NDA Syllabus 2020 - Check Section Wise Syllabus

Algebra

• Sets and 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 in equations of two variables by graphs.
• Permutation and Combination. Binomial theorem and its applications.
• Logarithms and their applications.

Matrices And Determinants

• Types of matrices, operations on matrices.
• Determinant
• Basic Properties
• Adjoint and inverse of a square matrix,
• Applications- Solution of a system of linear equations in two or three unknowns

Trigonometry

• 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.

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 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.

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 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 to another function, derivative of a composite function.
• Second order derivatives.
• Increasing and decreasing functions.
• Application of derivatives in problems of maxima and minima.

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 equations, solution of first order and first-degree differential
• equations of various types—examples.
• Application in problems of growth and decay.

Vector Algebra

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

Statistics And Probability

• Statistics
• Graphical representation
• Measures of Central tendency—Mean, median and mode.
• Variance and standard deviation
• 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.

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 Non-conductors,

Ohm’s Law, Simple Electrical Circuits, Heating, Lighting and Magnetic effects of Current, Measurement of Electrical Power, Primary and Secondary Cells, Use of X-Rays.

General Principles in the working of the following:

Simple Pendulum, Simple Pulleys, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Mariner’s Compass, Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Lightening Conductors, Safety Fuses.

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.

Material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches and Gun-Powder.

Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon dioxide, Oxidation and Reduction. Acids, bases and salts.

Carbon— different forms.

Fertilizers— Natural and Artificial.

Elementary ideas about the structure of Atom, Atomic Equivalent and Molecular Weights, Valency.

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.

Subject

Code

Duration

Maximum Marks

Mathematics

01

2½ hours

300

General Ability Test

02

2½ hours

600

Total

900

SSB Test/Interview

900