**National defence Academy & naval academy****Syllabus**

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.

Sections

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

**1.Algebra**

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 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.** 4.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.**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

Trigonometric,

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

Events

Mutually Exclusive and Exhaustive Events

Impossible and Certain Events

Union and Intersection of Events

Complementary

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

Vocabulary

Comprehension and Cohesion In Extended Text

Use of Words**Part B-GENERAL KNOWLEDGE Paper**

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. **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.

**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 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**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**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