NDA Syllabus 2019
Supriya Kumari, 29 Aug 2019, #NDA

NDA Syllabus 2019 - Union Public Service Commission (UPSC) has prescribed NDA 2019 syllabus along with NDA II notification 2019. Candidates who wish to appear for NDA exam can check the syllabus for both the papers - Paper I Mathematics and Paper II (General Ability Test (GAT). The syllabus of NDA II 2019 is prescribed separately for both the papers where candidates can check topics and sub-topics. By referring to NDA syllabus 2019, candidates can plan well for the exam by knowing the topics from where the question will be asked. NDA II syllabus 2019 for Mathematics will be designed based on class 12 standards. However, the syllabus of GAT will consist of subjects such as Physics, Chemistry, General Science, Social Studies, Geography, Current Events and English language.
Latest: UPSC has released NDA admit card 2019 on October 25. Candidates can download admit card till November 17.

NDA syllabus 2019 will be designed to assess candidates’ basic knowledge about Maths, current affairs, proficiency of English language etc. NDA II 2019 exam is scheduled to be held on November 17, 2019. Check below the detailed NDA II syllabus 2019.

NDA Syllabus 2019 for Mathematics

The syllabus of NDA II for Paper I is given topic-wise. Candidates preparing for NDA II can check the detailed syllabus below.


  1. Representation of real numbers on a line.

  2. Complex numbers—basic properties, modulus, argument, cube roots of unity.

  3. Binary system of numbers.

  4. Conversion of a number in decimal system to binary system and vice-versa.

  5. Arithmetic, Geometric and Harmonic progressions.

  6. Quadratic equations with real coefficients.

  7. A solution of linear inequalities in two variables by graphs.

  8. Permutation and Combination.

  9. Binomial theorem and its applications.

  10. Logarithms and their applications.

  11. Concept of set

  12. Operations on sets

  13. Venn diagrams.

  14. De Morgan laws, Cartesian product, relation, equivalence relation.

Statistics and Probability

  1. Statistics: Classification of data, Frequency distribution, cumulative frequency distribution, Graphical representation Histogram, Pie Chart, frequency polygon, Measures of Central tendency—Mean, median and mode. Variance and standard deviation—determination and comparison. Correlation and regression.

  2. 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 a function on a sample space. Binomial distribution, examples of random experiments giving rise to Binomial distribution.


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

  2. Trigonometric ratios.

  3. Trigonometric identities Sum and difference formulae.

  4. Multiple and Sub-multiple angles. Inverse trigonometric functions.

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

Analytical Geometry of two and three dimensions

  1. Rectangular Cartesian Coordinate system. Distance formula.

  2. Distance formula.

  3. The equation of a line in various forms.

  4. The angle between two lines.

  5. The distance of a point from a line.

  6. The equation of a circle in standard and in general form. Standard forms of

  7. Standard forms of a parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in

  8. Eccentricity and axis of a conic. Point in a three-dimensional space, the distance between two points.

  9. Direction Cosines and direction ratios.

  10. Equation two points. Direction Cosines and direction ratios.

  11. Direction Cosines and direction ratios.

  12. Equation two points. Direction Cosines and direction ratios. The equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

  13. Direction Cosines and direction ratios. The equation of a plane and a line in various forms. The angle between two lines and angle between two planes. The equation of a sphere.

  14. The equation of a plane and a line in various forms. The angle between two lines and angle between two planes. The equation of a sphere.

  15. The angle between two lines and angle between two planes. The equation of a sphere.

Vector Algebra

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

  2. Unit and null vectors, the 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. Applications—work was done by a force and moment of a force and in geometrical problems.

Differential Calculus

  1. The concept of a real-valued function–domain, range and graph of a function.

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

  3. The notion of limit, Standard limits—examples.

  4. Continuity of functions—examples, algebraic operations on continuous functions.

  5. Derivative of the function at a point, geometrical and physical interpretation of a derivative—applications.

  6. Derivatives of sum, product, and quotient of functions, the derivative of a function with respect to another function, derivative of a composite function.

  7. Second-order derivatives.

  8. Increasing and decreasing functions.

  9. Application of derivatives in problems of maxima and minima.

Integral Calculus and Differential Equations

  1. Integration as the 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, the solution of first order and first-degree differential equations of various types—examples.

  5. Application in problems of growth and decay.

Matrices and Determinant

  1. Types of matrices, operations on matrices.

  2. Determinant of a matrix, basic properties of determinants.

  3. 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.

NDA 2019 Syllabus for GAT

Paper II ( General Ability Test) of NDA II 2019 syllabus consists of two parts - Part A: English and Part B: General Knowledge.

NDA syllabus for Part A (English) is designed to test candidates’ proficiency in English which includes grammar and its usage, vocabulary, comprehension and cohesion, etc. Part B is further bifurcated into different sub-section which includes Physics, Chemistry, General Science, Social Studies, Geography and Current Events. Through NDA syllabus 2019 for part B, UPSC evaluates candidates’ knowledge, understanding and expertise in each of the subjects. Check below for the complete NDA II syllabus 2019 of Paper 2: General Ability Test.




