**NDA exam is being organised in two stages. The first stage is of written test of Mathematics and General Ability. The second test generally known as Interview round is a test of intelligence and personality test. Here we are giving scheme for written examination. In this article, we are giving detailed NDA syllabus for written Exam.**

__ NDA EXAM PATTERN__

Click to learn preparation tips for NDA written exam

Code | Subject | Time | Max Marks |

01 | Mathematics | 2.30 hrs | 300 |

02 | General Ability Test | 2.30 hrs | 600 |

Total | 900 | ||

SSB Test and Interview | 900 |

### All About NDA Written Exam and Pattern

- The Paper will consist of objective type questions only.
- The Paper will be bilingual (Hindi as well as English)
- Paper is to be written by the candidate in his own handwriting.
- Its discretion of UPSC to fix qualifying marks.
- Use of calculator or Mathematical or logarithmic table is not permitted to answer.
__Negative Marking__

In the objective type question, four options will be given to each question. Carefully attempt the question as 0.33 marks will be deducted for each wrong answer.

In case a candidate has given more than one answer for any question, that will be treated as the wrong answer.

You can leave questions unattended as there is no negative marking for the same.

**NDA Syllabus For Written Exam **

**PAPER-I (Code No 01)**

**NDA SYLLABUS OF MATHEMATICS (Max.Marks-300)**

**ALGEBRA**

Set Theory, Set Operations, Introduction to Venn diagrams. Laws of De Morgan and their application, Cartesian product, Relations, Relation with equivalence. Graphical representation of real numbers. Basic properties of Complex Numbers, mod, argument, Unity and its cube root. Binary number system. Conversion number in decimal to binary system and vice-versa conversion.AP, GP and Harmonic Progression. Quadratic equations having real coefficients. Graphical solution of the pair of inequations with the help of graph.Permutation and Combination. Binomial Theorem along with its application. Properties and applications of Logarithm.

**MATRICES AND DETERMINANTS**:

Matrices and its types, operations related to matrices.The Determinant of matrices, fundamental properties of determinants. Adjoint and inverse of a square matrix, Applying Cramers rule for finding solutions of equations and matrix method.

**TRIGONOMETRY :**

Measurement of angles in degrees and radians. Trigonometric ratios. Identities of trigonometry.Sum and difference formula. Sub-multiple and multible angles. Inverse trigonometric functions. Application of relation oh height and distance with trignometry, solutions of triangles.

**ANALYTICAL GEOMETRY OF TWO AND THREE DIMENSIONS:**

Cartesian Coordianates. Formula for finding distance. Various kind of equation of line. Angle between any two lines. Distance of a point from a line. Standard and general equation of circle. Standard and parametric form of conic sections. Eccentricity and axis of ellipse, parabola and hyperbola. Point in a three dimensional system, Distance formula in 3-D. Direction Cosines and direction ratios. Equation of two points. various forms of equation of lines and planes. Angle between two lines and between two planes. Equation of sphere.

**DIFFERENTIAL CALCULUS :**

Functions and their range, domain. Composite functions, one to one functions, onto and inverse functions. Concept of limit, Standard examples of limits. Continuity and differentiability. Derivative of a function along with geometrical and physical interpretation of a derivative and applications of concepts.Sum, quotient and product rule of differentiation, differentiation of a function with respect to another function, differantiation of a composite function. Second order derivatives. Increasing and decreasing functions. Maxima minima and monotonicity.

**INTEGRAL CALCULUS AND DIFFERENTIAL EQUATIONS :**

Integration as anti-differentiation, integration by substitution and method of by parts, standard form of integrals involving algebraic expressions, trigonometric integrals, exponential and hyperbolic kind of functions . Properties of definite integrals, area under curve and application of definite integrals.

Concept of order and degree of a differential equation, forming a differential equation from examples. General and particular solution of differential equations, method of finding solution of first order and first degree differential equations and their examples. Applying concept in growth and decay problems.

**VECTOR ALGEBRA :**

Vectors in 2D and 3D space, magnitude and direction of a vectors. Unit and null vectors, operations related to vectors. Vector product or cross product of two vectors. Applications in physics problems and Euclidean geometry.

**STATISTICS AND PROBABILITY :**

Statistics : Classification of data, Frequency distribution, examples of cumulative frequency ditribution. Different type of graphs and their examples.Measures of Central tendency that are-Mean, median and mode. Variance and standard deviation which includes determination and comparison along with Correlation and regression.

Probability : Random experiment and the outcomes with associated sample space, basics of events, concepts of mutually exclusive and exhaustive events, certain and impossible events. Information about Union and Intersection of events. Complementary, elementary and composite events. Definition of probability which comprises classical and statistical and their examples. Elementary theorems on probability and simple problems based on them. Conditional probability, Bayes’ theorem and application in simple problems. Random variable as function on a sample space. Binomial distribution, applications of random experiments giving rise to Binominal distribution.

