NDA Syllabus 2021 – Maths and General Ability Test

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NDA Syllabus 2021 – Maths and General Ability Test

NDA Syllabus 2021 – Maths and General Ability Test: National Defence Academy Examination is conducted every year by the Union Public Service Commission. The exam is held to recruit several candidates in the National Defence Academy under several categories including the Indian Air Force, Indian Navy and Indian Army. Since the level of competition remains tough, a deep knowledge of the syllabus and marks distribution of the NDA Examination is very important. NDA Syllabus 2021

Best NDA Coaching In Lucknow, India | NDA Syllabus 2021 - Maths and General Ability Test
Best NDA Coaching In Lucknow, India | NDA Syllabus 2021 – Maths and General Ability Test

We at Vedantu, have provided detailed information about NDA Exam Pattern and syllabus. Through this article, we aim to help the candidates understand the NDA exam process and subject-wise marks distribution for better preparation. Aspirants can download the free PDFs of NDA Syllabus 2021 [Mathematics and General Ability] here. NDA Syllabus 2021

NDA Exam Pattern 2021 – NDA Syllabus 2021 – Maths and General Ability Test

UPSC has categorised the NDA selection process in two stages: written exam and SSB interview. 

It is important for the candidates to pass the written exam to be eligible for the interview. The written exam for NDA is again conducted for 2 categories, i.e., Mathematics and General Ability. Refer to the table below for a better understanding of the exam pattern. NDA Syllabus 2021

2021 NDA Exam Pattern – NDA Syllabus 2021

NDA Exam 2021

Conducting Body

Union Public Service Commission

NDA Exam Papers

Mathematics (Paper-I)

General Ability (Paper-II)

Total Marks



Total number of questions



Time Allotted

2 hours 50 minutes

Type of Questions

Multiple Choice Questions (MCQs)

Medium of Examination

English & Hindi

NDA Exam 2021 Marking Scheme – NDA Syllabus 2021

NDA examination mainly covers questions from 10+2 level. Hence, candidates must know the basic concepts of all the subjects. According to the NDA Marking Scheme 2021, there is a negative marking for every wrong attempted question. Therefore, candidates are advised to choose their answers wisely. NDA Syllabus 2021

Marking pattern for Mathematics category: 0.83 marks are deducted for each wrong answer and 2.5 marks are added for each correct answer. There is no negative marking for unattempted answers.

NDA Exam Pattern General Ability – NDA Syllabus 2021

NDA General Ability paper is conducted for 600 marks including 150 questions. 1.33 marks are deducted for each wrong answer and 4 marks are added for each correctly attempted answer. There is no negative marking for unattempted answers. The General Ability Test (GAT) comprises two parts: English (Part A) and General Awareness (Part B)

Given Below Are the 6 Subjects Included Under NDA General Awareness Paper:

  1. Physics

  2. Chemistry

  3. History

  4. Geography

  5. General Science

  6. Current Events

The table below gives a subject-wise mark distribution of the NDA General Ability exam.

NDA General Ability Exam Subject-Wise Mark Distribution

General Ability Test (GAT)



Subject-wise Marks









General Science


Current Events






Total Marks


NDA Syllabus – General Ability – NDA Syllabus 2021

The syllabus for National Defence Academy Examination is prescribed by the Union Public Service Commission. It is released every year on their official website along with the exam notification.

The General Ability syllabus is broadly divided into two categories: English and General Awareness. 

Candidates need to prepare well especially for the General Awareness section as it is a vast section which includes physics, chemistry, general science, history, geography and current events.

Given below is the detailed subject-wise syllabus for NDA Paper-II Exam 2021.

NDA Syllabus for English – NDA Syllabus 2021

Syllabus for English

Topics Included

Adjective Degree Of Comparison Rules

List of Synonyms and Antonyms

List of One Word Substitutions

List of Homophones/Homonyms

Candidates are advised to be very thorough with their grammar and vocabulary to score well in this section. They can find the important questions for NDA 2021 Exam on the official website of Vedantu. Solving these questions on a regular basis will help the aspirants to gain a clearer concept of each subject.

