National Defence Academy & Naval
Academy Examination (I), 2012
Scheme of Examination
The subjects of the written examination, the time allowed and the maximum
marks allotted to each subject will be as follows: (Total: 900)
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 TESTS 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
logirithmic table for answering objective type papers (Test Booklets). They
should not therefore, bring the same inside the Examination Hall.
B. Syllabus of the Examination
Paper-I Mathematics (Code No. 01)
(Maximum Marks - 300)
1Algebra : Concept of a 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 application. Logarithms and their
2.Matrices and Determinants:
Types of matrices, operations on matrices Determinant of a matrix, basic
properties of determinant. 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.
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 of a plane and a line in various forms.
Angle between two lines and angle between two planes. Equation of a sphere.
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 a function at a point,
geometrical and physical interpreatation of a derivative - applications.
Derivatives of sum, product and quotient of functions, derivative of a function
with respect of 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 equation, solution of first order and first degree differential
equations of various types - examples. Application in problems of growth and
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 vector,
scalar product or dot product of two-vectors. Vector product and cross product
of two vectors. Applications-work done by a force and moment of a force, and in
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)
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
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 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
- 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
- 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
- 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
- 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 appoximately
25%, 15%, 10%, 20%, 20% and 10% weightages 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 calibre 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.