**PAPER-II (Code No. 02)**

**NDA SYLLABUS OF ****GENERAL ABILITY TEST Max. Marks—600**

**Part ‘A’—ENGLISH Max.Marks—200**

This paper in English will be designed to test the candidate’s understanding of English and working knowledge like use of words.

The syllabus covers

Comprehension

Vocabulary

Grammar and usage

**Part ‘B’—G. K. Max.Marks—400**

The question paper on General Knowledge will be in six parts.

Sections | Subjects | Approx. Weightages |

A | Physics | 25 % |

B | Chemistry | 15% |

C | General Science | 10% |

D | Social Studies | 20% |

E | Geography | 20% |

F | Current Events | 10% |

Below is the subject wise syllabus but this is not exhaustive list. Questions on topics of similar nature may also be asked. This is just to give a guideline for the preparation.

**Section ‘A’ (NDA Syllabus of Physics)**

Properties of matter. Concepts of density an volume. Archimedes Principle and its appliactions. Buoyancy.

Kinematics in 2 dimensions. Newton’s Laws of Motion, Force and concept of Momentum, Vectorial representation of forces as parallelogram, Static and dynamic equilibrium , Gravitation, Work and work-energy theorem. Conservative field and energy relations.

Thermal properties of matter and thermodynamics.

Sound Waves and their propagation. Application in musical instruments.

Optics-refraction and reflection, thin lenses and application in human eye.

Magnetism and properties of magnetism.

Electrostatics, current electricity, power of electric current. Magnetic effect of current.

Physics concept applications in- Pendulum, Pulleys, Levers, Siphon, Balloons, Fluid Pumps, Hydrometer, Pressure Cooker, Thermo Flask, Gramophone and similar devices, Telephone , Telegraphs, Microscope, Telescope, Periscope, , Safety Fuses. Mariner’s Compass; Lightening Conductors

**Section ‘B’ (****NDA Syllabus of ****Chemistry)**

Chemical and physical changes.

Basic concepts of stoichiometry, chemical reactions and basic laws related to conservation of mass and law of proportion.

Properties of gaseous state and liquid state.

Properties of some essential elements and compounds like oxygen, nitrogen , carbon dioxide.

Properties of acids, bases and salts.

Different forms of carbon.

Types of fertilizers.

Material used in the production of essential substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches and Gun-Powder.

Atomic structure and properties(basics only).

**Section ‘C’ (****NDA Syllabus of ****General Science)**

Living Vs Non-living things.

Basis of Life—Cells, Tissues and Protoplasms

Growth and Reproduction in Animals and Plants .

Basic knowledge of Human Body and its important organs.

Common Epidemics and their causes and prevention.

Food and Source of Energy for human being.

Constituents of food and Balanced Diet.

The Solar System and concept of Meteors and Comets, Eclipses.

Achievements of Eminent Scientists.

**Section ‘D’ (****NDA Syllabus of ****History, Freedom Movement etc.)**

Indian History with special emphasis on Culture and Civilisation.

Indian Freedom Movement .

Indian Constitution and Components of Administration.

Understanding of Five Year Plans of India.

Co-operatives and Community Development, Panchayati Raj

Sarvodaya, Bhoodan, National Integration and Welfare State,

Basic Teachings of Mahatma Gandhi.

Renaissance, Exploration and Discovery;

Forces shaping the modern world;

War of American Independence.

Industrial Revolution and Russian Revolution.

French Revolution,

Impact of Science and Technology on Society.

Concept of one World & United Nations,

Panchsheel, Democracy, Communism and Socialism

Role of India in the present world.

**Section ‘E’ (****NDA Syllabus of ****Geography)**

The Earth and its size and shape.

Longitudes and Lattitudes

Concept of time. International Date Line.

Origin of Earth. Movements of Earth and their effects.

Rocks and their classification;

Weathering—Chemical and Mechanical

Ocean Currents and Tides

Earthquakes and Volcanoes.

Atmosphere and its composition; Temperature and Atmospheric Pressure,

Humidity; Condensation and Precipitation; Types of Climate,

Planetary Winds,

Cyclones and Anti-cyclones;

Natural regions of the World.

Geography of India & itsClimate,

Natural vegetation.

Mineral and Power resources;

location and distribution of industrial and agricultural activities.

Important Sea ports and main sea, air and land routes of India.

Main items of Export and Imports of India.

**Section ‘F’ (****NDA Syllabus of ****Current Events)**

India and important events in the recent years,

Current World Events

Personalities : Indian and International (includes also those connected cultural and sports activities)

Click to read preparation tips for SSB Interview.

We wish you good luck for your success in NDA Exam.