## NDA Exam Syllabus

The National Defence Academy (NDA) written exam has two parts- Mathematics and General Ability. The mathematics paper is of 300 marks and a duration of 2.5 hours. The General Ability paper is of 600 marks and a duration of 2.5 hours. Both papers have objective-type questions only.

The detailed syllabus for the NDA exam written test is given below:

## NDA Maths Syllabus

### 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 a decimal system to a binary system and vice-versa
- Arithmetic, Geometric and Harmonic progressions
- Quadratic equations with real coefficients
- Solution of linear inequalities 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
- Determinants 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
- Trigonometric 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
- The 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, the 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
- The angle between two lines and the 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
- The 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 sum, product and quotient of functions, the derivative of a function with respect to another function, and the 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 solutions of differential equations, solutions 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 done by a force and moment of a force and in geometrical problems

### Statistics and Probability

- 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

### How to score 200 plus in NDA Maths?

Scoring 200+ in NDA Maths requires focused preparation and strategic study. Here’s a plan to help you achieve your goal:

**Understand the Syllabus:**Thoroughly understand the NDA Maths syllabus, covering topics like algebra, trigonometry, calculus, and geometry.**Quality Resources:**Use recommended textbooks and study guides for conceptual clarity.**Conceptual Clarity:**Focus on understanding the fundamental concepts of each topic.**Practice Regularly:**Solve a variety of practice questions and previous years’ papers to enhance problem-solving skills.**Time Management:**Practice solving questions within the time limits to improve speed.**Focus on Important Topics:**Identify high-weightage topics and allocate more time to master them.**Consistent Revision:**Regularly revise concepts and formulas to ensure retention.**Mock Tests:**Take mock tests to simulate exam conditions, improve time management, and assess your performance.**Analyzing Mistakes:**Review mistakes in practice tests and work on improving those areas.**Shortcuts and Techniques:**Learn time-saving tricks and techniques for solving complex problems.**Positive Mindset:**Stay confident, positive, and manage stress effectively.**Seek Help:**If you face challenges, seek guidance from teachers, mentors, or online resources.**Practice Previous Years’ Papers:**Familiarize yourself with the pattern and types of questions asked in previous NDA Maths papers.**Stay Consistent:**Consistency and dedication are key to scoring well. Regular practice and revision are essential.

**NDA Syllabus Highlights**

Name of the Exam | National Defence Academy Exam or NDA exam |

Exam Conducting Body | Union Public Service Commission, UPSC |

Frequency of NDA Exam | Two times a year (NDA 1 & NDA 2) |

Selection Process | Written Test Intelligence & Personality Test (SSB) |

Mode of exam | Offline (Pen and Paper mode) |

Total Papers in NDA Exam | Mathematics General Ability Test (GAT) |

Total Marks for NDA Exam | Total: 900 Marks Mathematics: 300 Marks GAT: 600 Marks |

Total No. of Questions | Mathematics: 120 GAT: 150 |

Negative Marking | Mathematics: -0.83 GAT: -1.33 marks |

Exam Duration | Mathematics: 2 Hours 30 Minutes GAT: 2 Hours 30 Minutes |

## NDA General Ability Test Syllabus

#### Part ‘A’—English (Maximum Marks – 200)

The question paper is designed to check the candidate’s understanding of English and the usage of words. The syllabus includes various aspects such as Grammar and usage, vocabulary, comprehension, and cohesiveness in an extended text to assess a candidate’s English skills

#### Part ‘B’—General Knowledge (Maximum Marks – 400)

The General Knowledge question paper will cover the subjects: General Science, Physics, Chemistry, Social Studies, Geography, and Current Events.

**NOTE**: Out of the maximum marks assigned to part ‘B’ of this paper, each section has a designated weightage. The questions on Sections ‘A’, ‘B’, ‘C’, ‘D’, ‘E’ and ‘F’ carry approximately 25%, 15%, 10%, 20%, 20% and 10% weightage respectively.

#### Section ‘A’ (Physics)

- Physical Properties and States of Matter, Weight, Mass, Volume, Principle of Archimedes, Density and Specific Gravity, Pressure Barometer
- The motion of objects, Force and Momentum, Velocity and Acceleration, Stability and Equilibrium of bodies, Newton’s Laws of Motion, Parallelogram of Forces, Gravitation, Power and Energy, elementary ideas of work
- Effects of Heat, change of State and Latent Heat, Measurement of Temperature and Heat, Modes of Transference of Heat
- Sound waves and their properties, Rectilinear propagation of Light, Simple musical instruments., Reflection and refraction
- Spherical mirrors and lenses, the human eye
- Natural and artificial magnets, Earth as a magnet, properties of a magnet
- Static and Current Electricity, Ohm’s Law, conductors and Non- conductors, Simple Electrical Circuits, Lighting and Magnetic effects of Current, Heating, Measurement of Electrical Power, Use of X-Rays, Primary and Secondary Cells, 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

#### 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
- Fertilisers—Natural and Artificial
- The 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 nonliving
- Basis of life— cells, protoplasms and tissues
- Growth and reproduction in plants and animals
- Elementary knowledge of the Human body and its important organs
- Common Epidemics, their causes and prevention
- Food— the 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 civilisation
- The freedom movement in India
- Elementary study of Indian constitution and administration
- Elementary knowledge of five-year plans for 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
- 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 on earth and their effects
- Origin of earth
- Rocks and their classification, weathering— mechanical and chemicals, 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

#### 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 sport

## How to Prepare NDA Exam Syllabus

Preparing for the NDA (National Defence Academy) exam requires focused and systematic study. Here are five points to help you prepare effectively:

**Understand the Syllabus:**Familiarize yourself with the NDA exam syllabus, including the topics and subtopics for each subject. This will help you create a structured study plan and allocate appropriate time for each section.**Study Material:**Gather the recommended study materials, such as NDA-specific books, reference guides, previous years’ question papers, and online resources. Choose reliable sources that cover the entire syllabus comprehensively.**Time Management:**Create a study schedule that allows you to allocate sufficient time for each subject. Ensure that you give equal importance to Mathematics and General Ability Test (GAT) sections. Set specific goals for each study session and adhere to the schedule.**Practice and Mock Tests:**Regularly practice solving questions from previous years’ papers and take mock tests to simulate the exam environment. This will help you become familiar with the exam pattern, improve your time management skills, and identify areas where you need to improve.**Stay Updated and Stay Fit:**Stay updated with current affairs, national and international news, and important developments in areas like history, geography, and science. Additionally, focus on physical fitness as the NDA exam also includes a physical fitness test. Engage in regular exercise, practice running, and develop stamina and endurance.

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