NDA Syllabus 2021 – General Awareness – NDA Syllabus 2021

Candidates often find it difficult to prepare for the General Awareness category due to its vast syllabus. Therefore, it is very important for them to segregate the entire syllabus before starting with the preparation. By doing so, they will be familiar with their weaknesses and focus more on those areas.

Given below are the syllabus for each subject included under General Awareness section. NDA Syllabus 2021

NDA Syllabus for Physics – NDA Syllabus 2021

Syllabus for Physics

Topics Included

  1. Static and Current Electricity

  2. Newton’s Laws of Motion

  3. Earth as a Magnet

  4. Force and Momentum

  5. Spherical mirrors and Lenses

  6. Pressure Barometer

  7. Human Eye

  8. Reflection and refraction

  9. Principle of Archimedes

  10. Physical Properties and States of Matter

  11. Modes of transference of Heat

  12. Mass, Weight, Volume, Sound waves and their properties

  13. Simple musical instruments

  14. Rectilinear propagation of Light

  15. Density and Specific Gravity

  16. Parallelogram of Forces

  17. Conductors and Non-conductors

  18. Stability and Equilibrium of bodies

  19. Ohm’s Law

  20. Gravitation

  21. Simple Electrical Circuits

  22. Elementary ideas of work

  23. Motion of objects

  24. Natural and Artificial Magnets

  25. Velocity and Acceleration

  26. Properties of a Magnet

  27. Heating, Lighting and Magnetic effects of Current

  28. Power and Energy

  29. Measurement of Electrical Power

  30. Effects of Heat

  31. Primary and Secondary Cells

  32. Measurement of Temperature and Heat

  33. Use of X-Rays

  34. General Principles in the working of 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.

NDA Syllabus for Chemistry

Chemistry Topics for NDA Exam 2021

Physical and Chemical Changes

Acids, bases and salts

Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon Dioxide, Oxidation and Reduction

Elementary ideas about the structure of Atom

Symbols, Formulae and simple Chemical Equations

Atomic Equivalent and Molecular Weights

Mixtures and Compounds

Law of Chemical Combination (excluding problems)

Properties of Air and Water


Material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches and Gunpowder

Fertilizers—Natural and Artificial


NDA Syllabus for History

Syllabus for History

Topics Included

  1. Forces shaping the modern world; 

  2. Renaissance

  3. Exploration and Discovery; 

  4. A broad survey of Indian History, with emphasis on Culture and Civilisation

  5. Freedom Movement in India

  6. French Revolution, Industrial Revolution and Russian Revolution

  7. War of American Independence,

  8. Impact of Science and Technology on Society

  9. Elementary study of Indian Constitution and Administration

  10. Concept of one World

  11. Elementary knowledge of Five Year Plans of India

  12. United Nations, 

  13. Panchsheel, 

  14. Panchayati Raj, Democracy, Socialism and Communism

  15. Role of India in the present world

  16. Co-operatives and Community Development

  17. Bhoodan, Sarvodaya, 

  18. National Integration and Welfare State

  19. Basic Teachings of Mahatma Gandhi

NDA Syllabus for Geography – NDA Syllabus 2021

Syllabus for Geography

Topics Included Under Geography

  1. The Earth, its shape and size

  2. Ocean Currents and Tides Atmosphere and its composition

  3. Latitudes and Longitudes

  4. Temperature and Atmospheric Pressure, Planetary Winds, Cyclones and Anticyclones; Humidity; Condensation and Precipitation

