

National Defence Academy Exam : NDA 


PaperI Mathematics (Code No. 01) (Maximum Marks  300) 


1. Algebra:
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 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
application. Logarithms and their applications.
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.
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. 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.
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 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. Appln 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
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 vector, scalar
product or dot product of twovectors. Vector product and cross product of two
vectors. Applicationswork 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. 





General Ability Test 


Paper  I General Ability Test (Code No. 02)(Maximum Marks600) 


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 Marks400) :
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 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, 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 appoximately 25%, 15%, 10%, 20%, 20%
and 10% weightages respectively. 





