NDA 2020 Free Test Series Online

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NDA Syllabus

Paper-1 : Mathematics

Algebra

1. relation, Logarithms and their applications.
2. equivalence relation.
3. Representation of real numbers on a line.
4. Complex numbers—basic properties,
5. modulus, argument, Binomial theorem and its applications
6. cube roots of unity.
7. Solution of linear inequations of two variables by graphs.
8. Binary system of numbers.
9. Conversion of a number in decimal system to binary system and

vice-versa.

1. Arithmetic, Permutation and Combination.
2. Geometric and Harmonic progressions.
3. Quadratic equations with real coefficients.
4. Solution of linear inequations of two variables by graphs.

Matrices and Determinants

1. Types of matrices, Adjoint and inverse of a square matrix,
2. operations on matrices.basic properties of determinants.
3. Determinant of a matrix,
4. Applications-Solution of a system of linear equations in two or three

unknowns by Cramer’s rule and by Matrix Method.

Trigonometry

1. Angles and their measures in degrees and in radians.
2. Trigonometrical ratios.
3. Trigonometric identities Sum and difference formulae.
4. Multiple and Sub-multiple angles.
5. Inverse trigonometric functions.
6. Applications-Height and distance,
7. properties of triangles.

Analytical Geometry of Two and Three Dimensions

1. Rectangular Cartesian Coordinate system.
2. Distance formula.Direction Cosines and direction ratios.
3. Equation of a line in various forms.
4. Angle between two lines.
5. Distance of a point from a line.
6. Equation of a circle in standard and in general form.
7. Standard forms of parabola,Equation of a sphere.
8. ellipse and hyperbola.Equation two points.
9. Eccentricity and axis of a conic.
10. Point in a three dimensional space,
11. distance between two points.
12. Direction Cosines and direction ratios.
13. Equation of a plane and a line in various forms.
14. Angle between two lines and angle between two planes.

Differential Calculus

1. Concept of a real valued function–domain,
2. range and graph of a function.
3. Composite functions, Derivatives of sum,
4. one to one, Increasing and decreasing functions.
5. onto and inverse functions.
6. Notion of limit, Second order derivatives.
7. Standard limits—examples.
8. Continuity of functions - examples,
9. algebraic operations on continuous functions.
10. Derivative of function at a point,
11. geometrical and physical interpretation of a derivative-application.
12. derivative of a function with respect to another function,
13. product and quotient of functions,
14. derivative of a composite function.
15. Application of derivatives in problems of maxima and minima

Integral Calculus and Differential Equations

1. Integration as inverse of differentiation,
2. integration by substitution and by parts,
3. standard integrals involving algebraic expressions,
4. trigonometric, Application in problems of growth and decay.
5. exponential and hyperbolic functions.
6. Evaluation of definite integrals—determination of areas of plane regions

bounded by curves—applications.

1. Definition of order and degree of a differential equation,
2. formation of a differential equation by examples.
3. General and particular solution of a differential equations,
4. solution of first order and first degree differential equations

of various types—examples.

Victor Algebra

1. Vectors in two and three dimensions,
2. magnitude and direction of a vector.
3. Unit and null vectors, addition of vectors,
4. Applications—work done by a force and moment of a force and in

geometrical problems.

1. scalar multiplication of a vector,
2. scalar product or dot product of two vectors.
3. Vector product or cross product of two vectors.

Statistics and Probability

1. Statistics: Classification of data,
2. Frequency distribution, Conditional probability,
3. cumulative frequency distribution - examples.
4. Graphical representation - Histogram,
5. Pie Chart, frequency polygon—examples. Measures of Central tendency—

Mean, median and mode.

1. Variance and standard deviation determination and comparison.
2. Correlation and regression.Probability: Random experiment,
3. outcomes and associated sample space, events,
4. mutually exclusive and exhaustive events, impossible and certain events.
5. Union and Intersection of events. Complementary,
6. elementary and composite events. Definition of probability—classical

and statistical—examples.

12 .Elementary theorems on probability—simple problems.

13 .Bayes’ theorem—simple problems. Random variable as

function on a sample space.

14 .Binomial distribution,

1. examples of random experiments giving rise to Binominal distribution.

