NDA Syllabus for Preliminary Exam
This exam is conducted as −
- Mathematics &
- General Ability
Mathematics & General Ability Syllabus
The following table illustrates the detailed syllabus −
| Mathematics Syllabus (Paper I) | |
|---|---|
| Algebra | 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 | |
| Solution of linear in equations of two variables by graphs | |
| Permutation and Combination | |
| Binomial theorem and its applications | |
| Logarithms and their applications | |
| Matrices & Determinants | Types of matrices, operations on matrices |
| 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 | |
| Trigonometry | 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 | |
| Analytical Geometry of Two and Three Dimensions | 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 general form | |
| Standard forms of parabola, ellipse and hyperbola | |
| Eccentricity and axis of a conic | |
| Point in a three dimensional space, 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 angle between two planes | |
| Equation of a sphere | |
| 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, derivative of a function with respect to another function, derivative of a composite function | |
| Second order derivatives. Increasing and decreasing functions | |
| Application of derivatives in problems of maxima and minima | |
| Integral Calculus & Differential Equations | Integration as inverse of differentiation |
| Integration by substitution and by parts | |
| Standard integrals involving algebraic expressions | |
| Trigonometric | |
| Exponential | |
| 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 a differential equations, solution of first order and first degree differential equations of various types—examples | |
| Application in problems of growth and decay | |
| Vector Algebra | 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 | |
| Statistics | Classification of data |
| Frequency distribution | |
| 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 Syllabus | |
| Part ‘A’ (Paper II) | |
| English | Grammar and usage |
| Vocabulary | |
| Comprehension and cohesion in extended text | |
| Part ‘B’ General Knowledge | |
| Physics | 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. | |
| Chemistry | 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 | |
| General Science | Difference between the living and non-livin |
| Basis of Life—Cells, Protoplasm 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 | |
| History, Freedom Movement | A broad survey of Indian History, with emphasis on Culture and Civilization |
| 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 | |
| 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 | Current National events |
| Current World events | |
| Prominent personalities—both Indian and International | |
| Current cultural activities | |
| Sports | |
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