SYLLABUS
OF THE EXAMINATION
PAPER I
MATHEMATICS (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 (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.