Paper-2 : General Ability Test

English

Grammar and usage, vocabulary, comprehension

General Knowledge

Physics

1. Physical Properties and States of Matter,
2. Mass, Weight, Volume,
3. Density and Specific Gravity, Principle of Archimedes,
4. Pressure Barometer. Motion of objects,
5. Velocity and Acceleration, Newton’s Laws of Motion,
6. Force and Momentum, Parallelogram of Forces,
7. Stability and Equilibrium of bodies, Gravitation,
8. elementary ideas of work, Power and Energy.
9. Effects of Heat, Measurement of Temperature and Heat,
10. change of State and Latent Heat, Modes of transference of Heat.
11. Sound waves and their properties, Simple musical instruments.
12. Rectilinear propagation of Light, Reflection and refraction.
13. Spherical mirrors and Lenses, Human Eye.
14. Natural and Artificial Magnets, Properties of a Magnet,
15. Earth as a Magnet.Static and Current Electricity,
16. conductors and Non-conductors,Ohm’s Law,
17. Simple Electrical Circuits, Heating,
18. Lighting and Magnetic effects of Current,
19. Measurement of Electrical Power,
20. Primary and Secondary Cells, Use of X-Rays.
21. General Principles in the working of the following:
22. Simple Pendulum, Simple Pulleys, Siphon,
23. Levers, Balloon,Pumps, Hydrometer,
24. Pressure Cooker, Thermos Flask, Gramophone,
25. Telegraphs, Telephone, Periscope, Telescope,
26. Microscope, Mariner’s Compass;
27. Lightening Conductors, Safety Fuses

Chemistry

1. Physical and Chemical changes.
2. Elements, Carbon - different forms.
3. Mixtures and Compounds,
4. Symbols, Fertilizers—Natural and Artificial.
5. Formulae and simple Chemical Equations,
6. Law of Chemical Combination (excluding problems).
7. Properties of Air and Water.
8. Preparation and Properties of Hydrogen,
9. Oxygen,Glass, Ink, Paper, Cement,
10. Nitrogen and Carbondioxide,
11. Oxidation and Reduction.
12. Acids, bases and salts.
13. Material used in the preparation of substances like Soap,
14. Paints, Safety Matches and Gun-Powder.
15. Elementary ideas about the structure of Atom,

Atomic Equivalent and Molecular Weights, Valency.

General Science

1. Difference between the living and non-living. Basis of Life—Cells,
2. Protoplasms and Tissues. Growth and Reproduction in

Plants and Animals.

1. Elementary knowledge of Human Body and its important organs.
2. Common Epidemics, their causes and prevention.
3. Food—Source of Energy for man. Constituents of food,
4. Balanced Diet. The Solar System—Meteors and Comets,
5. Eclipses. Achievements of Eminent Scientists.

History Freedom Movement

A broad survey of Indian History, with emphasis on

Culture and Civilisation.

Freedom Movement in India. Elementary study of Indian

Constitution and Administration.

1. Elementary knowledge of Five Year Plans of India.
2. Panchayati Raj, Co-operatives and Community Development.
3. Bhoodan, Sarvodaya, National Integration and Welfare State,
4. Basic Teachings of Mahatma Gandhi.Exploration and Discovery;
5. Forces shaping the modern world; Renaissance,
6. War of American Independence. French Revolution,
7. Industrial Revolution and Russian Revolution.
8. Impact of Science and Technology on Society.
9. Concept of one World, United Nations, Panchsheel,
10. Democracy, Socialism and Communism. Role of

India in the present world.

Geography

1. The Earth, its shape and size. Lattitudes and Longitudes,
2. Concept of time. International Date Line. .
3. Origin of Earth. Rocks and their classification;
4. Weathering-Mechanical and Chemical,
5. Earthquakes and Volcanoes.Movements of Earth and their effects.
6. Ocean Currents and Tides Atmosphere and its composition;
7. Temperature and Atmospheric Pressure,
8. Planetary Winds, Cyclones and Anti-cyclones;
9. Humidity; Condensation and Precipitation;
10. Types of Climate, Major Natural regions of the World.
11. Regional Geography of India—Climate, Natural vegetation.
12. Mineral and Power resources;
13. location and distribution of agricultural and Industrial activities.
14. Important Sea ports and main sea,
15. land and air routes of India. Main items of Imports and Exports of India.

Current Events

Knowledge of Important events that have happened in

India in the recent years.

1. Current important world events.
2. Prominent personalities—both Indian and International including

those connected with cultural activities and sports.

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