  5. Concept of time

  6. Types of Climate

  7. International Date Line

  8. Major Natural Regions of the World

  9. Movements of Earth and their effects

  10. Regional Geography of India

  11. Climate, Natural vegetation. Mineral and Power resources; 

  12. Location and distribution of agricultural and Industrial activities

  13. Origin of Earth. Rocks and their classification

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

  15. Weathering—Mechanical and Chemical, Earthquakes and Volcanoes

  16. Main items of Imports and Exports of India

Syllabus for General Science – NDA Syllabus 2021

The general science syllabus for NDA General Awareness section includes the following topics:

  1. Common Epidemics, their causes and prevention

  2. Difference between the living and non-living

  3. Food—Source of Energy for man

  4. Basis of Life—Cells, Protoplasms and Tissues

  5. Constituents of food

  6. Growth and Reproduction in Plants and Animals

  7. Balanced Diet

  8. Elementary knowledge of Human Body and its important organs

  9. The Solar System—Meteors and Comets, Eclipses. Achievements of Eminent Scientists

The questions in the General Science section mostly cover the Class 9 to Class 12 levels. It mainly test the basic concepts of the candidates regarding the subject. Therefore, regular revision of the NCERT textbooks will help them score higher marks.

Syllabus for Current Events – NDA Syllabus 2021

For the current events category, students must be aware of the latest happenings in the world. These may include sports, economics, politics, national and international events. Reading the daily newspapers, listening to current affairs and news channels will help you know the latest updates of the world. 

NDA Syllabus 2021 Mathematics – NDA Syllabus 2021

NDA Mathematics paper mainly includes questions from 10+2 level and tests the basic concepts of the candidates. Therefore, it is very important for the candidates to prepare each topic thoroughly. 

Although, the subject Mathematics is considered tough by many aspirants but a proper analysis of the syllabus will help them understand the exam pattern.

The table below gives a detailed list of topics included in NDA Mathematics syllabus.

NDA Syllabus for Mathematics – NDA Syllabus 2021

Topics-wise Syllabus

Sub-Topics Included 


  1. Sets

  2. Venn diagrams

  3. De Morgan laws

  4. Cartesian product, relation, equivalence relation

  5. Real numbers, Complex numbers, Modulus, Cube roots

  6. Conversion of a number in Binary system to Decimals and vice-versa. 

  7. Arithmetic, Geometric and Harmonic progressions

  8. Quadratic equations, Linear inequations

  9. Permutation and Combination

  10. Binomial theorem and Logarithms.


  1. Concept of a real valued function

  2. Domain, range and graph of a function

  3. Composite functions, one to one, onto and inverse functions

  4. Notion of limit

  5. Standard limits

  6. Continuity of functions, algebraic operations on continuous functions

  7. Derivative of function at a point

  8. Geometrical and physical interpretation of a derivative-application

  9. Derivatives of sum, product and quotient of functions

  10.  Derivative of a function with respect to another function

  11. Derivative of a composite function

  12. Second order derivatives, increasing and decreasing functions, application of derivatives in problems of maxima and minima

Matrices and Determinants

  1. Types of matrices, operations on matrices

  2. Determinant of a matrix, basic properties of determinants

  3. Adjoint and inverse of a square matrix

  4. Applications-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method

Integral Calculus and Differential Equations

  1. Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions.

  2. Evaluation of definite integrals—determination of areas of plane regions bounded by curves—applications.

  3. Definition of order and degree of a differential equation, formation of a differential equation by examples.

  4. General and particular solution of differential equations, solution of first order and first degree differential equations of various types—examples. Application in problems of growth and decay.


  1. Angles and their measures in degrees and in radians. Trigonometric ratios. 

  2. Trigonometric identities Sum and difference formulae.

  3. Multiple and Sub-multiple angles.

  4.  Inverse trigonometric functions. 

  5. Applications-Height and distance, properties of triangles.

Vector Algebra

  1. Vectors in two and three dimensions, magnitude and direction of a vector. 

  2. Unit and null vectors, addition of vectors, scalar multiplication of a vector, scalar product or dot product of two vectors. 

