NDA Syllabus for Paper I MATHEMATICS

Algebra 
 Concept Of A Set
 Operations On Sets
 Venn Diagrams
 De Morgan Laws
 Cartesian Product
 Relation
 Equivalence Relation
 real numbers on a line
 Complex numbers
 decimal system to binary system
 Arithmetic, Geometric and Harmonic progressions
 Quadratic equations with real coefficients
 Permutation and Combination
 Binomial theorem/ Logarithms and their applications.

Matrices and Determinants 
 Types of matrices
 operations on matrices Determinant of a matrix
 properties of determinant
 Adjoint and inverse of a square matrix
 Applications – Solution of a system of linear equations in two or three unknowns by Cramers rule and by Matrix Method.

Trigonometry 
 Angles and their measures
 Trigonometrical ratios
 Trigonometric identities Sum and difference formulae.
 Multiple and Submultiple angles
 Inverse trigonometric functions
 Applications – Height and distance
 Properties of triangles.

Analytical Geometry of two and three dimensions 
 Rectangular Cartesian Coordinate system.
 Equation of a plane and a line in various forms
 Angle between two lines and angle between two planes. Equation of a sphere.
 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.

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 a function at a point, geometrical and physical interpreatation of a derivative – applications.
 Derivatives of sum, product and quotient of functions, derivative of a function with respect of 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 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 a differential equation, 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 vector, scalar product or dot product of twovectors
 Vector product and cross product of two vectors.
 Applicationswork done by a force and moment of a force, and in geometrical problems.

Statistics and Probability 
 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

NDA Syllabus for Paper II GENERAL ABILITY TEST

Part A – ENGLISH 
The question paper in English will be designed to test the candidates understanding of English and workman like use of wordsThe syllabus covers various aspects like Grammar and usage, vocabulary, comprehension and cohesion in extended text to test the candidate’s proficiency in English. 
Part B – GENERAL KNOWLEDGE 
The question paper on General Knowledge will broadly cover the subjects Physics, Chemistry, General Science, Social Studies, Geography and Current Events.GK Questions with Answers 
Section A (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, Newtons 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 Nonconductors, Ohms Law, Simple Electrical Circuits, Heating, Lighting and Magnetic effects of Current, Measurement of Electrical Power, Primary and Secondary Cells, Use of XRays.
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, Mariners Compass; Lightening Conductors, Safety Fuses.

Section B (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 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 GunPowder
 Elementary ideas about the Structure of Atom, Atomic, Equivalent and Molecular Weights, Valency

Section C (General Science) 
 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.

Section D (History, Freedom Movement etc.) 
 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, Cooperatives 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.
