NDA Syllabus: Union public service commission (UPSC) conducts NDA exam twice in a year for admission to Indian Navy, Army & Air Force Wings. NDA exams Syllabus is divided into two papers – Mathematics and General Ability. It aims to judge a candidate on his logical ability and general awareness.

## UPSC Conducts NDA Exam in Two Stages :

Written Examination: The NDA exam will constitute 2 subjects, Maths and General Ability Test and each subject is given the time limit 2 ½ Hours, maximum marks for Maths is 300 and General ability is 600. The papers in all the subjects will consist of objective type questions only. Both papers (Maths and General Ability Test) will be set bilingually in Hindi as well as English.

Interview: Qualified candidates in the NDA written examination will be eligible for Interview conducted by SSB (Services selection board). The Interview Consists of both Intelligence & Personality Test.

## NDA Syllabus Paper-I MATHEMATICS

(Max. Marks- 300)

TOPIC |
NO. OF QUESTIONS |

Calculus |
20-25 |

Quadratic equation |
20-15 |

Matrices & Determinants |
30 |

Probability |
10 |

Trigonometry |
30 |

Complex number |
10-15 |

**ALGEBRA:** Concept of a set, operations on sets, Venn diagrams. De Morgan laws. Cartesian product, relation, equivalence relation. Representation of real numbers on a line. Maple numbers – basic properties, modulus, argument, cube roots of unity. The binary system of numbers. Conversion of a number in decimal system to binary system and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. A solution of linear in equations 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. The 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. Trigonometrical ratios. Trigonometric identities Sum and difference formulas. 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. The equation of a line in various forms. The angle between the two lines. The distance of a point from a line. The 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. The equation of a plane and a line in various forms. The angle between the two lines and the angle between the two planes. The 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 derivative – applications. Derivatives of the sum, product and quotient of functions, derivative of a function with respect to another function, a 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 solution of differential equations, a 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, 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 is done by a force and moment of a force and in geometrical problems.

**STATISTICS AND PROBABILITY: **Statistics: Classification of data, Frequency distribution, And 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 Binominal distribution.

**NDA Syllabus PAPER-II: GENERAL ABILITY TEST (Max. Marks-600)**

GENERAL ABILITY TEST of NDA syllabus is divided into two parts :

**PART A: ENGLISH**

**PART B: GENERAL ABILITY TEST (GAT):** Contains Physics, Chemistry, General Science, History, Geography and current affairs

## NDA Syllabus PAPER-II Part ‘A’ – ENGLISH

(Maximum Marks 200)

Topic |
No. of Questions |
No. of Marks |

Spotting Errors |
5 |
20 |

Comprehension |
6 |
24 |

Selecting Words |
10 |
40 |

The ordering of Words in a Sentence |
9 |
36 |

Sentence Improvement |
10 |
40 |

Antonyms |
5 |
20 |

Synonyms |
5 |
20 |

Total |
50 |
200 |

The English portion of the NDA Syllabus is designed to judge a candidate’s knowledge of the basic grammar and vocabulary, ability to form correct sentences and use of words, knowledge and usage of grammar, vocabulary, comprehension, and his mental ability to remember and place the meaning of words in their proper places.

NDA EXAM SYLLABUS PAPER-II Part ‘B’ – GENERAL KNOWLEDGE

(Maximum Marks-400)

Topic |
No. of Questions |
No. of Marks |

Physics |
23 |
92 |

Chemistry |
16 |
64 |

General Science |
11 |
44 |

History & Freedom Movement |
16 |
64 |

Geography |
17 |
68 |

Current Events |
17 |
68 |

Total |
100 |
400 |

Section ‘A’ (Physics) :?

NDA syllabus for physics: Physical Properties and States of Matter, Mass, Weight, Volume, Density and Specific Gravity, Principle of Archimedes, Pressure Barometer. The 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) :**

**NDA syllabus for 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):

**NDA syllabus for general Science:** Difference between the living and non- living. The basis of Life – 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. 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, the Industrial Revolution and the Russian Revolution. Impact of Science and Technology on Society. The concept of one World, United Nations, Panchsheel, Democracy. Socialism and Communism. Role of India in the present world.

## Section ‘E’ (Geography):

**NDA syllabus for 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 in 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

NOTE : Out of maximum marks assigned to part ‘B’ of NDA Syllabus paper, questions on Sections ‘A’, ‘B’, ‘C’, ‘D’, ‘E’ and ‘F’ will carry approximately 25%, 15%, 10%,20%, 20% and 10% weights respectively.