# NDA SYLLABUS

## NDA Exam Pattern

 Paper Subject Name Duration Containing Marks No. of Questions I Mathematics 2.5 Hours (150 Min) 300 120 II General Ability Test 2.5 Hours (150 Min) 600 150 Total Marks 900 270

## Pattern of General Ability Test

 Section Subject Name Marks No. of Questions I English 200 50 II General Knowledge 400 100 Total Marks 600 150

#### General Knowledge Marks distribution

 Subject Name Marks Physics 100 Chemistry 60 General Science 40 History, Freedom Movement 80 Geography 80 Current Events 40

## NDA Maths Syllabus

### Trigonometry

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

### Algebra

• Complex numbers
• Basic properties
• Modulus
• Argument
• Cube roots of unity
• Conversion of a number in decimal system to binary system and vice-versa
• Arithmetic
• Geometric and Harmonic Progressions
• Solution of linear inequations of two variables by graphs
• Binomial theorem and its application
• Representation of real numbers on a line
• Binary system of numbers
• Quadratic equations with real coefficients
• Permutation and Combination
• Logarithms and their applications.

### Differential Calculus

• Composite functions – one to one, onto and inverse functions
• Continuity of functions
• Algebraic operations on continuous functions
• Geometrical and physical interpretation of a derivative – applications
• Increasing and decreasing functions
• Application of derivatives in problems of maxima and minima
• Concept of a real valued function – domain, range, and graph of a function, Notion of limit,
• Standard limits – Derivative of a 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
• The derivative of a composite function and Second order derivatives.

### Vector Algebra:

• Vectors in two and three dimensions
• Magnitude and direction of a vector
• Scalar multiplication of vector
• Scalar product or dot product of two vectors
• Applications – work done by a force and moment of a force, geometrical problems, Unit and null vectors, the addition of vectors, Vector product and cross product of two vectors.

### Integral Calculus and Differential equations

• Integration by substitution and by parts
• Trigonometric
• Exponential and hyperbolic functions
• Definition of order and degree of a differential equation
• Formation of a differential equation by examples
• A solution of the first order and first-degree differential equations of various types – examples, Integration as the inverse of differentiation, Standard integrals involving algebraic expressions.
• Evaluation of definite integrals
• Determination of areas of plane regions bounded by curves – applications, General and particular solution of a differential equation, Application in problems of growth and decay.

### Matrices and Determinants

• Types of Matrices
• Determinant of a matrix
• Adjoint and inverse of a square matrix
• Operations on matrices
• Basic properties of determinant
• Applications – Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.

### Analytical Geometry of two and three dimensions:

• Distance formula
• Angle between two lines
• Equation of a circle in standard and in general form
• Ellipse and hyperbola
• Rectangular Cartesian Coordinate system
• Equation of a line in various forms
• Distance of a point from a line
• Standard forms of parabola
• Eccentricity and axis of a conic.

### Three dimensions:

• Point in a three-dimensional space
• Distance between two points
• Equation of a plane and a line in various forms
• Equation of a sphere
• Direction Cosines and direction ratios
• An angle between two lines and an angle between two planes.

### Statistics:

• Frequency distribution
• Measures of Central tendency – mean, median and mode, Classification of data
• Cumulative frequency distribution – examples
• Graphical representation – Histogram, Pie Chart
• Frequency Polygon – examples,
• Variance and standard deviation – determination and comparison, Correlation and regression.

### Probability:

• Outcomes and associated sample Space
• Bayes’ theorem
• Simple problems
• Binomial distribution
• Random experiment
• Examples of random experiments giving rise to Binominal distribution
• #### Events

• Mutually exclusive and exhaustive events,
• Impossible and certain events
• Complementary
• Elementary and composite events
• Union and Intersection of events
• Definition of probability
• Classical and statistical – examples,
• Elementary theorems on probability
• Simple problems
• Conditional probability
• Random variable as function on a sample space
• Binomial distribution
• Examples of random experiments giving rise to Binomial distribution.

