(Syllabus) National Defence Academy & Naval Academy Examination
1. The subjects of the written examination, the time allowed and the maximum
marks allotted to each subject will be as follows :—
|General Ability Test
|SSB Test/Interview :
2. THE PAPERS IN ALL THE SUBJECTS WILL CONSIST OF OBJECTIVE
TYPE QUESTIONS ONLY. THE QUESTION PAPERS (TEST BOOKLETS) OF MATHEMATICS AND PART
“B” OF GENERAL ABILITY TEST WILL BE SET BILINGUALLY IN HINDI AS WELL AS ENGLISH.
3. In the question papers, wherever necessary, questions involving the metric
system of Weights and Measures only will be set.
4. Candidates must write the papers in their own hand. In no circumstances
will they be allowed the help of a scribe to write answers for them.
5. The Commission have discretion to fix qualifying marks in any or all the
subjects at the examination.
6. The candidates are not permitted to use calculator or Mathematical or
logarithmic table for answering objective type papers (Test Booklets). They
should not therefore, bring the same inside the Examination Hall.
:: Detailed Syllabus ::
MATHEMATICS (Code No. 01) (Maximum Marks-300)
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—
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
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
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
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.
Fertilizers—Natural and Artificia
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
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
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
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.