NDA 2021 Syllabus, Mathematics & General Ability Test (GAT) Syllabus

NDA 2021 SyllabusNDA 2021 Syllabus comprises of Mathematics & General Ability sections. National Defence Academy (NDA) is the Joint Services academy of the Indian Armed Forces. The UPSC (Union Public Service Commission) conducts a national level exam called as NDA Exam. This exam is held for the candidates who want to join Indian Defence Forces (Army, Navy & Air Force). Every year many aspirants come forward to take this exam. NDA Examination will be organized two times in a year. Here, we have updated the complete information about NDA Syllabus 2021.

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NDA Syllabus 2021

Before start NDA preparation, it is very important to introduce yourself with the overall syllabus from where the questions will be raised.

The NDA Exam pattern comprises of Mathematics subject and General Ability. Below we have mentioned the detailed UPSC NDA Syllabus 2021.

Mathematics Syllabus

The Mathematics paper covers the following chapters and topics:

Trigonometry: Trigonometrical ratios,properties of triangles, Angles and their measures in degrees and in radians, Inverse trigonometric functions, Trigonometric identities Sum and difference formulae, Applications – Height and distance, Multiple and Sub-multiple angles.

Algebra: Complex numbers – basic properties, modulus, Conversion of a number in decimal system to binary system and vice-versa, Arithmetic, argument, cube roots of unity, Geometric and Harmonic progressions, Solution of linear inequations of two variables by graphs, Representation of real numbers on a line, Binary system of numbers, Binomial theorem and its application, Quadratic equations with real coefficients, Permutation and Combination, Logarithms and their applications.

Differential Calculus: Composite functions, one to one, onto and inverse functions, geometrical and physical interpretation of a derivative – applications, increasing and decreasing functions, Continuity of functions – examples, algebraic operations on continuous functions, Application of derivatives in problems of maxima and minima, Concept of a real valued function – domain, range and graph of a function, Notion of limit, Standard limits – examples, geometrical and physical interpretation of a derivative – applications, Derivative of a function at a point, Derivatives of sum, product and quotient of functions, derivative of a function with respect of another function, derivative of a composite function and Second order derivatives.

Vector Algebra: Vectors in two and three dimensions, scalar multiplication of vector, scalar product or dot product of two-vectors, Applications-work done by a force and moment of a force, and in geometrical problems, magnitude and direction of a vector, Unit and null vectors, addition of vectors, Vector product and cross product of two vectors.

Integral Calculus and Differential equations: Integration by substitution and by parts, trigonometric, Definition of order and degree of a differential equation, formation of a differential equation by examples, exponential and hyperbolic functions, solution of first order and first degree differential equations of various types – examples, standard integrals involving algebraic expressions, Evaluation of definite integrals – determination of areas of plane regions bounded by curves – applications, General and particular solution of a differential equation, Integration as inverse of differentiation, Application in problems of growth and decay.

Matrices and Determinants: Types of Matrices, Determinant of a matrix, adjoin and inverse of a square matrix, operations on matrices, Applications – Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method, basic  properties of determinant.

Analytical Geometry of two and three dimensions: Distance formula, Equation of a circle in standard and in general form, Ellipse and hyperbola, Angle between two lines, Rectangular Cartesian Coordinate system, Equation of a line in various forms, Standard forms of parabola, Distance of a point from a line, Eccentricity and axis of a conic.

Point in a three-dimensional space, distance between two points, Equation of a plane and a line in various forms, Equation of a sphere, Direction Cosines and direction ratios, angle between two lines and angle between two planes.

Statistics: Frequency distribution, Classification of data, cumulative frequency distribution – examples Graphical representation – Histogram, Measures of Central tendency – mean, median and mode, Pie Chart, Frequency Polygon – examples, Variance and standard deviation – determination and comparison, Correlation and regression.

Probability: Outcomes and associated sample space, Binomial distribution, Random experiment, examples of random experiments giving rise to Binominal distribution, events, mutually exclusive and exhaustive events, Bayes’ theorem – simple problems, impossible and certain events, Complementary, elementary and composite events, Union and Intersection of events, Definition of probability – classical and statistical – examples, Conditional probability, Random variable as function on a sample space, Elementary theorems on probability – simple problems, Binomial distribution, examples of random experiments giving rise to Binominal distribution.

