**NDA Syllabus**: Union public service commission conducts National Defence Academy (NDA) & Naval Academy (NA) exam twice in a year for admission to Indian Navy, Army & Air Force Wings. Minimum Educational Qualification is 12th class pass in 10+2 pattern. The examination conducts in 2 stages, written examination and interview.The details regarding Syllabus are as follows…

**Syllabus of the Examination:****PAPER-I:**(Maximum Marks- 300)

**MATHEMATICS**###
**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. Maple 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 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, And
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 **(Maximum Marks-600)** **

**GENERAL ABILITY TEST**

###
**Part ‘A’ – ENGLISH** (Maximum Marks 200)

The question paper in English will be
designed to test the candidate’s understanding of English and workman
like use of words. The 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 **(Maximum Marks-400)

The question paper on General Knowledge
will broadly cover the subjects: Physics, Chemistry, General Science,
Social Studies, Geography and Current Events. The syllabus given below
is designed to indicate the scope of these subjects included in this
paper. The topics mentioned are not to be regarded as exhaustive and
questions on topics of similar nature not specifically mentioned in the
syllabus may also be asked. Candidate’s answers are expected to show
their knowledge and intelligent understanding of the subject.

###
**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 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.

###
**Section ‘C’ (General Science):**

Difference
between the living and non- living. Basis of Life – Cells, Protoplasm’s
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
Civilizations. 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. 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.

###
**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.

**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% weight ages respectively.

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