  3. Vector product or cross product of two vectors. 

  4. Applications—work done by a force and moment of a force and in geometrical problems.

Analytical Geometry of Two and Three Dimension

  1. Rectangular Cartesian Coordinate system. 

  2. Distance formula.

  3.  Equation of a line in various forms. Angle between two lines. Distance of a point from a line. 

  4. Equation of a circle in standard and in general form. 

  5. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic. 

  6. Point in a three-dimensional space, distance between two points. 

  7. Direction Cosines and direction ratios. Equation of two points.

  8.  Direction Cosines and direction ratios. Equation of a plane and a line in various forms. 

  9. Angle between two lines and angle between two planes. 

  10. Equation of a sphere.

Statistics and Probability

  1. Probability: Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. 

  2. Union and Intersection of events. 

  3. Complementary, elementary and composite events. 

  4. Definition of probability—classical and statistical—examples. 

  5. Elementary theorems on probability—simple problems. 

  6. Conditional probability, Bayes’ theorem—simple problems. 

  7.  Binomial distribution, examples of random experiments giving rise to Binomial distribution.

NDA SSB Interview

After clearing the NDA Written Examination, candidates are eligible to sit for the SSB Interview. This is the final selection test to get selected into the National Defence Academy and hence, it includes two stages- Stage 1 and Stage 2.

Stage 1 is a screening test which examine the verbal and non-verbal skills of the candidates. While, Stage 2 includes Psychological test and Group Testing Officers Test. 

After clearing both the stages, candidates are selected for a round of personal interview. Based on the interview performance, he/she will be selected for the eligible post in the Defence Academy.

NDA Booklist for Mathematics and General Ability

Books are always considered to be helpful in understanding any subject more precisely. But many times, candidates face difficulty in selection of correct reference material. Therefore, we have provided below a list of books for Mathematics and General Ability which can be handy for kickstarting their preparation.

NDA Booklist for Mathematics – NDA Syllabus 2021

Booklist for Mathematics

Name of the books


Pathfinder NDA & NA 

Arihant Publications

Mathematics for NDA and NA

RS Aggarwal

Solved Subject-wise Papers for NDA and ND

Arihant Publications

10 Practice Sets for NDA Exam

Arihant Publications

NDA Booklist for General Ability

Booklist for General Ability

Name of the books


Objective General English for Competitive Exams

S.P. Baksh

Success Series General Knowledge 

Sachchida Nand Jha

History Of Modern India

Bipan Chandra

Science and Technology in India

Kalpana Rajaram

Apart from the above given list, candidates must also follow the NCERT Class 9-12 Textbooks of all the subjects. Most of the questions asked in the NDA Written Exam are upto 10+12 level. 

For General Awareness, it is important for the aspirants to read the daily newspaper regularly to stay updated with the latest national and international events. NDA Syllabus 2021

Important Preparation Tips for NDA Exam 2021 – NDA Syllabus 2021

The Union Public Service Commission will soon release the NDA exam dates for the year 2021. Since there are are hardly a few days left for the exam aspirants must kick start their preparation by keeping the following tips in mind:

  1. Prepare a daily time table and distribute the syllabus according to the level of difficulty. Doing so will help up the candidates to prepare every topic equally.

  2. Make a habit of solving the previous year question papers on a daily basis. It is very important to know the type of questions asked as well as the difficulty level of the question paper.

  3. Candidates are also advised to visit the official UPSC website for any updates regarding the change of syllabus and exam dates.

  4. Try to note down important formulas and tricks to solve the numerical problems easily and quickly. Also do not enter the examination hall with a stressful mind, this will often lead to creating silly mistakes.

  5. Try to focus on your weak areas and start practicing questions based on those topics regularly. This will help you to get a clear understanding of all the topics.

  6. Try to download the admit card at least five days before the exam to avoid any last minute tension. 

Following these above mentioned tips regularly will definitely help you in passing the exam with flying colours.