UPSC (Union
Public Service Commission) conducts NDA (National Defence Academy) 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 given below…
- MATHEMATICS: PAPER-I (Maximum Marks- 300)
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.
- GENERAL ABILITY TEST – PAPER-II (Maximum Marks-600)
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. Intelligence and personality test In addition to the
interview the candidates will be put to Intelligence Tests both verbal and
non-verbal, designed to assess their basic intelligence. They will also be put
to Group Tests such as group discussions, group planning, outdoor group tasks,
and asked to give brief lectures on specified subjects. All these tests are
intended to judge the mental calibers of a candidate. In broad terms, this is
really an assessment of not only his intellectual qualities but also his social
traits and interests in current affairs.
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