NDA 2023 Syllabus and Exam Pattern

Exam

Section

Questions

Marks 

Time Allotted

Paper I

Mathematics

120

300

2.5 hrs

Paper-II

General Ability Test

150

600

2.5 hrs

Sections of General Ability Test

Weightage

English

200 Marks

Physics

100 Marks

Chemistry

60 Marks

General Science

40 Marks

History

80 Marks

Geography

80 Marks

Current Affairs

40 Marks

Mathematics

Topic-wise syllabus (Maximum Marks: 300)

Algebra

Concept of set, Venn diagram, operations on sets. De Morgan laws, relation, Cartesian product, equivalence relation. Representation of real numbers on a line. Complex numbers—basic properties, argument, modulus, cube roots of unity. Conversion of a number in decimal system to the binary system & vice-versa. Binary system of numbers. Arithmetic, Geometric & Harmonic progressions. Quadratic equations with real coefficients. Binomial theorem and its applications. Permutation & Combination. Logarithms & their applications. Solution of a linear inequations of the two variables by graphs.

Matrices & Determinants

Determinant of a matrix, Types of matrices, operations on the matrices. basic properties of the determinants. Adjoint & inverse 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.

Trigonometry

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

Analytical Geometry of Two & Three  Dimensions

Rectangular Cartesian Coordinate system. Equation of a line in various forms. Distance formula. Angle between the two lines. The distance of a point from a line. Standard forms of parabola, ellipse & hyperbola. Equation of a circle in standard as well as in general form. Direction Cosines & direction ratios. Eccentricity and axis of a conic. Direction Cosines & direction ratios. Equation two points. Equation of a sphere. Equation of a plane and a line in many forms. Point in the three-dimensional space, distance between the two points. The angle between the two lines and angle between two planes.

Differential Calculus

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

Integral Calculus & Differential Equations

Integration as inverse of differentiation, integration by the substitution as well as by parts, standard integrals involving algebraic expressions, trigonometric, exponential & hyperbolic functions. Definition of order & degree of a differential equation, formation of a differential equation by examples. Evaluation of the definite integrals includes determination of areas of plane regions bounded by the curves—applications. General and particular solution of a differential equations, solution of first order and first degree differential equations of many types—examples. Application in the problems of growth & decay.

Vector Algebra

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

Statistics & Probability

Statistics: Frequency distribution, Classification of data, cumulative frequency distribution—examples. Graphical representation—Histogram, Pie Chart, frequency polygon—examples. Correlation & regression. Measures of Central tendency—Mean, median and mode. Variance and standard deviation—determination & comparison.

Probability: Outcomes and associated sample space, Random experiment, events, mutually exclusive and exhaustive events, impossible and certain events. Complementary, elementary and composite events. Definition of probability—classical and statistical—examples. Elementary theorems on probability—simple problems. Binomial distribution, examples of random experiments giving rise to Binominal distribution.’ Union and Intersection of events. Conditional probability, Bayes’ theorem—simple problems. Random variable as function on a sample space.

General Studies

Topic-wise syllabus (Maximum Marks: 400)

Physics

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

Chemistry

Physical & Chemical changes. Properties of Air and Water. Properties and preparations of Hydrogen, Nitrogen & Carbon dioxide, Oxygen, Oxidation and Reduction. Elements, Mixtures & Compounds, Symbols, Formulae & simple Chemical Equations, Law of Chemical Combination (excluding the problems). Acids, bases and salts. Carbon— different forms. Material used in the preparation of substances such as Soap, Glass, Ink, Cement, Paper, Paints, Safety Matches and Gun-Powder. Fertilizers—Natural as well as Artificial. Elementary ideas about the structure of Atom, Valency, Atomic Equivalent & Molecular Weights.

General Science

Difference between the living & non-living. Basis of Life—Cells, Tissues & Protoplasm. Growth and Reproduction in Plants & Animals. Common Epidemics, their causes and prevention. Food—Source of Energy for the man. Elementary knowledge of the Human Body and its important organs. The Solar System—Meteors and Comets, Eclipses. Constituents of food, Balanced Diet. Achievements of Eminent Scientists.

History

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

Geography

The Earth, its shape and size. Latitudes & Longitudes, Concept of time. Origin of Earth. International Date Line. Movements of the Earth & their effects. Rocks and their classification; Weathering—Mechanical & Chemical, Earthquakes & Volcanoes. Mineral & Power resources; location & distribution of agricultural & Industrial activities. Regional Geography of India—Climate, Natural vegetation. Temperature as well as Atmospheric Pressure, Ocean Currents & Tides Atmosphere & its composition; Humidity; Cyclones & Anti-cyclones, Planetary Winds; Condensation and Precipitation; Types of Climate, Major Natural regions of the World. Important Sea ports & main sea, land and air routes of India. Main items of the Imports and Exports of India.

Current Affairs

Knowledge of essential events that have happened in India in recent years. Prominent personalities—both the Indian and International including those connected with cultural activities and sports. Current important world events.