NATIONAL DEFENCE ACADEMY
&
NAVAL ACADEMY EXAMINATION (II)
2024
(Commission’s Website http://upsc.gov.in)
Last Date: 4-6-2024
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The National Defence Academy (NDA) written exam has two parts- Mathematics and General Ability. The mathematics paper is of 300 marks and a duration of 2.5 hours. The General Ability paper is of 600 marks and a duration of 2.5 hours. Both the papers have objective type questions only.
The detailed syllabus for the NDA exam 2022 written test is given below:
Syllabus for Mathematics Paper
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
- Determinants 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 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, and the 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 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 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.
Syllabus for General Ability Test
Part ‘A’—English (Maximum Marks – 200)
The question paper is designed to check the candidate’s understanding of English and the usage of words. The syllabus includes various aspects such as Grammar and usage, vocabulary, comprehension, and cohesiveness in an extended text to assess a candidate’s English skills
Part ‘B’—General Knowledge (Maximum Marks – 400)
The General Knowledge question paper will cover the subjects: General Science, Physics, Chemistry, Social Studies, Geography, and Current Events.
NOTE: Out of the maximum marks assigned to part ‘B’ of this paper, each section has a designated weightage. The questions on Sections ‘A’, ‘B’, ‘C’, ‘D’, ‘E’ and ‘F’ carry approximately 25%, 15%, 10%, 20%, 20% and 10% weightage respectively.
Section ‘A’ (Physics)
- Physical Properties and States of Matter, Weight, Mass, Volume, Principle of Archimedes, Density and Specific Gravity, Pressure Barometer
- The motion of objects, Force and Momentum, Velocity and Acceleration, Stability and Equilibrium of bodies, Newton’s Laws of Motion, Parallelogram of Forces, Gravitation, Power and Energy, elementary ideas of work
- Effects of Heat, change of State and Latent Heat, Measurement of Temperature and Heat, Modes of Transference of Heat
- Sound waves and their properties, Rectilinear propagation of Light, Simple musical instruments., Reflection and refraction
- Spherical mirrors and lenses, the human eye
- Natural and artificial magnets, Earth as a magnet, properties of a magnet
- Static and Current Electricity, Ohm’s Law, conductors and Non- conductors, Simple Electrical Circuits, Lighting and Magnetic effects of Current, Heating, Measurement of Electrical Power, Use of X-Rays, Primary and Secondary Cells, 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
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
- Fertilisers—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, Valency
Section ‘C’ (General Science)
- 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— the 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.)
- A broad survey of Indian history, with emphasis on culture and civilisation
- The freedom movement in India
- Elementary study of Indian constitution and administration
- Elementary knowledge of five-year plans for 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 the 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
- Latitudes and longitudes, concept of time
- International date line
- Movements on earth and their effects
- Origin of earth
- Rocks and their classification, weathering— mechanical and chemicals, 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
Section ‘F’ (Current Events)
- Knowledge of important events that have happened in India in the recent years
- Current important world events
- Prominent personalities— both Indian and International including those connected with cultural activities and sports.