


Union Public Service Commission
UPSC NDA & NA ExaminationII Syllabus 2021


Scheme Of Examination

Subject

Code

Duration

Maximum Marks

Mathematics

01

2½ Hours

300

General Ability Test

02

2½ Hours

600

SSB Test/Interview:

900

Syllabus of The Examination

PaperI 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. 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 viceversa.
Arithmetic, Geometric and Harmonic progressions. Quadratic equations with
real coefficients. Solution of linear inequations 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, ApplicationsSolution 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. Trigonometrical
ratios. Trigonometric identities Sum and difference formulae. Multiple and
Submultiple angles. Inverse trigonometric functions. ApplicationsHeight and
distance, properties of triangles.

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.

PaperII General Ability Test

Part ‘A’—English

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

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 Nonconductors,
Ohm’s 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, 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 GunPowder. Elementary ideas about the structure of Atom,
Atomic Equivalent and Molecular Weights, Valency.

Section ‘C’ (General Science)

Difference between the living and nonliving. 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.

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 Anticyclones; 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% weightages respectively.

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