Also Check:

NDA 2021 Admit Card

NDA 2021 Exam Pattern

NDA Preparation Tips

NDA Books

General Ability Syllabus

The general ability section comprises of two parts which are mentioned below:

Part – A

English: The English syllabus covers the topics like vocabulary, Grammar and usage, comprehension and cohesion in extended text to test the candidate’s proficiency in English.

Part – B

General Knowledge: The question paper comprises of general knowledge and covers the subjects that include Physics, Chemistry, Social Studies, General Science, Geography and Current Events.

Click here to check official syllabus.

Section A – Physics

Motion of objects, Newton’s Laws of Motion, Force and Momentum, Parallelogram of Forces, Stability and Equilibrium of bodies, Gravitation, elementary ideas of work, Velocity and Acceleration, Power and Energy, Sound waves and their properties, Simple musical instruments, Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariner’s Compass; Lightening Conductors, Safety Fuses, Simple Pendulum.

Simple Pulleys, Physical Properties and States of Matter, Mass, Weight, Volume, Density and Specific Gravity, Principle of Archimedes, Pressure Barometer, Effects of Heat, change of State and Latent Heat, Modes of transference of Heat, Rectilinear propagation of Light, Reflection and refraction. Spherical mirrors and Lenses. Human Eye, Static and Current Electricity, Measurement of temperature and heat, 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.

Section B – Chemistry

Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon-Di-oxide, Oxidation and Reduction, Material used in the preparation of substances like soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and Gun-Powder, Carbon – different forms, Physical and Chemical changes. Symbols, Formulas and simple Chemical Equations, Law of Chemical Combination (excluding problems). Properties of Air and Water, Acids, bases and salts, Elements, Mixtures and Compounds, Fertilizers – Natural and Artificial, Elementary ideas about the Structure of Atom, Atomic, Equivalent and Molecular Weights, Valency.

Section C – General Science

Basis of Life – Cells, Protoplasms and Tissues, Constituents of food, Balanced Diet, Achievements of Eminent Scientists, Difference between the living and non-living, Elementary knowledge of human Body and its important organs, Food – Source of Energy for man, Growth and Reproduction in Plants and Animals, Common Epidemics, their causes and prevention, The Solar System – Meteors and Comets, Eclipses.

Section D – History

Freedom Movement in India, Bhoodan, Sarvodaya, National Integration and Welfare State, Basic Teachings of Mahatma Gandhi, A broad survey of Indian History, with emphasis on Culture and Civilisation, Elementary knowledge of Five Year Plans of India, Elementary study of Indian Constitution and Administration, Panchayati Raj, Forces shaping the modern world; Renaissance, Exploration and Discovery; War of American Independence, French Revolution, Industrial Revolution and Russian Revolution, Impact of Science and Technology on Society, Concept of one World, United Nations, Panchsheel, Democracy, Socialism and Communism, Co-operatives and Community Development, Role of India in the present world.

Section E – Geography

Origin of Earth, Weathering – Mechanical and Chemical, Earthquakes and volcanoes, Atmosphere and its composition, Temperature and Atmospheric Pressure, Rocks and their classification, Planetary Winds, cyclones and Anti-cyclones, Humidity, Condensation and Precipitation,  Major Natural regions of the World, Important Sea ports and main sea, land and air routes of India. Main items of Imports and Exports of India, Types of Climate, The Earth, its shape and size, Lattitudes and Longitudes, Concept of time, International Date Line, Movements of Earth and their effects, Ocean Currents and Tides, Regional Geography of India – Climate, Natural vegetation. Mineral and Power resources, location and distribution of agricultural and industrial activities.

Section F – Current Events

Current important world events, Knowledge of Important events that have happened in India in the recent years, prominent personalities – both Indian and International including those connected with cultural activities and sports.

It is not compulsory that the topics mentioned above will surely come in the examination. The question paper does not remain consistent, it changes every year. It may happen that the question paper will consists of the topic not discussed here.

In case of any queries regarding NDA 2021 Syllabus, you may ask us by leaving your queries below.

Displaying 1,201 Comments
  1. kaushal kishor says:

    Hello, when I qualified the NDA exzam then what will I do???????

  2. Lohit dubey says:

    NDA is a best exame to join army ,air forse , nevy and to became a offisar.

