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NDA Syllabus 2021: Maths & General Ability Test Syllabus, Exam Pattern

UPSC NDA Syllabus 2021

NDA Syllabus 2021: The Union Public Service Commission (UPSC) conducts the National Defence Academy (NDA) Exam twice a year. It is held for the candidates who want to join the Indian Defence Forces of India. This is one of the most sought-after defence jobs in India to join the Defence of India as an Officer by the male candidates. The selection into NDA is on the basis of the written test followed by the Personality Test. NDA examination is divided into two papers – Mathematics and General Ability Test (GAT).

NDA Syllabus 2021: Highlights

Name of the Exam National Defence Academy (NDA)
Conducting Body  Union Public Service Commission, UPSC.
Frequency Of Exam Twice in a Year
Selection Process
  1. Written Test consisting of Objective Type Questions
  2. Intelligence & Personality Test (SSB)
Mode of exam Offline
Papers in NDA Exam
  1. Mathematics
  2. General Ability Test
Marks Segregation
  1. Mathematics: 300 Marks
  2. GAT: 600 Marks
Total No. of Questions
  1. Mathematics: 120
  2. GAT: 150
Negative Marking
  1. Mathematics: -0.83
  2. GAT: -1.33 marks
Exam Duration 2.5 Hours For Each Paper
Language of Question Paper English & Hindi

UPSC NDA Exam Pattern 2021

Before getting into the NDA Syllabus let us have a look at the NDA Exam Pattern. The NDA Exam Pattern is different from that of the CDS Exam, which is also conducted by the UPSC for selecting meritorious candidates into the Defence Forces of India. The GAT will have English and GK Papers of 200 & 400 marks respectively.

Check out the table for the exam pattern that is given below.

NDA Mathematics Exam Pattern

Paper I- Mathematics
Total Marks 300 Marks
Total No. of Questions 120
Marks awarded for Correct answer 2.5 marks
Marks deducted for the wrong answer -0.83
Exam Duration 2.5 Hours

General Ability Test Exam Pattern

Paper-II- General Ability Test
Total Marks 600 marks
Total No. of Questions 150
No. of questions in English Section 50
No. Of questions in General knowledge Section 100
Maximum Marks for English 200 marks
Maximum Marks for G.K. 400 marks
Marks for Correct Answer 4 marks in both sections
Marks for Incorrect Answer -1.33 marks in both sections
Exam Duration 2.5 Hours


NDA Syllabus 2021: Exam Pattern & Syllabus for Maths, General Ability Test_40.1

NDA Syllabus 2021

After getting to know the NDA Exam Pattern it is important for the candidates to know the Syllabus of the NDA Exam. The NDA Syllabus is discussed below.

NDA Paper I: Mathematics Syllabus

The chapters covered for NDA Maths Syllabus are given in the table below.

Algebra Matrices & Determinants Trigonometry
Differential Calculus Analytical Geometry 2D & 3D Integral Calculus
Differential Equations Vector Algebra Probability

Read the detailed syllabus for the NDA Maths paper discussed below.


  1. Concept of set, operations on sets, Venn diagrams.
  2. De Morgan laws, Cartesian product, relation, equivalence relation.
  3. Representation of real numbers on a line.
  4. Complex numbers—basic properties, modulus, argument, cube roots of unity.
  5. Binary system of numbers.
  6. Conversion of a number in decimal system to binary system and vice-versa.
  7. Arithmetic, Geometric and Harmonic progressions.
  8. Quadratic equations with real coefficients.
  9. Solution of linear inequations of two variables by graphs.
  10. Permutation and Combination.
  11. Binomial theorem and its applications.
  12. Logarithms and their applications.

Differential Calculus

  1. Composite functions, one to one, onto and inverse functions, geometrical and physical interpretation of a derivative – applications, increasing and decreasing functions,
  2. Continuity of functions – examples, algebraic operations on continuous functions,
  3. Application of derivatives in problems of maxima and minima,
  4. Concept of a real-valued function – domain, range, and graph of a function,
  5. The notion of limit, Standard limits – examples, geometrical and physical interpretation of a derivative – applications,
  6. Derivative of a function at a point,
  7. Derivatives of sum, product, and quotient of functions, a derivative of a function with respect of another function, a derivative of a composite function, and Second order derivatives.

Vector Algebra

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

Integral Calculus and Differential equations

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

Matrices and Determinants

  1. Types of Matrices,
  2. Determinant of a matrix, adjoin and the inverse of a square matrix, operations on matrices,
  3. 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:

  1. Distance formula,
  2. Equation of a circle in standard and in general form,
  3. Ellipse, and hyperbola,
  4. The angle between two lines,
  5. Rectangular Cartesian Coordinate system,
  6. Equation of a line in various forms,
  7. Standard forms of parabola,
  8. Distance of a point from a line,
  9. Eccentricity and axis of a conic.
  10. The point in a three-dimensional space, distance between two points,
  11. Equation of a plane and a line in various forms,
  12. Equation of a sphere,
  13. Direction Cosines and direction ratios, the angle between two lines, and the angle between two planes.


