National defence Academy & naval academy


NDA Syllabus comprises of Mathematics & General Ability sections. National Defence Academy (NDA) Entrance Exam Is Conducted by Union Public Service Commission (UPSC) For Enrolling Candidates to The Indian Defence Forces That Includes Indian Army, Indian Navy, And Indian Air Force. The National Defence Academy (NDA) Exam Is Carried Out Twice in A Year. NDA (I) In the Month of April And NDA (II) In the Month of September.

Both the National Defence Academy (NDA) 1 And National Defence Academy (NDA) 2 Exam Consist of Two Papers. The first One Is Mathematics and The Second One Is General Ability Test.
Mathematics: The Mathematics Paper Carries Out 300 Marks and Consists of Mcqs Based on The Syllabus of Class 10th, 11th, And 12th. The Duration of This Exam Will Be 2.5 Hours. There Is Also A Negative Marking for The Wrong Responses Given by Candidates.
General Ability: In This Part There Are Two Sections. The first Section Is of English with 200 Marks and The Second Section Consists of General Knowledge With 400 Marks.
The Paper Will Be of Multiple Choice Question with Four Options in Which Candidates Have to Choose the Correct One.
There Will Be 120 Questions Of 300 Marks in Paper I and 150 Questions Of 600 Marks in Paper II.
Marks for SSB Interview Is 900 Marks

Mathematics Syllabus

Trigonometry: trigonometric proportions, properties of triangles, angles and their measurements in degrees and radians, inverse trigonometric functions, trigonometric identities, sum and difference formulas, applications – height and distance, multiple angles and submultiples.

Algebra: complex numbers – basic properties, module, conversion of a decimal system number into a binary system and vice versa, arithmetic, argument, cubic roots of the unit, geometric and harmonic progressions, solution of linear inequalities 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.
Vector algebra: Vectors in two and three dimensions, scalar multiplication of vector, scalar product or scalar product of two vectors, Applications-work done by a force and a moment of a force, and in geometric problems, magnitude and direction of a vector, unit and null vectors, vector addition, vector product and crossed product of two vectors.

Integral calculus and differential equations: Substitution and part integration, trigonometric, Definition of the order and degree of a differential equation, formation of a differential equation by examples, exponential and hyperbolic functions, solving of differential equations of prime order and first degree of different types – examples, standard integrals involving algebraic expressions, evaluation of definite integrals – determination of areas of planar regions delimited by curves – applications, general and particular resolution of a differential equation, Integration as inverse of differentiation, application in the problems of growth and decay.

Matrices and Determinants: Matrix types, matrix determinants, adjacent 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 the Matrix Method, determining.

Concepts (Topics)
Concept of A 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.
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 Application
Logarithms and Their Applications.

2.Matrices and Determinants
Types of Matrices
Operations on Matrices Determinant of A Matrix
Basic Properties of Determinant.
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.Analytics Geometry of Two And Three Dimensions
Rectangular Cartesian Coordinate System
Distance Formula
Equation of A Line in Various Forms
Angle Between Two Lines
Distance of A Point from A Line
Equation of A Circle in Standard and In General, Form
Standard Forms of Parabola
Ellipse and Hyperbola
Eccentricity and Axis of A Conic
Point in a Three-Dimensional Space, Distance between Two Points.
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.

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.

5.Differential Calculus
Concept of A Real-Valued Function – Domain
Range and Graph of A Function
Composite Functions
Derivative of 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
Second Order Derivatives
Increasing and Decreasing Functions
Application of Derivatives in Problems of Maxima and Minima.

6.Integral Calculus
Integration as Inverse Differentiation
Integration by Parts And Substitution
Standard Integrals Involving
Expression of Algebraic,
Hyperbolic and Exponential Function
 Evaluation of Definite Integrals – Determination of Areas of Plane Regions Bounded by Curves – Applications.

7. Differential Equations
Definition of Order and Degree Of A Differential Equation
Formation of A Differential Equation\General and Particular Solution of A Differential Equation
Solution of First Order and First Degree Differential Equations of Various Types
Application in Problems Of Growth And Decay

8. 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

9 Probability
Random Experiment
Outcomes and Associated Sample Space
Mutually Exclusive and Exhaustive Events
Impossible and Certain Events
Union and Intersection of Events
Elementary and Composite Events
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.

10 Vector Algebra
Vectors in Two and Three Dimensions
Magnitude and Direction of A Vector
Unit and Null Vectors Addition of Vectors
Scalar Multiplication of Vector

Subject – General Ability (Paper 2)

This Paper Is Divided into Two Parts. Part A (English Paper) And Part B (General Knowledge Paper)

Part A –English Paper
English Section
Grammar and Usage
Comprehension and Cohesion In Extended Text
Use of Words


The question paper on General Knowledge will broadly cover the subjects: Physics, Chemistry, General Science, Social Studies, Geography and Current Events. General Knowledge section carries a score of 400 with 100 questions. 


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.


 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 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

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 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

Social Studies

A broad survey of Indian History
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


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

Current Events
Knowledge of Important events that have happened in India in the recent years

Current important world events

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


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