NDA EXAM SYLLABUS

 

NDA Mathematics syllabus 2022

1. 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 decimal system to binary system and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications.

2. MATRICES AND DETERMINANTS: Types of matrices, operations on matrices. Determinant 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.

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

4. 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 a 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.

5. 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 derivative applications. Derivatives of sum, product and quotient of functions, the derivative of a function with respect to another function, the derivative of a composite function. Second-order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.

6. 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 solution of differential equations, solution of first order and first degree differential equations of various types - examples. Application in problems of growth and decay.

7. 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.

8. 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 Binominal distribution.

NDA Syllabus 2022 - General Aptitude Test (GAT)

For the NDA GAT syllabus 2022, candidates must have knowledge of basic English, Environmental Studies and Science and Technology subjects. Students need to have understanding of all the topics of NDA GAT syllabus 2022 to crack the NDA General Aptitude sections. To know more about the NDA GAT syllabus, check the details mentioned in the table that is given below.

NDA GAT Syllabus 2022

Section A (Physics): 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 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.

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 Carbondioxide, Oxidation and Reduction. Acids, bases and salts. Carbon different forms. Fertilizers Natural and Artificial. 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 non-living. 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 - 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. 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. 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. Lattitudes 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 Anti-cyclones; 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 recent years. Current important world events. Prominent personalities - both Indian and International including those connected with cultural activities and sports.

Note: Out of maximum marks assigned to part ‘B’ of this paper, questions on Sections ‘A’, ‘B’, ‘C’, ‘D’, ‘E’ and ‘F’ will carry approximately 25%, 15%, 10%, 20%, 20% and 10% weightage respectively.

Intelligence and Personality Test

The SSB procedure consists of a two-stage Selection process - stage I and stage II. Only those candidates who clear stage I are permitted to appear for stage II. The details are :

(a) Stage I comprises of Officer Intelligence Rating (OIR) tests are Picture Perception * Description Test (PP&DT). The candidates will be shortlisted based on the combination of performance in the OIR Test and PP&DT.

(b) Stage II Comprises of Interview, Group Testing Officer Tasks, Psychology Tests and the Conference. These tests are conducted over 4 days. The details of these tests are given on the website joinindianarmy.nic.in.

The personality of a candidate is assessed by three different assessors viz. The Interviewing Officer (IO), Group Testing Officer (GTO) and the Psychologist. There is no separate weightage for each test. The mks are allotted by assessors only after taking into consideration the performance of the candidate holistically in all the tests. In addition, marks for Conference are also allotted based on the initial performance of the Candidate in the three techniques and decisions of the Board. All these have equal weightage.

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.

UPSC provides the  NDA exam pattern 2022  in the official notification along with the syllabus of NDA 2022. According to the NDA exam pattern 2022, there will be two papers - Mathematics and GAT consisting of a total number of 120 questions and 150 questions respectively. The total time duration for each paper of NDA 2022 is 2 hours and 30 minutes. Check the brief exam pattern of NDA 2022 in the table that is given below.

NDA 2022 exam pattern

Papers	Subject	Mark per question	No. of Questions	Maximum marks	Duration
Paper 1	Mathematics	2.5 marks	120	300	2 hours 30 minutes
Paper 2	GAT	4 marks	150	600	2 hours 30 minutes
Total			270	900	5 hours

DR OMAR CLASSES BARRA KANPUR

To begin with, the NDA entrance exam syllabus has two sections for the written exam, General Ability Test (GAT) and Mathematics. GAT aims to test your basic knowledge of History, GK, Current Affairs of National and International Events, English, Science, and Geography. On the other hand, the Mathematics paper of NDA will have questions based on 10+2. The GAT paper holds the maximum weightage of 600 marks while the Mathematics section is for 300 marks. Lastly, UPSC will conduct the SSB/Interview for the candidates who obtain the cut off marks in the written exam. 

This post informs you about the detailed syllabus for the UPSC NDA 2022 exam. Knowing the syllabus will help you to plan a strategy to ace the exam, thereby, setting the right direction for your preparation for the exam. You can also download the official NDA Syllabus PDF in this post like the History syllabus for NDA.

NDA Syllabus 2022 Overview

Before jumping onto the NDA Syllabus 2022 you must get an idea about its pattern, frequency, and other relevant details. Check out the table given below presents a brief idea of the NDA entrance exam syllabus. 

Name of the Exam	National Defence Academy, NDA
Exam Conducting Body	Union Public Service Commission, UPSC
Frequency of NDA Exam	Two times a year (NDA 1 & NDA 2)
Selection Process	Written Test consisting of Objective Type Questions 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
Official Website	www.upsc.gov.in

NDA Subjects

NDA exam subjects are basically dived into two categories  Mathematics and General ability test. The general ability part of NDA subjects contains questions from different various topics such as General Knowledge (GK), English, Chemistry, Physics, Geography, General Science, and Current Events.

NDA Syllabus 2022: Mathematics, GAT & SSB Pattern

It is important to first get acquainted with the pattern of the UPSC NDA syllabus as per the latest official notification. As you know NDA comprises two papers, Mathematics and GAT for 200 marks and 400 marks respectively, therefore, here is the exam pattern to understand the marking scheme. 

