and Anticyclones, Humidity, Condensation and Precipitation |
Latitudes and Longitudes | Types of Climate |
International Date Line | Major Natural Regions of the World |
Origin of Earth. Rocks and their classification | Regional Geography of India: Climate, Natural vegetation. Mineral and Power resources; location and distribution of agricultural and Industrial activities |
Weathering—Mechanical and Chemical, Earthquakes and Volcanoes | Important Sea ports and main sea, land, and air routes of India |
Ocean Currents and Tides Atmosphere and its composition | Main items of Imports and Exports of India |
6. English:
the question
Spotting Errors |
Spotting Errors |
Ordering of Words in a Sentence |
Sentence Improvement |
Antonyms |
Synonyms |
7. Current Events:
Important and Recent Events in India |
Important Indian or Non-Indian Personalities related to Cultural Activities and Sports |
Current important world events |