NDA Exam (I) 2016: Syllabus
Union Public Service Commission (UPSC) organizes National Defence Academy & Naval Academy (NDA &NA) Examination. This Exam will be held on 17th April 2016. Through NDA Exam, candidates get admission to the courses at National Defence Academy and Naval Academy.
Exam Paper Pattern of NDA & NA Examination
The Examination consists of 2 Papers, Mathematics – 120 questions (300 marks) General Ability Test – 150 Questions (600 marks) and with objective type questions. The duration for each Paper is 2 Hours 30 minutes. There will be penalty (one –third) for the each wrong answer.
SYLLABUS OF THE EXAMINATION
1. 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.
2. MATRICES AND 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.
3. TRIGONOMETRY
Angles and their measures in degrees and in radians. Trigonometrically
ratios. Trigonometric identities Sum and difference formulae. Multiple and
Sub-multiple angles. Inverse trigonometric functions. Applications-Height
and distance, properties of triangles.
4. 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.
5. 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.
6. 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 equations, solution of first order and first degree differential
equations of various types—examples. Application in problems of growth
and decay.
7. 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.
8. 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.
Paper II
General Ability Test -It will be divided into two parts:-
Part A: English Language- The motive of this paper to test the candidate’s understanding of English Language. The syllabus covered various aspects like- Grammar and usage, vocabulary, comprehension etc.
Part B: GENERAL Knowledge
In Part B of Question Paper I Question will be on various topics including History of India & freedom movement, Geography, Polity, General Science, Physics, Chemistry, Economics, and Currents Affairs etc. The detailed syllabus is given below:-
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, 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.
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 Gun-Powder.
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, 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.
Section ‘E’ (Geography)
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.
Section ‘F’ (Current Events)
Knowledge of Important events that have happened in India in the
recent years. Current important world events.
Prominent personalities—both Indian and International including
those connected with cultural activities and sports.
Important Note:
Out of maximum marks assigned to part ‘B’ of this paper, questions on
Sections ‘A’, ‘B’, ‘C’, ‘D’, ‘E’ and ‘F’ will carry approximately 25%, 15%, 10%,
20%, 20% and 10% weightages respectively.
Exam Paper Pattern of NDA & NA Examination
The Examination consists of 2 Papers, Mathematics – 120 questions (300 marks) General Ability Test – 150 Questions (600 marks) and with objective type questions. The duration for each Paper is 2 Hours 30 minutes. There will be penalty (one –third) for the each wrong answer.
SYLLABUS OF THE EXAMINATION
1. 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.
2. MATRICES AND 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.
3. TRIGONOMETRY
Angles and their measures in degrees and in radians. Trigonometrically
ratios. Trigonometric identities Sum and difference formulae. Multiple and
Sub-multiple angles. Inverse trigonometric functions. Applications-Height
and distance, properties of triangles.
4. 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.
5. 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.
6. 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 equations, solution of first order and first degree differential
equations of various types—examples. Application in problems of growth
and decay.
7. 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.
8. 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.
Paper II
General Ability Test -It will be divided into two parts:-
Part A: English Language- The motive of this paper to test the candidate’s understanding of English Language. The syllabus covered various aspects like- Grammar and usage, vocabulary, comprehension etc.
Part B: GENERAL Knowledge
In Part B of Question Paper I Question will be on various topics including History of India & freedom movement, Geography, Polity, General Science, Physics, Chemistry, Economics, and Currents Affairs etc. The detailed syllabus is given below:-
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, 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.
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 Gun-Powder.
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, 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.
Section ‘E’ (Geography)
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.
Section ‘F’ (Current Events)
Knowledge of Important events that have happened in India in the
recent years. Current important world events.
Prominent personalities—both Indian and International including
those connected with cultural activities and sports.
Important Note:
Out of maximum marks assigned to part ‘B’ of this paper, questions on
Sections ‘A’, ‘B’, ‘C’, ‘D’, ‘E’ and ‘F’ will carry approximately 25%, 15%, 10%,
20%, 20% and 10% weightages respectively.