NDA Mathematics Exam Pattern

Total Marks for NDA Mathematics paper	300 Marks
Total No. of Questions	120
Correct Answer	2.5 marks
Marks deducted for the wrong answer	-0.83
Total duration of Mathematics Paper	2 Hours 30 Minutes

NDA GAT Exam Pattern

The NDA GAT Paper will comprise of the following subjects: 

• English 

• Physics

• Chemistry

• General Science

• History, Freedom Movement, etc.

• Geography

• Current Affairs

Here is the NDA GAT marking scheme. 

Total Marks for NDA GAT Paper	600 marks
Total No. of Questions	150 Questions
Total questions in English	50 Questions
Total Questions in GK	100 Questions
Total Marks for English	200 marks
Total Marks for GK	400 marks
Marks for Correct Answer	4 marks in each section
Marks for Incorrect Answer	-1.33 marks in each section
Total Duration of GAT Paper	2 Hours 30 Minutes

NDA SSB Exam Pattern

The NDA SSB/Interview is the last stage of the exam pattern for the UPSC NDA recruitment process. Candidates who will obtain the NDA Cut Off marks in the written exam will only be eligible to appear for the NDA SSB/Interview round. Given below is the table depicting the NDA SSB pattern explaining the stages in it. 

Stage 1	Picture Perception * Description Test (PP&DT).
Stage 2	Interview Group Testing Officer Tasks Psychology Tests Conference

Now that you have known the exam pattern and marking scheme for both paper 1 and paper 2, i.e. Mathematics and GAT, it is time to know the detailed NDA entrance exam syllabus. Here, we have described the NDA syllabus 2022 for both Mathematics and GAT papers. You will topic wise important topics that have high weightage in the UPSC NDA exam. 

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NDA GAT Syllabus 2022

The NDA GAT Paper holds the maximum weightage. Hence, you should be thoroughly prepared to answer a  maximum number of questions for the NDA General Ability Test Paper. Check the NDA GAT syllabus below section wise. 

NDA English Syllabus 

The NDA English Syllabus is given below in the table. Check the important topics for the NDA exam for English below. 

Subject	Syllabus
English	Grammar & usage Comprehension & cohesion Spotting of errors Para Jumbling Fill in the blanks Synonyms & Antonyms Vocabulary Cloze Test Idioms & Proverbs Completion of Sentence & Para Sentence Correction & Improvement

NDA GK Syllabus

The NDA GK Syllabus will cover the following subjects in it. We have given the NDA Syllabus for GK for the following subjects below. 

|| Physics, Chemistry, General Science, Social Studies, Geography, and Current Events ||

NDA Syllabus for Physics

The NDA Physics Syllabus is given below in the table. Check the important topics for the NDA exam for Physics below. 

Subject

Syllabus

Physics

Matter and its properties(mass, weight, etc)and specific gravity, Archimedes principle, Motion, Velocity and Acceleration, Newton's Laws of Motion, Force and Momentum, Force Parallelogram, Stability, and Body Equilibrium, Gravity, Elementary Work Ideas, Power and Energy. Heat effects, temperature, and heat measurement, state change, latent heat, heat transfer modes. Rectilinear light, reflection, and refraction propagation. Spherical mirrors and human eye lenses. Natural and artificial magnets, a magnet's properties, earth as a magnet. Electricity, Ohm's Law, conductors and non-conductors, Simple Electrical Circuits, Current Heating, Lighting and Magnetic Effects, Electrical Power Measurement, Primary and Secondary Cells, X-Ray Use. Simple Pendulum, Simple Pulleys, Telegraph, Telephone, Periscope, Telescope, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Microscope, Mariner's Compass.

NDA Syllabus for Chemistry

The NDA Chemistry Syllabus is given below in the table. Check the important topics for the NDA exam for Chemistry below. 

Subject

Syllabus

Chemistry

Changes in physical and chemical conditions. Chemical Combination Law. Air and water properties. Hydrogen, oxygen, nitrogen, and carbon dioxide preparation and properties, oxidation, and reduction. Acids, bases, salts, etc. Carbon— various forms. Fertilizers— Artificial and Natural. Material used in the preparation of substances such as Soap, Glass, Ink, Paper, Cement, Paints, Gun-Powder and Safety Matches. Basic ideas on Atom, Atomic Equivalent and Molecular Weights structure, Valence.

NDA General Science Syllabus

The NDA General Science Syllabus is given below in the table. Check the important topics for the NDA exam for GS below. 

Subject	Syllabus
General Science	Living and non-living differences. Life basis — cells, protoplasms, tissues. Plant and animal growth and reproduction. Human Body's basic knowledge and its important organs. Common epidemics, causes, and prevention of them. Food — man's energy source. Food constituents, balanced diet. Meteors and Comets Solar System, Eclipses. Eminent Scientists ' achievements.

NDA History Syllabus

The History syllabus for NDA is given below in the table. You should make sure to study the topics of Indian Polity and National Movement in great detail.

