UPSC NDA and NA Syllabus 2020


UPSC NDA and NA Syllabus 2020

SYLLABUS OF THE EXAMINATION 

PAPER-I 
MATHEMATICS 
(Code No. 01) 
(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. 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 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, 
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. Trigonometrical 
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 
(Code No. 02) 
(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 
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. 
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. 
Intelligence and Personality Test 
 The SSB procedure consists of two stage Selection process – stage I and 
stage II. Only those candidates who clear the stage I are permitted to appear 
for stage II. The details are : 
(a) Stage I comprises of Officer Intelligence Rating (OIR) tests are Picture 
Perception * Description Test (PP&DT). The candidates will be shortlisted 
based on combination of performance in OIR Test and PP&DT.
(b) Stage II Comprises of Interview, Group Testing Officer Tasks, Psychology 
Tests and the Conference. These tests are conducted over 4 days. The details 
of these tests are given on the website joinindianarmy.nic.in
 The personality of a candidate is assessed by three different assessors 
viz. The Interviewing Officer (IO), Group Testing Officer (GTO) and the 
Psychologist. There are no separate weightage for each test. The mks are 
allotted by assessors only after taking into consideration the performance of 
the candidate holistically in all the test. In addition, marks for Conference are 
also allotted based on the initial performance of the Candidate in the three 
techniques and decision of the Board. All these have equal weightage. 
 The various tests of IO, GTO and Psych are designed to bring out the 
presence/absence of Officer Like Qualities and their trainability in a 
candidate. Accordingly candidates are Recommended or Not Recommended 
at the SSB.




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