# What is the UPSC NDA Exam Syllabus

## What is NDA

NDA stands for ( National Defence Academy ) it is the Premier Joint Training Institution and Center for Indian Army Force. In NDA examination there is three type of course i.e. (Indian Army, Indian Air and Indian Navy).  The NDA is located at Khadakwasla near Pune, Maharashtra. NDA examination is conducted by UPSC ( Union Public Service Commission), and The Examination conducts Twice in the year. After that SSB take the interview.

## What is UPSC

UPSC stands for ( Union Public Service Commission ) is Indian centre organisation approval, UPSC conducted the many examinations. Candidates can apply for filling online application by using the UPSC website www.upsconline.nic.in

## Examination Marks pattern for NDA

NDA examination total marks for 900.

SSB test and interview total marks for 900.

Mathematics:-

Mathematics paper total marks for 300.

And duration will be 2½ Hours.

The mathematics paper consists of objective type question only.

General Ability Test:-

General ability test total marks for 600.

And duration will be 2½ Hours.

The General ability test paper consists of objective type question only.

NDA Examination Syllabus

There are two types of examination

• Mathematics
• General Ability Test

Mathematics:-

1. Algebra
2. Trigonometry
3. Differential Calculus
4. Matrices and Determination
5. Analytical Geometry of two and three Dimensions
6. Integral Calculus and Differential Equations
7. Vector Algebra
8. Statistics and Probability

Algebra

Venn Diagrams, Concept of the set, operations on sets. De Morgan laws, relation, equivalence relation, Cartesian product. Complex numbers—basic properties, modulus, and Binary system of numbers. Arithmetic, Geometric and Harmonic progressions. Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications.

Trigonometry

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

Differential Calculus

Composite functions, one to one, onto and inverse functions. Derivative of function at a point, geometrical and physical interpretation of a derivative — applications. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.

Matrices and Determination

Types of matrices, operations on matrices. The determinant of a matrix, basic properties of determinants. Adjoin and the 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.

Analytical Geometry of two and three Dimensions

Distance formula, Angle between two lines, Distance formula, Distance of a point from a line, Direction Cosines and direction ratios, Angle between two lines and an angle between two planes, the distance between two points, Standard forms of parabola, ellipse and hyperbola.

Integral Calculus and Differential Equations

Evaluation of definite integrals—determination of areas of plane regions bounded by curves—applications. Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. General and particular solution of differential equations, the solution of first order and first-degree differential equations of various types—examples. Application in problems of growth and decay.

Vector Algebra

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

Statistics and Probability

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

Probability: Random variables function on a sample space. Binomial distribution, examples of random experiments giving rise to Binominal distribution. 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.

General Ability Test

In General ability test there are two types of test they are:-

• English
• General Knowledge

English

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 Grammar and usage, vocabulary, comprehension and cohesion in extended text to test the candidate’s proficiency in English.

General Knowledge

• Physics
• General Science
• Chemistry
• Geography
• Current Events

Physics

The 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.

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

Elementary knowledge of human body and its important organs.

Food—Source of Energy for man. Constituents of food, Balanced Diet.

The Solar System—Meteors and Comets, Eclipses.

The difference between the living and non-living.

The basis of Life—Cells, Protoplasms and Tissues.

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.

Geography

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. Important Sea ports and main sea, land and air routes of India. Main items of Imports and Exports of India. The Earth, its shape and size. Latitudes and Longitudes, Concept of time. International Date Line. Movements of Earth and their effects.

Current Events

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

Current significant world events.

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

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