NDA-2 2023 Exam Syllabus and Exam Pattern

                                                           NDA Written Exam Pattern

                        Particulars

                                    Details

Papers

• Mathematics
• GAT(General Aptitude Test)

Total Questions

• Mathematics- 120
• GAT-150

Total Marks

• Mathematics- 300
• GAT- 600
• Total- 900

Time Duration

• Mathematics- 2.5 Hours or 150 Minutes
• GAT- 2.5 Hours or 150 Minutes

SSB Interview

• 900 Marks

                                                       NDA Mathematics Syllabus

                       Sections

                           Syllabus

ALGEBRA

Concept of set, operations on sets, 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 a decimal system to a binary system and vice-versa. Arithmetic,

Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequalities 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 of a

matrix, basic properties of determinants. Adjoint and 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 and in radians.

Trigonometric 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. The angle between two lines.

Distance of a point from a line. Equation of a circle in standard

and in a general form. Standard forms of parabola, ellipse, and

hyperbola. Eccentricity and axis of a conic. Point in a three-dimensional space, the 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.

The angle between two lines and the 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. The 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, a derivative of

a function with respect to another function, a 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. A general and particular solution of differential equations, solution of the 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, magnitude, and

direction of vector. Unit and null vectors, the 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: Classification of data, Frequency distribution,

cumulative frequency distribution—examples. Graphical

representation—Histogram, Pie Chart, frequency polygon—

examples. Measures of Central tendency—Mean, median, and

mode. Variance and standard deviation—determination and

comparison. Correlation and regression.

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 Binomial distribution.

                                        NDA General Ability Test Paper Syllabus

                        Parts

                            Sections

Part (A)- English

Grammar & usage, Comprehension & cohesion, Spotting of errors, Para Jumbling, Fill in the blanks, Synonyms & Antonyms, Vocabulary, Cloze Test, Idioms & Proverbs, Completion of Sentence & Para, Sentence Correction & Improvement.

Part (B)- General Knowledge

Physics

Physical Properties and States of Matter, Mass, Weight, Volume, Density, and Specific Gravity, Principle of Archimedes,

Pressure Barometer. The 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 Nonconductors, Ohm’s Law, Simple Electrical Circuits, Heating,

Lighting and Magnetic effects of Current, Measurement of Electrical Power, Primary and Secondary Cells, and Use of X-Rays.General Principles in the working of the following: Simple Pendulum, Simple Pulleys, Siphon, Levers,

Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask,

Gramophone, Telegraphs, Telephone, Periscope, Telescope,

Microscope, Mariner’s Compass; Lightning Conductors, Safety

Fuses.

Chemistry

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.Preparation and Properties of Hydrogen, Oxygen, Nitrogen, and Carbon Dioxide, Oxidation, and Reduction. 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 Gun-Powder. Elementary ideas about the structure of Atom, Atomic

Equivalent and Molecular Weights, and Valency.

Biology

Difference between the living and nonliving. Basis of Life—Cells,

Protoplasms and Tissues. Growth and Reproduction in Plants and

Animals.Elementary knowledge of the 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.

History

A broad survey of Indian History, with emphasis on Culture and

Civilization.Freedom Movement in India. Elementary study of Indian

Constitution and Administration. Elementary knowledge of Five

Year Plans of India. Panchayati Raj, Co-operatives, and Community

Development. Bhoodan, Sarvodaya, National Integration and

Welfare State, Basic Teachings of Mahatma Gandhi.Forces shaping the modern world; Renaissance, Exploration, and Discovery; War of American Independence. 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. Role of India in the present world.

Geography

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

Current Affairs

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