NDA 2019 Syllabus

NDA Syllabus - Paper 1 (Mathematics)

Algebra:

- Quadratic 17 equations with real coefficients
- Solution of linear inequalities by graphs
- Permutations and Combinations
- The concept of sets, operations on sets, Venn diagrams.
- De Morgan laws, Cartesian product, relation, equivalence relation.
- Representation of real numbers on a line
- Complex numbers — modulus, argument, basic properties, cube roots of unity
- Binary system of numbers
- Conversion of decimal system to binary system and vice-versa
- Arithmetic, Geometric and Harmonic Progressions
- Binomial theorem and its applications
- Logarithms and their applications

- Types of matrices
- Operations on matrices
- Determinant of a matrix, basic properties of determinants
- Inverse and adjoint 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

- Trigonometric ratios
- Trigonometric identities Sum and difference formulae
- Angles and their measures in radians and degrees
- Applications-distance and Height, properties of triangles
- Multiple and Submultiple angles
- Inverse trigonometric functions

- Equation of a line in various forms
- Rectangular Cartesian Coordinate system
- Distance formula
- Angle between two lines
- Angle between two planes
- Direction Cosines and direction ratios
- Equation of a plane and a line in various forms
- 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
- Equation of a sphere
- Angle between two lines
- Point in a three-dimensional space, distance between two points
- Direction Cosines and direction ratios
- Equation two points

- The concept of a real-valued function–range, domain, and graph of a function
- Derivative of function at a point, geometrical and physical interpretation of a derivative—applications
- Second order derivatives
- Increasing and decreasing functions
- Application of derivatives in problems of maxima and minima
- Composite functions, one to one, onto and inverse functions
- The notion of limit, Standard limits—examples
- Continuity of functions—examples, algebraic operations on continuous functions
- Derivatives of sum, product, and quotient of functions, derivative of a function with respect to another function, derivative of a composite function

- 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
- Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions
- Application in problems of growth and decay
- General and particular solution of differential equations, solution of first order and first degree differential equations of various types—examples

- Addition of vectors, Unit and null vectors, scalar multiplication of a vector, scalar product or dot product of two vectors
- Vectors in three and two magnitude , dimensions, and direction of a vector
- Cross product or Vector product of two vectors
- Applications—work done by a force and moment of a force and in geometrical problems

- Measures of Central tendency—Mean, median and mode
- Variance and standard deviation—determination and comparison
- Correlation and regression
- 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
- Probability: Random experiment, outcomes, and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events
- Statistics: Classification of data, Frequency distribution, cumulative frequency distribution—examples
- Graphical representation—Histogram, Pie Chart, frequency polygon—examples
- Complementary, elementary and composite events
- Binomial distribution, examples of random experiments giving rise to Binomial distribution

- General Knowledge question paper will hold subjects - Chemistry, General Science, Social Studies, Geography, Physics, and Current Events.
- The syllabus provided below is just 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.

- States of Matter and physical properties, Density, and Specific Gravity, Principle of Archimedes,Mass, Weight, Volume, Pressure Barometer
- The motion of objects, Force and Momentum, Parallelogram of Forces, Stability and Equilibrium of bodies, Velocity and Acceleration, Newton’s Laws of Motion, Gravitation, elementary ideas of work, Power and Energy
- Measurement of Temperature and Heat, Effects of Heat, change of State and Latent Heat, Modes of transference of Heat
- Sound waves and their properties, Simple musical instruments
- Reflection,Rectilinear Propagation of Light,and refraction.Human Eye Spherical Mirrors and Lenses.
- Artificial and natural Magnets, Properties of a Magnet, Earth as a Magnet
- Static and Current Electricity, conductors and Non-conductors, Ohm’s Law, Measurement of Electrical Power, Primary and Secondary Cells, Use of X-Rays,Simple Electrical Circuits, Heating, Lighting and Magnetic effects of Current.
- General Principles in the working of the following: Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Simple Pendulum, Simple Pulleys, Siphon, Balloon, Levers, Pumps,Telegraphs, Periscope, Telephone, Telescope, Microscope, Mariner’s Compass,Lightning Conductors, Safety Fuses.

- Physical and Chemical changes. Mixtures, Elements and Compounds, Formulae, Symbols, and simple Chemical Equations, Law of Chemical Combination
- Properties of Air and Water. Properties and preparation of Oxygen, Nitrogen, Hydrogen, and Carbon dioxide, Reduction and Oxidation, Acids, bases, and salts.
- Carbon— different forms
- Fertilizers—Natural and Artificial
- The material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and Gunpowder
- Elementary ideas about the Atomic Equivalent, Structure of Atom, and Molecular Weights, Valency.

- Difference between the living and nonliving
- The 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

- Indian History - Survey, providing emphasis on Culture and Civilisation
- Freedom Movement in India
- Elementary study of Indian Constitution and Administration
- Knowledge of Five Year Plans of India. Panchayati Raj, Co-operatives, and Community Development
- National Integration,Bhoodan, Sarvodaya, and Welfare State, Basic Teachings of Mahatma Gandhi
- Modern world shaping ; Renaissance, Exploration, and Discovery; War of American Independence
- Industrial Revolution, French Revolution, and the Russian Revolution. Impact of Science and Technology on Society
- Concept of one World, Panchsheel, Democracy, United Nations, Socialism, and Communism
- Role of India in the present world

- 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 with their classification; Weathering—Chemical and Mechanical, Earthquakes and Volcanoes
- Regional Geography of India—Climate, Natural vegetation
- Power and Mineral Resources: distribution and location of Industrial and agricultural activities
- Important main sea and Sea ports , land, and air routes of India
- Main items of Imports and Exports of India
- Ocean Currents and Tides; Atmosphere and its composition; Pressure, Planetary Winds, Cyclones, and Anticyclones; Humidity; Condensation and Precipitation; Temperature and Atmospheric Types of Climate, Major Natural Regions of the World’

- Deep information of all the Important events happened in India in few recent years
- Current important world events
- Prominent personalities—including both Indian and International, those connected with cultural activities and sports.

Those candidates who qualify stage I will only be permitted to appear for Stage II. The details are as follows:

- Part I comprises of Officer Intelligence Rating (OIR) tests and the Picture Perception & Description Test (PP & DT). The candidates will be shortlisted based on the combination of their performance in their OIR Test and their PP & DT.
- Part II Comprises of the Interview session, Group Testing Officer Tasks, Psychology Tests and the last is Conference. These tests are organized over a duration of 4 days.

- The personality of a candidate is assessed by 3 different assessors viz. The IO knew as Interviewing Officer, GTO known as - Group Testing Officer and the Psychologist.
- There is no separate preference for any of the tests. The marks are allotted by the assessors only after taking into consideration the applicant's performance of the candidate holistically in all their tests.
- Marks for the conference are also allotted based on the initial performance of the candidate in the 3 techniques and decision of the Board. All the tests have equal preference.

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