## General Ability Syllabus

• ### Part A

#### English

• Vocabulary
• Grammar and usage
• Comprehension and cohesion in extended text to test the candidate’s proficiency in English.

### Part B

#### NDA Syllabus for General Knowledge

The question paper comprises of general knowledge and covers the subjects that include Physics, Chemistry, General Science, Social Studies, Geography and Current Events.

#### Section A – NDA Exam Syllabus – Physics

• 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
• Sound waves and their properties
• Simple musical instruments
• Natural and Artificial Magnets
• Properties of a Magnet
• Earth as a Magnet
• Simple Pendulum – Simple Pulleys, Balloon, Siphon, Pressure Cooker, Levers, Pumps, Hydrometer, Gramophone, Thermos Flask, Telegraphs, Periscope, Telephone, Microscope, Telescope, Mariner’s Compass.
• Lightning Conductors
• Safety Fuses
• Physical Properties and States of Matter – Mass, Weight, Volume, Density and Specific Gravity
• Principle of Archimedes
• Pressure Barometer
• Effects of Heat
• Measurement of temperature and heat
• Change of State and Latent Heat
• Modes of transference of Heat
• Rectilinear propagation of Light
• Reflection and refraction.
• Spherical mirrors and Lenses – Human Eye
• Static and Current Electricity
• Conductors and Non-conductors
• Ohm’s Law – Simple Electrical Circuits, Lighting and Magnetic effects of Current, Heating, Measurement of Electrical Power, Primary and Secondary Cells, Use of X-Rays.

#### Section B – UPSC NDA Syllabus of Chemistry

• Preparation and Properties of Hydrogen
• Oxygen
• Nitrogen and Carbon-Di-oxide
• Oxidation and Reduction
• Carbon – different forms, Material used in the preparation of substances like soap, Ink, Glass, Cement, Paper,  Paints, Safety Matches, and Gun-Powder, Physical and Chemical changes.
• Elements, Symbols, Mixtures and Compounds, Formulas and simple Chemical Equations, Law of Chemical Combination (excluding problems).
• Properties of Air and Water, Acids, bases, and salts.
• Fertilizers – Natural and Artificial, Elementary ideas about the Structure of Atom, Atomic, Equivalent and Molecular Weights, Valency.

#### Section C – Syllabus of NDA – General Science

• The basis of Life – Cells, Protoplasms and Tissues, Elementary knowledge of human Body and its important organs.
• Food – Source of Energy for man, Balanced Diet, Constituents of food, Achievements of Eminent Scientists, Difference between the living and non-living, Common Epidemics, their causes, and prevention
• The Solar System – Meteors and Comets, Eclipses.

#### Section D – Syllabus for NDA Exam – History

• Freedom Movement in India
• Elementary knowledge of Five Year Plans of India
• Bhoodan
• Sarvodaya
• National Integration and Welfare State
• Basic Teachings of Mahatma Gandhi
• A broad survey of Indian History
• With emphasis on Culture and Civilisation
• Elementary study of Indian Constitution and Administration
• Panchayati Raj, Co-operatives, and Community Development
• Forces shaping the modern world; Renaissance
• Exploration and Discovery
• War of American Independence.
• French Revolution, Industrial Revolution and Russian Revolution.
• The 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

#### Section E – Syllabus for NDA Entrance Exam – Geography

• Origin of Earth
• Rocks and their classification
• Weathering – Mechanical and Chemical, Atmosphere and its composition, Earthquakes, and volcanoes.
• Temperature and Atmospheric Pressure
• Planetary Winds
• Cyclones and Anti-cyclones
Humidity
• Condensation and Precipitation
• Types of Climate
• Major Natural regions of the World
• Important Sea ports and main sea
• Land and air routes of India.
• Main items of Imports and Exports of India
• The Earth, its shape, and size
• Latitudes and Longitudes
• Concept of time
• International Date Line
• Movements of Earth and their effects
• Ocean Currents and Tides
• Regional Geography of India – Climate, Natural vegetation.
• Mineral and Power resources
• Location and distribution of agricultural and industrial activities.

#### Section F – Current Events

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