NDA-2 2023 - Subject Wise Weightage, Exam Pattern & Syllabus

                       Chapter Wise Weightage in Maths Paper in the NDA Exam

                 Algebra and Vector Algebra

                                   40%

                             Trigonometry

                                   20%

                  Determinants and Matrices

                                   10%

                    Statistics and Probability

                                   10%

                       Analytical Geometry

                                    20%

             Differential and Integral Calculus

                                    20%

                  English Topics

                                      Weightage

                   Spotting Errors

                                          3.33%

                   Comprehension

                                             4%

                   Selecting Words

                                          6.66%

         Ordering of Words in a Sentence

                                             6%

                Sentence Improvement

                                          6.66%

                          Antonyms

                                          3.33%

                         Synonyms

                                          3.33%

          General Studies Topics

                        Chapter Wise Weightage

                     Physics

                                      15.33%

                   Chemistry

                                      10.66%

               General Science

                                       7.33%

       History & Freedom Movement

                                      10.66%

                    Geography

                                       11.33%

                 Current Events

                                       11.33%

                                                         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 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, the 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 solutions of differential equations, solutions 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 the direction of a 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. 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, 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 Atoms, 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.