NDA Exam Syllabus 2021: Check Detailed Exam Pattern And Syllabus For NDA & NA I, II Exam 2021

1. Written Test consisting of Objective Type Questions
2. Intelligence & Personality Test (SSB)

1. Mathematics
2. General Ability Test

1. Mathematics: 300 Marks
2. GAT: 600 Marks

1. Mathematics: 120
2. GAT: 150

1. Mathematics: -0.83
2. GAT: -1.33 marks

• Concept of set, operations on sets, Venn diagrams
• De Morgan laws, Cartesian product, relation, equivalence relation
• Representation of real numbers on a line
• Complex 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

• 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

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

• Rectangular Cartesian Coordinate system
• Distance formula
• Equation of a line in various forms
• Angle between two lines
• Distance of a point from a line
• Equation of a circle in standard and in a general form
• Standard forms of parabola, ellipse and hyperbola
• Eccentricity and axis of a conic
• Point in a three-dimensional 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
• Angle between two lines and the angle between two planes
• Equation of a sphere

• 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
• Continuity of functions
• 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

• 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 first order and first-degree differential equations of various types
• Application in problems of growth and decay

• Vectors in two and three dimensions, magnitude and direction of a vector
• Unit and null vectors, 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

• Classification of data
• Frequency distribution
• Cumulative frequency distribution
• Graphical representation—Histogram, Pie Chart, frequency polygon
• 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

• Physical Properties and States of Matter, Mass,  Weight, Volume, Density and Specific Gravity, Principle of Archimedes, Pressure Barometer
• 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.

• 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 Carbondioxide, 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

• Difference between the living and non-living
• Basis of Life—Cells, Protoplasms and Tissues
• Growth and Reproduction in Plants and Animals
• Elementary knowledge of 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

• 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

• The Earth, its shape and size
• Lattitudes 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

• Knowledge of Important events that have happened in India in recent years
• Current important world events
• Prominent personalities—both Indian and International including those connected with cultural activities and sports