While the age of 20's is to enjoy life and merry making, there are only few brave youngsters who write an exam conducted by UPSC to get into the National Defence Academy and prepare relentlessly for a life of supreme sacrifice and valour. They live the most difficult three years of their lives to become a proud soldier of their nation, to pass out from one of the most prestigious military academies in the world and most of all, to serve the nation as a top-notch officer.

## What is NDA?

The **National Defence Academy** (**NDA**) is the joint services academy of the Indian Armed Forces, where cadets of the three services, the Army the Navy and the Air Force train together before they go on to respective service academy for further pre-commission training. The NDA is located in Khadakwasla Pune, Maharashtra. It is the first tri-service academy in the world.

UPSC NDA Selection process

Candidates applying for the posts of UPSC NDA (National Defence Acadamy) Exam will be selected based on the following two steps:

- Written Examination
- Interview

NDA EXAM PATTERN | |
---|---|

Mathematics | 300 |

General Ability | 600 |

Total | 900 |

SSB Test/ Interview |
900 |

**2 hrs 30 mins**for each subject.

UPSC NDA Syllabus

**SSB-** Intelligent and Personality Test

TOP WISE DETAILED SYLLABUS

PAPER 1

### 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 decimal system to binary system and vice-versa. Arithmetic, 19 Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequations 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 Cramerâ€™s rule and by Matrix Method.

### TRIGONOMETRY

Angles and their measures in degrees and in radians. Trigonometrical 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. 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, 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. 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, one to one, onto and inverse functions. 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 derivativeâ€”applications. 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 involving algebraic expressions, trigonometric, exponential and hyperbolic functions. 20 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 solution of a differential equations, solution 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, addition of vectors, scalar multiplication of a vector, scalar product or dot product of two vectors. Vector product or cross product of two vectors. Applicationsâ€”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 distributionâ€”examples. Graphical representationâ€”Histogram, Pie Chart, frequency polygonâ€” examples. Measures of Central tendencyâ€”Mean, median and mode. Variance and standard deviationâ€”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 probabilityâ€”classical and statisticalâ€”examples. Elementary theorems on probabilityâ€”simple problems. Conditional probability, Bayesâ€™ theoremâ€”simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binominal distribution.

PAPER 2

### Part â€˜Aâ€™â€”ENGLISH

(Maximum Marksâ€”200)

Grammar and usage, vocabulary, comprehension and cohesion in extended text to test the candidateâ€™s proficiency in English.

### Part â€˜Bâ€™â€”GENERAL KNOWLEDGE

(Maximum Marksâ€”400) - There will be questions on following subjects

### 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, Newtonâ€™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, Ohmâ€™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, Marinerâ€™s Compass; Lightening 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 Carbondioxide, Oxidation and Reduction. Acids, bases and salts. Carbonâ€”different forms. Fertilizersâ€”Natural and Artificial. Material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches and GunPowder. Elementary ideas about the structure of Atom, Atomic Equivalent and Molecular Weights, Valency.

### General Science

Difference between the living and non-living. Basis of Lifeâ€”Cells, Protoplasms and Tissues. Growth and Reproduction in Plants and Animals. Elementary knowledge of Human Body and its important organs. Common Epidemics, their causes and prevention. Foodâ€”Source of Energy for man. Constituents of food, Balanced Diet. The Solar Systemâ€”Meteors and Comets, Eclipses. Achievements of Eminent Scientists.

### History, Freedom Movement etc.

A 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.

### Geography

### Current Events

Knowledge of Important events that have happened in India in the recent years. Current important world events. Prominent personalitiesâ€”both Indian and International including those connected with cultural activities and sports. 23 NOTE : Out of maximum marks assigned to part â€˜Bâ€™ of this paper, questions on Sections â€˜Aâ€™, â€˜Bâ€™, â€˜Câ€™, â€˜Dâ€™, â€˜Eâ€™ and â€˜Fâ€™ will carry approximately 25%, 15%, 10%, 20%, 20% and 10% weightages respectively.

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