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


  1. Outcomes and associated sample space,
  2. Binomial distribution,
  3. Random experiment, examples of random experiments giving rise to
  4. Binominal distribution, events, mutually exclusive and exhaustive events,
  5. Bayes’ theorem – simple problems, impossible and certain events,
  6. Complementary, elementary and composite events,
  7. Union and Intersection of events,
  8. Definition of probability – classical and statistical – examples,
  9. Conditional probability,
  10. Random variable as function on a sample space,
  11. Elementary theorems on probability – simple problems,
  12. Binomial distribution, examples of random experiments giving rise to Binominal distribution.

NDA Syllabus 2021: Exam Pattern & Syllabus for Maths, General Ability Test_40.1

NDA Paper II: General Ability Test Syllabus

The General ability test comprises of two papers:

English 200 Marks
General Knowledge 400 Marks


The question paper in English will be designed to test the candidate’s understanding of English and workman-like use of words. The syllabus covers various aspects like as given below:

  • Grammar and usage
  • Vocabulary
  • Comprehension and cohesion
  • Cloze Test
  • Spotting Errors
  • Sentence Improvement/Correction
  • Para Jumbles
  • Fill in the Blanks
  • Para/Sentence Completion
  • Synonyms-Antonyms
  • Idioms and Proverbs

General Knowledge

General Science
Current Affairs

The topics for each of the subjects are given below.


  1. Physical Properties and States of Matter,  Mass, Weight, Volume, Density and Specific Gravity, Principle of Archimedes, Pressure Barometer.
  2. The motion of objects, Velocity, and Acceleration,
  3. Newton’s Laws of Motion,
  4. Force and Momentum,
  5. Parallelogram of Forces, Stability and Equilibrium of bodies,
  6. Gravitation, elementary ideas of work, Power and Energy.
  7. Effects of Heat, Measurement of Temperature and Heat, change of State and Latent Heat, Modes of transference of Heat.
  8. Sound waves and their properties,
  9. Simple musical instruments.
  10. Rectilinear propagation of Light, Reflection, and refraction.
  11. Spherical mirrors and Lenses, Human Eye.
  12. Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet.
  13. Static and Current Electricity, conductors and Nonconductors,
  14. 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.
  15. 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; Lightening Conductors, Safety Fuses.


  1. Physical and Chemical changes.
  2. Elements, Mixtures and Compounds, Symbols, Formulae and simple Chemical Equations, Law of Chemical Combination (excluding problems).
  3. Properties of Air and Water.
  4. Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon dioxide, Oxidation and Reduction. Acids, bases, and salts.
  5. Carbon—different forms.
  6. Fertilizers—Natural and Artificial.
  7. The material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and GunPowder.
  8. Elementary ideas about the structure of Atom, Atomic Equivalent and Molecular Weights, Valency.

General Science

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

History, Freedom Movement

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


  1. The Earth, its shape and size.
  2. Lattitudes and Longitudes, Concept of time. International Date Line. Movements of Earth and their effects. Origin of Earth.
  3. Rocks and their classification;
  4. Weathering—Mechanical and Chemical, Earthquakes and Volcanoes.
  5. Ocean Currents and Tides Atmosphere and its composition;
  6. Temperature and Atmospheric Pressure, Planetary Winds, Cyclones and Anti-cyclones;
  7. Humidity; Condensation and Precipitation; Types of Climate, Major Natural regions of the World.
  8. 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.
  9. Main items of Imports and Exports of India.

Current Affairs

  1. Knowledge of Important events that have happened in India in recent years.
  2. Current important world events.
  3. Prominent personalities—both Indian and International including those connected with cultural activities and sports.
  4. Award and Honors, Books and Authors, Important Dates, Scientific Research.

NDA Syllabus 2021: Exam Pattern & Syllabus for Maths, General Ability Test_40.1

Intelligence and Personality Test

The SSB procedure consists of two stages: stage I and stage II. Only those candidates who clear the stage I
are permitted to appear for stage II. The details are:

NDA SSB Personality Test
Stage I
  • Officer Intelligence Rating (OIR)
  • Picture Perception Description Test (PP&DT).
Stage II
    • Interview (IO)
    • Group Testing Officer Tasks (GTO)
    • Psychology Tests (Psych)
    • Conference

The various tests of IO, GTO, and Psych are designed to bring out the presence/absence of Officer Like Qualities and their trainability in a candidate. Accordingly, candidates are Recommended or Not Recommended at the SSB.

NDA Syllabus 2021: FAQs

Q. How many stages NDA Exam have?

Ans. There are only two stages, a written exam and a Personality Test or SSB.

Q. How many Papers will be there for NDA Exam 2021?

Ans. There will be two papers for the NDA Exam 2021: Mathematics and General Ability Test (GAT).

Q. What is the General Ability Test?

Ans. General Ability Test or GAT will test the aptitude of the candidates. It will have two papers: English and General Knowledge.

Q. What will be the total marks of the NDA Written Test?

Ans. The total marks of the NDA Written Test will be 900 Marks.

Q. What is the Marks Distribution for the NDA Written test?

Ans. The Mathematics Paper will be of  300 Marks and the GAT will be of 600 Marks.

Q. What is the Marking Scheme for the NDA Exam Written Test?

Ans. For every correct answer, in Mathematics, you get +2.5 marks and for every wrong answer, -0.83 are deducted. For GAT, you will get +4 marks for correct, and for every wrong answer, there is a negative marking of 1.33 marks.

Q. Will the test be conducted online or Offline?

Ans. The NDA Written Test will be conducted offline i.e. Pen and Paper mode.

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