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NDA/NA (National Defence Academy & Naval Academy) written examination is conducted twice in a year by UPSC. The written exam is conducted in two parts, Paper code 1 (Mathematics) and Paper code 2 (General Ability Test). After the written exam, UPSC prepares a list of candidates who obtain the minimum qualifying marks in the written examination as fixed by UPSC at their discretion. Successful candidates then appear before SSB for their interview.

Paper Name |
Paper Code |
No. of Ques. |
Max Marks |
Marks/Ques |
Negative Marking |
Duration (hrs) |
Time/Ques. (s) |

Mathematics |
01 | 120 | 300 | 2.5 | 0.83 | 2.5 | 72 |

General Ability Test (GAT) |
02 | 150 | 600 | 4.0 | 1.33 | 2.5 | 60 |

- The paper in all subjects will consist of objective type questions only. The student will be awarded marks for choosing the correct option out of four given options. There will be a penalty of 1/3 marks of the question for choosing the wrong option but there will be no penalty or award for unattempted questions.
- The exam will be set bilingually, in Hindi as well as in English.
- Wherever necessary, questions involving the metric system of Weights and Measures only will be set.
- Candidates must write the papers in their own hand. In no circumstances will they be allowed the help of a scribe to write answers for them.
- UPSC have the discretion to fix qualifying marks in any or all the subjects at the examination.
- The candidates are not permitted to use a calculator or Mathematical or logarithmic table for answering objective type papers (Test Booklets). They should not, therefore, bring the same inside the Examination Hall.

The 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. The binary system of numbers. Conversion of a number in decimal system to a binary system and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. A solution of linear inequalities of two variables by graphs. Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications.

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.

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.

Rectangular Cartesian Coordinate system. Distance formula. The equation of a line in various forms. An angle between two lines. The distance of a point from a line. An 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. An 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.

Get free access to our online Maths videos on youtube for NDA preparation https://www.youtube.com/watch?v=rYCzmFiXMUM

The concept of a real-valued function–domain, range, and a 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.

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.

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: 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.

Subject |
No. of Questions |
Tentative Maximum Marks |
---|---|---|

Part A |
||

English |
50 | 200 |

Part B |
||

Physics |
25 | 100 |

Chemistry |
15 | 60 |

General Science |
10 | 40 |

History etc |
20 | 80 |

Geography |
20 | 80 |

Current Events |
10 | 40 |

The question paper for English will be set only in English. The syllabus covers various aspects like:

- Grammar and usage
- Vocabulary
- Comprehension
- Cohesion in an extended text

The question paper on General Knowledge will broadly cover the following subjects

- Physics
- Chemistry
- General Science
- Biology
- Environmental Science
- Social Studies
- History
- Political Science
- Economics
- Geography
- Current Events

- 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; Lightning Conductors, Safety Fuses.

- 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.
- The 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.

- Difference between the living and nonliving. 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 etc (Tentative Maximum Marks – 80)**

- 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 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.

- 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 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.

- 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.

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