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{**Latest*} UPSC – NDA Exam Syllabus, Pattern and Eligibility Criteria

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UPSC – NDA Exam Syllabus, Pattern and Eligibility Criteria

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Scheme of the Examination for UPSC NDA
The Examination will be conducted in Two Phase.
Phase – I Written Examination (Objective Type)
Phase – II SSB Test/Interview


RBI UPSC NDA Exam Pattern
Subjects No. of Questions Time
Mathematics 300 2½ Hours
General Ability Test 600 2½ Hours
Total 900
SSB Test/Interview 900
The SSB procedure consists of two stages Selection process stage I and stage II. Only those candidates who clear stage I are permitted to appear for stage II.

Syllabus For UPSC NDA Examination
MATHEMATICS (Maximum Marks- 300)
ALGEBRA: Concept of set, De Morgan laws, operations on sets, Venn diagrams. Representation of real numbers on a line. Cartesian product, relation, equivalence relation.  Maple numbers – basic properties, cube roots of unity modulus, argument, Geometric and Harmonic progressions, Binary system of numbers. Conversion of a number in decimal system to binary system and vice-versa. Arithmetic, Quadratic equations with real coefficients. The solution of linear in equations of two variables by graphs. Binomial theorem and its applications, Permutation and Combination,  Logarithms and their Applications
MATRICES AND DETERMINANTS: Types of matrices, operations on matrices, basic properties of determinants,  Determinant of a matrix, Adjoint and inverse of a square matrix, Applications – Solution of a system of linear equations in two or three unknowns by Matrix Method and by Cramer’s rule .
TRIGONOMETRY: Angles and their measures in radians and in degrees, Trigonometric identities Sum Trigonometrically ratios and difference formulae, Inverse trigonometric functions, Multiple and Sub-multiple angles, propties of triangles, Applications – Height and distance.
ANALYTICAL GEOMETRY OF TWO AND THREE DIMENSIONS: Distance formula, Angle between two lines,  Equation of a line in various forms, Rectangular  Cartesian Coordinate system,   Distance of a point from a line, Standard forms of parabola, ellipse and hyperbola, Equation of a circle in standard and in general form, Point in a three dimensional space, distance between two points, Eccentricity and axis of a conic, Equation of a plane and a line in various forms, Angle between two lines and angle between two planes, Equation of a sphere, Direction Cosines and direction ratios.
DIFFERENTIAL CALCULUS: Concept of a real valued function – domain, range and graph of a function,  one to one, onto and inverse functions, Composite functions, Notion of limit, Standard limits – examples, Application of derivatives in problems of maxima and minima, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivative – applications, Continuity of functions – examples, Derivatives of sum, product and quotient of functions, derivative of a composite function, derivative of a function with respect to another function, Second order derivatives. Increasing and decreasing functions.
INTEGRAL CALCULUS AND DIFFERENTIAL EQUATIONS: Integration as inverse of differentiation, exponential and hyperbolic functions, standard integrals involving algebraic expressions, integration by substitution and by parts, trigonometric, Evaluation of definite integrals – determination of areas of plane regions bounded by curves – applications, formation of a differential equation by examples,  Definition of order and degree of a differential equation, Application in problems of growth and decay, General and particular solution of a differential equations, solution of first order and first degree differential equations of various types – examples.
VECTOR ALGEBRA: Vectors in two and three dimensions, Unit and null vectors, addition of vectors, scalar multiplication of a vector, magnitude and direction of a vector, scalar product or dot product of two vectors,  Applications-work done by a force and moment of a force and in geometrical problems, Vector product or cross product of two vectors.
STATISTICS AND PROBABILITY: Statistics: Classification of data, cumulative frequency distribution – examples, Frequency distribution, Pie Chart, frequency polygon – examples. Measures of Central tendency – Mean, Graphical representation – Histogram, median and mode, Correlation and regression, Variance and standard deviation – determination and comparison,  Probability: Random experiment,  events, mutually exclusive and exhaustive events, outcomes and associated sample space,  impossible and certain events, Complementary, elementary and composite events, Union and Intersection of events, Definition of probability – classical and statistical – examples, Elementary theorems on probability – simple problems, Binomial distribution, Random variable as function on a sample space, examples of random experiments giving rise to Binominal distribution, Conditional probability, Bayes’ theorem – simple problems.
GENERAL ABILITY TEST (Maximum Marks-600)
Part ‘A’ – ENGLISH (Maximum Marks 200)The question paper in English is going to be made to check the candidate’s comprehension of English and workman like words. The syllabus covers various aspects like: Grammar and usage, vocabulary, comprehension and cohesion in prolonged text to check the candidate’s proficiency in English.
Part ‘B’ – GENERAL KNOWLEDGE (Maximum Marks-400)The question paper on General Knowledge will broadly cover the Topics: General Science, Chemistry, Physics, Social Studies, Geography and Current Events.The syllabus given below is intended to indicate these subjects included in this paper’s scope. The subjects aren’t to be regarded as exhaustive and questions on topics of similar character not specifically mentioned in the syllabus may also be requested. Candidate’s answers are expected to demonstrate intelligent understanding and their expertise of the subject.
Section ‘A’ (Physics): Physical Properties and States of Matter, Mass, Density and Specific Gravity, Weight, Volume, 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 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 the following : 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 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 non- living. Basis of Life – Cells, Protoplasm’s 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.) A broad survey of Indian History, with emphasis on Culture and Civilizations. 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. 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 Anti-cyclones; 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.
Eligibility Criteria
12th Class pass of the 10+2 pattern of School Education or equivalent examination.



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