National Defence Academy (NDA) Exam Syllabus and Pattern

Introduction to NDA Exam

The National Defence Academy (NDA) examination is conducted by the Union Public Service Commission (UPSC) twice a year. It is a gateway for aspiring candidates who wish to join the Indian Army, Navy, and Air Force. The exam recruits candidates to the prestigious NDA for training before they are commissioned into the armed forces. Successful candidates undergo a rigorous training program at the National Defence Academy in Khadakwasla, Pune.

NDA Exam Pattern

The NDA examination consists of two papers: Mathematics and General Ability Test (GAT). Both papers are conducted on the same day in two sessions. The exam follows an objective-type format with multiple-choice questions.

Paper	Subject	Duration	Maximum Marks
Paper I	Mathematics	2 Hours	300
Paper II	General Ability Test	2 Hours	600

Marking Scheme

For each correct answer, candidates will be awarded marks, while for each wrong answer, one-third of the marks assigned to that question will be deducted as negative marking. No marks will be deducted for unattempted questions.

NDA Mathematics Syllabus (Paper I)

The Mathematics paper tests the candidate's mathematical skills and understanding. The syllabus covers various topics from class 11th and 12th mathematics curriculum.

Key Topics in Mathematics 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, Binary number system, Conversion between binary and decimal, Arithmetic, Geometric and Harmonic progressions, Quadratic equations, Linear inequations, 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 radians, Trigonometric ratios, Trigonometric identities, Sum and difference formulae, Multiple and Sub-multiple angles, Inverse trigonometric functions, Applications - Height and distance.
• 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 general form, Standard forms of parabola, ellipse and hyperbola, Eccentricity and axis of conic. Point in a three-dimensional space, Distance between 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, Derivative of function at a point, 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, Definite integrals, Evaluation of definite integrals determining areas of the regions bounded by curves, General and particular solution of a differential equation, Solution of first order and first degree differential equations of various types, Application in problems of growth and decay.
• Vector Algebra: Vectors in two and three dimensions, magnitude and direction of a vector, 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: Classification of data, Frequency distribution, Cumulative frequency distribution, examples, Graphical representation, 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 Syllabus (Paper II)

The General Ability Test is divided into two parts: Part A covering English and Part B covering General Knowledge. This paper assesses the candidate's proficiency in English and awareness of current events and general knowledge.

Part A - English (Max. Marks: 200)

The question paper in English is designed to test the candidate's understanding of English and usage of words. The syllabus covers various aspects such as:

• Grammar and usage
• Vocabulary
• Comprehension
• Cohesion in extended text
• Proficiency in English

Part B - General Knowledge (Max. Marks: 400)

The question paper on General Knowledge will broadly cover subjects: Physics, Chemistry, General Science, Social Studies, Geography and Current Events. The syllabus given below is designed to indicate the scope of these subjects included in the paper. The topics mentioned are not exhaustive and questions on topics of similar nature not specifically mentioned in the syllabus may also be asked. Candidate's answers are expected to show their knowledge and intelligent understanding of the subject.

Section A: 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
• Vapours
• 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 Simple Pendulum, Simple Pulleys, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariner's Compass; Lightening Conductors, Safety Fuses

Section B: 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
• Materials used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, Gunpowder
• Common items and their uses
• Elementary ideas about the structure of Atom, Atomic Equivalent and Molecular Weights, Valency

Section C: General Science

• Difference between the living and non-living
• Basis of Life - Cells, Protoplasm 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

Section D: History, Freedom Movement, etc.

• Broad survey of Indian History, with emphasis on Culture and Civilisation
• 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

Section E: Geography

• The Earth, its shape and size
• Lattitudes 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
• Oceans and Ocean Currents
• Atmosphere and its composition
• Temperature and Atmospheric Pressure
• Planetary Winds, Cyclones and Anti-cyclones
• Humidity, Condensation and Precipitation
• Types of Climate
• Major Natural Regions of the World
• Regional Geography of India
• Climate, Natural vegetation
• Land use and patterns of population distribution in India
• Agriculture and Industrial activities of India
• Important Sea Ports and main sea, land and air routes of India
• Main items of Imports and Exports of India

Section F: Current Events

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.