Subject

Syllabus

History

A comprehensive survey of Indian History, focusing on culture and civilization. Freedom movement. Indian Constitution and Administration elementary study. India's Five Year Plans. Panchayati Raj, Community Development Co-operatives. Bhoodan, Sarvodaya, Mahatma Gandhi's Basic Teachings, National Integration and Welfare State. Modern world forces; Renaissance, Exploration, and Discovery; American Independence War. French Revolution, Russian Revolution, and the Industrial Revolution. Impact on society of science and technology. One World Concept, UN, Panchsheel, Democracy, Socialism, and Communism. India's role in today's world.

NDA Syllabus for Geography

The NDA Geography Syllabus is given below in the table. Check the important topics for the NDA exam for Geography below. 

Subject

Syllabus

Geography

The shape and size of the Earth. Lattitudes, Longitudes, Time Concept. Date-Line International. Earth's movements and effects. Earth's origin. Rocks and their classification; mechanical and chemical weathering, earthquakes, and volcanoes. Ocean Currents and Tides Atmosphere and their composition; Temperature and Atmospheric Pressure, Planetary Winds, Cyclones, and Anti-cyclones; Humidity; Condensation 23 and Precipitation; Climate Types, World's Major Natural Regions. India's regional geography— climate, natural vegetation. Resources for minerals and power; location and distribution of agricultural and industrial activities. Important seaports and major seaports, land, and air routes

NDA Current Affairs Syllabus 

The NDA Current Affairs Syllabus is given below in the table. You must go through the latest current affairs events of India and the world. The current affairs of the last 8 to 12 months should be studied in great detail.

Subject	Syllabus
Current Events	Knowledge of major events that have occurred in India over the past few years. Important exercises conducted between countries worldwide with special reference to India Current major events in the world. Latest appointments Important personalities around the world including those related to cultural and sports activities

NDA Mathematics Syllabus 2022

You must take note that the NDA mathematics syllabus is based on the 10+2 level. Hence, you must have a good knowledge of the formulas and concepts of all the important topics. Here is the syllabus for the NDA Mathematics paper. 

Name of Topic	Subtopics
Algebra	Set concept, sets operations, Venn diagrams. Laws of De Morgan, Cartesian product, relationship, the relationship of equivalence. Real number representation on a line. Complex numbers— basic properties, module, argument, unity cube roots. Binary number system. Conversion to the binary system of a number in the decimal system and vice versa. Progressions in arithmetic, geometry, and harmony. Real-coefficient quadratic equations The solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications.
Matrices and Determinants	Matrix types, matrix operations. The determinant of a matrix, determinants ' properties. Application-Solution of a system of linear equations in two or three unknowns by the Cranmer's Rule and by the Matrix method
Trigonometry	Angles and their degree and measurements. Trigonometric ratios. Sum of trigonometric identities and formulas. Multiple angles and sub-multiples. Trigonometric functions & their inverse. Applications-Height and Distance, Triangle Properties.
Analytical geometry of two and three dimensions	The Cartesian Rectangular Coordinate System. Formula of distance. Equation of a line in different shapes. Two lines of angle. A point's distance from a line. Standard and general equation of a circle. Parabola, ellipse, and hyperbola are standard forms. A conic's eccentricity and axis. Point the distance between two points in a three-dimensional space. Cosines of direction and ratios of direction. Two points of the equation. Cosines of direction and ratios of direction. A plane equation and a line in different forms. Two lines of the angle between two planes. Sphere's equation.
Differential calculus	Concept of a valued function–a function's domain, range, and graph. Composite functions, one by one, on, and vice versa. Limit notion, default limits — examples. Continuity of functions— examples, continuous functional algebraic operations. Function derivative at a point, geometric and physical interpretation of an application derivative. Summary derivatives, product, and function quotient derivatives, function derivatives for another function, 20 composite function derivatives. Derivatives of the second order. Increasing and diminishing functions. Application of derivatives in maxima and minima problems.
Integral Calculus and Differential Equations	Differentiation and integration, standard integrals with algebraic expressions, trigonometric, exponential, and hyperbolic functions.Definite integrals — determination of areas of curved plane regions — applications. General and particular solution of differential equations, solution of the first order, and 1st-degree differential equations of various types—examples. Application in problems of growth and decay.
Vector Algebra	2D and 3D vectors, vector magnitude, and direction. Unit and null vectors, vector adding, scalar-vector multiplication, scalar product or dot product, vector product, or cross product. Applications — work done through force and moment of force and in geometric problems.
Statistics & Probability	Statistics: data classification, distribution of frequencies, the cumulative distribution of frequencies — examples. Examples of graphic representation— histogram, pie chart, polygon frequency. Central tendency measurements — mean, median, and mode. Variance and deviation of standard — determination, and comparison. Correlation and regression  Sample space, events, exhaustive events & mutually exclusive, impossible and certain events associated with random experiments, results and associated. Union and events intersection. Complementary, composite, and elementary events.  Probability definition— classical and statistical— examples. Elementary probability theorems — simple issues. The conditional likelihood, the theorem of Bayes — simple problems. Random variable on a sample space as a function. Binomial distribution, examples of random experiments, the binomial distribution.