  3. Anil Kalwaniya says:

    May I have surgery to cure myopia of -2.5 in one eye or glasses are allowed

    As my another eyesight is 0.00

  4. Y.TOHANBA YIM says:

    ST,candidate can apply for NDA o4 not.?

  5. Biswajit says:

    Sir sc candidate ka age kitna lagega.

  6. Rahul says:

    Sir I had completed 12th by commerce without maths can i apply for NDA are i am eligible for it sir
    Please help me……

  7. Tharun says:

    I have eye sight and I am a average student.
    Am I eligible for NDA .?

  8. Hari Krishnan says:

    Sir I’m a commerce student having maths. How can I answer questions related to physics, chemistry and all in the paper?

  9. Your Name...Mukesh gurjar says:

    exam date and sylabus

  10. jaydeep says:

    sir,which language in exam paper?

  11. Your Name... says:

    what about the minimum mark in each part???????????

  12. Abhijeet singh kushwah says:

    Sir my from bio. Stream i have applied for NDA i want to know that in exam would i also have to face mathematics question paper or any other

  13. Vikas mulik says:

    This syllabus can not be covered in 2-3 month

  14. Rathin Biswas says:

    My birthday 15-06-1998.can I apply for NDA?

  15. shilpareddy says:

    I want to know girls are elgeble for these NDA exam?
    imean 12th passed candidates

  16. Ganesh says:

    Is there any negative marking scheme in NDA exam?
    if yes how much is it?

  17. Sankalp Singh says:

    plzzz tell me about the syllabus for commerce stream (contains accounts economic English physical education and business studies ) without maths
    Plzzzz. Reply shortly
    Thank you

  18. ABHISHEK KUMAR says:

    what are the pass marks for nda

  19. anirudh says:

    how many marks are reqiured in 12th std to give
    NDA exam…

  20. RAKESH says:

    Sir kia Ncc Ka koi. Benefit hai

  21. Aamir Hussain says:

    Recently i did pass the examination now i am applying for this commission , so kindly give a further details forthcoming exams for NDA.

  22. Aditya Ranjan says:

    sir i m a commerce student,am i eligible for NDA exam because i even dont have maths.

  23. Bitu Kumar Singh says:

    national defence ACADEMY is my favourite academy

  24. sir iam doing diploma .....sir can i give nda exam says:

    Sir can I give exam by doing 10+diploma

  25. Yazur says:

    Can you provide me with past year NDA cutoffs?

  26. abhinav says:

    now i am studing in 11th and my DOB is 03/10/2000.
    please tell me that can i give the NDA exam.

  27. Gangadhar karadkar says:

    I am belongs to category NT/B and my DOB is 05/04/1998 I asked you me eligible for NDA exam or not
    .please kindly inform me

  28. ranjit pandey says:

    Sir, i am having spacs and wants to join nda. Am i eligible for nda

  29. Anuj mishra says:

    Is their any shorcut way to appear directely…in ssb ..please sir tell me…if is their .

  30. Surajnegi says:

    Sir can u plz give me a link .jisme old qus papers and pura syllabus mil jae .plz sir

  31. Alok Thakur says:

    Sir I m a student of 10 class from CBSE board can I give NDA test in 10th class only or after 10th but the syllabus is not matching so what I do plez. suggest me sir

  32. snehal says:

    i have completed my 12th this yr….[91%]from TS board..
    being a girl candidate, can i write nda exam in sept….
    or only after graduation ….
    pls reply……

  33. rohith says:

    I have passed 12 with PCB strem then how can I appear for mathematics exam how should I prepare

  34. Aravindhan says:

    i’m a diploma 2 year student now, is am i eligible to write the NDA entrance exam before the completion of my course?

  35. anusheel tiwari says:

    is there is all question are MCQs can i appear in the exam while studying in class 12 with maths and commerce

  36. Srajan thukral says:

    Sir i have given exam of 12th with PHY.chem.bio.and applicant for nda exams ,my admit card is with me,on the admit card time table mentioned for both subjects maths and genaral ability.
    Can i miss maths exam?
    Please reply in a short while.