Part A - English

Grammar and usage, vocabulary, comprehension and cohesion

Part B (Section A)


Physical Properties and States of Matter, Mass, Weight, Volume, Density, and Specific Gravity, Principle of Archimedes, Pressure Barometer

Motion of objects, Velocity and Acceleration, Newton’s Laws of Motion, Force and Momentum, Parallelogram of Forces, Stability and Equilibrium of bodies, Gravitation, elementary ideas of work, Power and Energy

Effects of Heat, Measurement of Temperature and Heat, change of State and Latent Heat, Modes of transference of Heat

Sound waves and their properties, Simple musical instruments

Rectilinear propagation of Light, Reflection, and refraction

Spherical mirrors and Lenses, Human Eye

Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet

Static and Current Electricity, 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

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

Section B


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

Fertilizers – Natural and Artificial

Material used in preparation of substances such as 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 living and non-living

The basis of Life – Cells, Protoplasms, and Tissues

Growth and Reproduction in Plants and Animals

Elementary knowledge of Human Body and its important organs

Common Epidemics, their causes and prevention

Food – Source of energy for man

Constituents of food, Balanced Diet

Solar System – Meteors, Comets, and Eclipses

Achievements of Eminent Scientists

Section D

History, Freedom Movement etc.

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

Freedom Movement in India

Elementary study of Indian Constitution and Administration

Elementary knowledge of Five Year Plans of 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 Russian Revolution

The impact of Science and Technology on Society

The concept of one World, United Nations, Panchsheel, Democracy, Socialism, and Communism

Role of India in the present world

Section E


Earth: Its shape and size

Latitudes and Longitudes, Concept of time

International Date Line

Movements of Earth and their effects

Origin of Earth

Rocks and their classification; Weathering – Mechanical and Chemical, 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 in India in recent years

Current important world events

Prominent personalities – Indian and International including those connected with cultural activities and sports

NDA Exam Pattern 2019

To prepare for any exam, candidates must know the exam pattern of NDA. As per NDA exam pattern 2019, the written exam will be held for 900 marks. Of the total marks, the Mathematics paper will comprise 300 marks while GAT paper will be conducted for 900 marks. Candidates will be given 2 hours 30 minutes to answer each. After the completion of the written test, candidates qualifying the written exam will be called for SSB Interview. The Interview stage will comprise a total of 900 marks. Candidates can check NDA exam pattern 2019 for written below

NDA Written Exam Pattern 2019



Maximum Marks


2.5 hours


General Ability Test

2.5 hours


Total Marks


How to prepare for NDA 2019

To prepare for NDA, candidates must be well informed about NDA exam pattern 2019 and syllabus. With the help of exam pattern & syllabus, candidates can properly plan their own preparation strategy. While planning they must also keep other important aspects in their mind. Candidates must ensure that they make a proper plan before starting their preparation for NDA exam. Below are few important preparation tips for NDA II written exam 2019.

  1. Solve previous years question papers

  2. Refer to the best books to prepare for NDA

  3. Take online mock test

  4. Revise the topics studied regularly

  5. Practice shortcut methods for solving maths

NDA Answer Key 2019

UPSC will release the answer key of NDA-II 2019 after all stages of the exam have been concluded. However, candidates can check NDA answer keys provided by several coaching institutes right after the written examination ends. NDA answer key 2019 will be published separately for Mathematics and GAT. The official answer key of NDA examination includes question IDs for all sets and their correct answer options. Candidates can calculate their score by counting the number of correct and incorrect responses by checking them against the correct answers provided in NDA answer key.

NDA Cutoff 2019

The exam body will release the cutoff of NDA 2019 along with release of scorecard and marks. NDA cutoff marks are the minimum qualifying marks that a candidate needs to score to qualify. NDA cutoff 2019 will show minimum marks required to qualify in the written examination, SSB interview and total marks out of 1800.

More like NDA

Questions related to NDA

Showing 1348 out of 1348 Questions

Is watch is allowed in NDA exam

Arya 14th Nov, 2019

Hi Mithun,

The National Defense Academy Examination is held twice a year for eligibility to join the Navy, Army and Air Force of India. It is held by UPSC.

According to the rules and regulations of the examination, all electronic devices like phones, calculators, digital watches, phones etc. are prohibited inside the examination hall. However, analog watches are allowed.


I want to crack nda and join armed forces.

Ashish pal Student Expert 14th Nov, 2019

Hello Hitesh.

NDA is among the top rank defence service of India.

If you are interested in NDA or armed forces then focus on three subjects maths physics and English. Maths and English are the primary requirements. And before starting preparation you have to ensure your physical and medical fitness else in the all hard will gone in vain. Once you are physically and medically fit then start your hard preparation you will surely succeed.

Good luck.


sir i have 30+3 marks in phy in std 12 and my all over result is 52%can i apper in nda exam and air force/nevy x-y group sir pls answer

Sharon Rose Student Expert 12th Nov, 2019
Hello Hardik,
The eligibility criteria for NDA is that a candidate must have passed 10+2 with Mathematics, Physics, Chemistry and English as compulsory subjects from a recognised board.
The eligibility criteria for Indian Navy is that a candidate must have passed 10+2 with atleast 60% aggregate with Mathematics, Physics and any one of the Chemistry/biology/ computer science from a recognised board.
The eligibility criteria for Indian airforce/ airmen x-y group is that a candidate must have atleast 50% aggregate in Mathematics, Physics and English together and atleast 50% in English.

You are eligible for NDA and Airmen x-y group.

I hope this is helpful to you.


Payal 10th Nov, 2019

Hii dear

let me clear your doubt.

The Candidates must have to get a minimum sectional cut off of minimum 35% marks to qualify  for nda exam. for final cutoff marks which mean that candidate have to score minimum 105 marks in mathematics section & 210 marks in General Ability Section to be able to qualify for overall cut off for nda exam.

I hope my answer will be helpful for you

Good luck


are gat and maths different exams in nda can one give only gat?

Manidipa Kundu Student Expert 10th Nov, 2019


according to the notification you need to give mathematics and GAT (general ability test) both of the exam . the exam has two papers mathematics and general ability test. mathematics question will be on 10+2 level. in general ability test there will be questions from english, general awareness, physical , history, chemistry.

you may know more details from below link:


The question have been saved in answer later, you can access it from your profile anytime. Access now

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