NDA Syllabus 2021 - Check Section Wise Syllabus & Exam Pattern

Subjects

Topics

Differential Calculus

• Concept of a real valued function–domain, range and graph of a function.

• Increasing and decreasing 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.

• Continuity of functions—examples, algebraic operations on continuous functions.

• Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits - examples.

• Second order derivatives.

• Application of derivatives in problems of maxima and minima.

Statistics and Probability

• Statistics

• Variance and standard deviation

• Union and Intersection of events.

• Conditional probability, Bayes’ theorem - simple problems.

• Complementary, elementary and composite events.

• Probability: Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events.

• Random variable as function on a sample space.

• Graphical representation

• Measures of Central tendency - Mean, median and mode.

• Binomial distribution, examples of random experiments giving rise to Binomial distribution.

• Definition of probability - classical and statistical - examples. Elementary theorems on probability - simple problems.

Vector Algebra

• Vector product or cross product of two vectors.

• Applications—work done by a force and moment of a force and in geometrical problems.

• Addition of vectors, scalar multiplication of a vector

• Vectors in two and three dimensions,

• Unit and null vectors

• Scalar product or dot product of two vectors.

Analytical Geometry Of Two And Three Dimensions

• Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola.

• Equation of a sphere.

• Angle between two lines.

• Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms.

• Distance of a point from a line.

• Equation two points.

• Equation of a plane and a line in various forms.

• dimensional space, distance between two points.

• Direction Cosines and direction ratios.

• Angle between two lines and angle between two planes.

• Eccentricity and axis of a conic. Point in a three

Trigonometry

• Angles and their measures in degrees and in radians. Trigonometric ratios.

• Inverse trigonometric functions.

• Applications-Height and distance, properties of triangles.

• Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles.

Matrices And Determinants

• Basic Properties

• Adjoint and inverse of a square matrix,

• Applications- Solution of a system of linear equations in two or three unknowns

• Determinant

• Types of matrices, operations on matrices.

Algebra

• Sets and Venn diagrams.

• Representation of real numbers on a line.

• Arithmetic, Geometric and Harmonic progressions.

• De Morgan laws, Cartesian product, relation, equivalence relation.

• Complex numbers—basic

• properties, modulus, argument, cube roots of unity. Binary system of numbers.

• Conversion of a number in the decimal system to binary system and vice-versa.

• Logarithms and their applications.

• Quadratic equations with

• real coefficients. Solution of linear in equations of two variables by graphs.

• Permutation and Combination. Binomial theorem and its applications.

Integral Calculus And Differential Equations

• General and particular solution of differential equations, solution of first order and first-degree differential equations of various types - examples

• Application in problems of growth and decay.

• Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions.

• Definition of order and degree of a differential equation, formation of a differential equation by examples.

• Evaluation of definite integrals— determination of areas of plane regions bounded by curves—applications.

Subjects

Topics

English language

• Comprehension

• Fill in the blanks

• Complete the sentences

• Idioms and phrases

• Synonym and antonym

• Active and passive voice

• Finding errors

History

• Indian history: Culture and civilization

• Bhoodan, Sarvodaya, National Integration and Welfare State, Basic Teachings of Mahatma Gandhi

• India freedom struggle

• Panchayati Raj, Co-operatives and Community Development

• 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

• Forces shaping the modern world; Renaissance, Exploration and Discovery

Geography

• Landforms of india

• Movements of Earth and their effects.

• Layers of earth

• Type of soils

• Climate and Atmosphere

• Rivers

• Cyclones and Anticyclones

• Solar system and universe

• Rocks and their classification;

Physics

• Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet.

• Spherical mirrors and Lenses, Human Eye.

• Density and Specific Gravity, Principle of Archimedes, Pressure Barometer.

• Rectilinear propagation of Light, Reflection and refraction.

• Static and Current Electricity, conductors and Non-conductors,

• Physical Properties and States of Matter, Mass, Weight, Volume,

• Heat, Measurement of Temperature and Heat, change of State and Latent Heat, Modes of transference of Heat

• 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.

• Equilibrium of objects

• Laws of motion

• Gravitation

• Work, power and energy

Chemistry

• Elements, Mixtures and Compounds, Symbols, Formulae and simple Chemical Equations, Law of Chemical Combination

• Properties of Air and Water

• Fertilizers— Natural and Artificial

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

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

• Preparation and Properties of Hydrogen

General Science

• Biotic and abiotic components

• Growth and Reproduction in Plants and Animals.

• Achievements of Eminent Scientists.

• Common Epidemics, their causes and prevention.

• Basis of Life—Cells, Protoplasms and Tissues.

Papers

Subject

No. of Questions

Maximum marks

Duration

Paper 1

Mathematics

120

300

2 hours 30 minutes

Paper 2

GAT

150

600

2 hours 30 minutes

Total

270

900

5 hours