  37. Ankush Kumar says:

    Sir my date of birth is 27-12-1997 can I eligible in september exam

  38. rutvik solanki says:

    fees structure for sc & physical fitness requirement

    • Mohit Negi says:

      The details regarding Fee Structure is mentioned in the article, you must be physically fir with no diseases.

  39. Maninder Singh says:

    why nda exam part(ii) conducted.

  40. Hasanur jaman says:

    I like it

  41. pankaj kumar prasad says:

    sir i am missing my registration code which i took out the print out but now i am missing it.please SIR help me

    • Hanif Khan says:

      may be you can get from the mail id and contact number which you have entered while application form filling.

  42. Rohit says:

    please sir tell me important topics to be covered from math section for NDA 1 2016 I am bio student so in just less than 30 days I have to prepare math to clear NDA written exam

  43. Rohit says:

    sir please tell me Mark wise or question wise destribution of question paper so that i can focus on important topics

  44. yashwanth.M says:

    What are physical fitness required

  45. Sanjay says:

    Kya +2 ke marks se nda ke result par asar padega?

  46. Siddhant says:

    it’s having a colossal syllabus.How can we cover this much syllabus in a short span of time?please help me as i have keen interest in defence field.It is my passion.otherwise its all okkkkkkkkkkkkkkkay………

  47. Pankaj says:

    Wht strategy should be adopt to clear Nda 2016?

  48. KRISHAN GOPAL says:

    My son is having Commerce Stream in 11th Class. How can he take exams of Chemistry, Physics for this NDA 2016? Please clarify.

  49. ARMAN MUJAWAR says:

    my dream is to join defence jobs I know nd a is the way of success then hownmuch hardwork I have do I will try to do sir


  50. krishan says:

    i am in 11class so i am also going to study 12 class syllabus …matrices ,etc.

  51. yoyo virsha munda says:

    Best book for NDA is pathfinder arihant

  52. Your Name...Vandit says:

    I am 10th pass student & I will Complete my Diploma in Mechanical Engineering course in June,2016 am I Elligible?
    & what is pattern of Interviews?

  53. SAYS says:


  54. dip says:

    now I m busy to prepare my HS final yr exm course which held on 15 Feb , but one thing that NDA has vast course so here is only ,1month ,I think if the exm time held on June. , Thnkx

  55. rushi says:

    sir last date ke bad late form submit karna ho to kya karna hoga….

  56. nawaz kohli says:

    Sir please suggest me some books for the preparation of NDA…

  57. what is syllabus for biology students for army branch...plzzz tell me says:

    plz tell me syllabus for biology students for army branch

  58. kumar satwik says:

    my right eye sight is 0.75 and left one is 1.75
    m i elligible for nda ?

  59. Aditya says:

    If i cannot pass it the first time ,
    can i attempt the 2nd exam ??

  60. shibham says:

    which book is preffered to for NDA examination held in 2016

  61. kunal singh says:

    sir i passed +2 2nd div.so can i apply nda writen test 2016.??

  62. stavan sheth says:

    if i clear written test and interview both, in which institute will i be absorbed ? in which state is it ?

  63. prashant jha says:

    Actually I come in the general category
    (brahmin). So what will be my feee if I pass the NDA.

  64. Rajeshwar shinde says:

    How much marks paper is there and what is the difficulty level of the paper and since i am in 11th i will give the paper in september so after clearing the paper what is the process and what i have to do in practicle

    • Sarvgyan Team says:

      NDA 2016 exam consists of 2 papers i.e. Mathematics and General Ability. The Mathematics paper contains 300 marks while General Ability test holds 600 marks. The type of the question paper is objective i.e. for every question four alternatives are provided.

  65. hy mein army ke liye nda krna chahta huu toh kya mathematical aur physics, chemistry ke questions mujhe bhi krne pde ge ************ aur ha sc candidates ke fee kitni ha says:

    [email protected]

  66. Akhil gupta says:

    what is cutoff for nda for gen

  67. Srikanth says:

    What is the fee for NDA exam

  68. Srikanth says:

    For how many marks paper will be conducted

  69. Ben says:

    Im a biology student so am i eligible for the nda exam! Is there any alternative pls inform

  70. Shivendra Singh Tomar says:

    Please suggest me best book NDA math preparation and general ability parapration

  71. Amir bashir says:

    Its having lot of syllabus it cannot cover in 2-3months history should be deleted

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