# 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
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
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