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 NDA & NA Paper I MATHEMATICS Syllabus (Maximum marks  300)
NDA Syllabus Overview for Paper 1

Total Marks

300 Marks

Total No. of Questions

120

Correct Answer

2.5 marks

Marks deducted for the wrong answer

0.83

Total duration of Mathematics Paper

2 Hours 30 Minutes

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 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 Cramers 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 threedimensional 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 interpretation 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 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.
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NDA & NA Paper I GENERAL ABILITY TEST Syllabus (Maximum marks  600)
Part A – NDA ENGLISH Syllabus (Maximum marks  200)
The NDA question paper in English will be designed to test the candidates 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 – NDA GENERAL KNOWLEDGE Syllabus (Maximum marks  400)
 The NDA question paper on General Knowledge will broadly cover the subjects: Physics, Chemistry, General Science, Social Studies, Geography and Current Events.
 The NDA 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. Candidates 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, Ohms 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, Mariners 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 Carbon dioxide, 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, Protoplasm’s 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. Latitudes 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.
#Important
Out of the maximum marks assigned to PartB of this NDA paper. Questions on Section A, B, C, D, E, and F will carry approximately 25%, 15%, 10%, 20%, 20%, and 10% weightages respectively.
NDA & NA Intelligence and personality tests
The SSB procedure consists of two stage selection process: Stage 1, and Stage 2. Only those candidates who clear the stage 1 are permitted to appear for Stage2. The details are:
 Stage 1 consists Officer Intelligence Rating (OIR) tests that are Picture Presentation* Description Test (PP&DT). The candidates will be shortlisted based on combination of performance in OIR and PP&DT.
 Stage 2 consists of Interview, Group Testing Officer Tasks, Psychology Tests and Conference. These tests are conducted over 4 days.