NATIONAL DEFENCE ACADEMY & NAVAL ACADEMY EXAMINATION (II)

(Commission's Website http://www.upsc.gov.in)

**SCHEME OF EXAMINATION**

1. The subjects of the written examination, the time allowed and the maximum marks allotted to each subject will be as follows :–

Code 01: Mathematics

Duration: 2-½ Hours

Maximum Marks : 300

Code 02: General Ability Test

Duration: 2-½ Hours

Maximum Marks : 600

Total Marks : 900

SSB Test/Interview Marks : 900

THE PAPERS IN ALL THE SUBJECTS WILL CONSIST OF OBJECTIVE TYPE QUESTIONS ONLY. THE QUESTION PAPERS (TEST BOOKLETS) OF MATHEMATICS AND PART "B" OF GENERAL ABILITY TEST WILL BE SET BILINGUALLY IN HINDI AS WELL AS ENGLISH.

SYLLABUS OF THE EXAMINATION

PAPER-I

**MATHEMATICS**

(Code No. 01)

(Maximum Marks- 300)

**1) ALGEBRA :**

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. 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. 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. Equation of a plane and a line in various forms. Angle between two lines and 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. 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 a derivative - applications. Derivatives of sum, product and quotient of functions, derivative of a function with respect to 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 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 a 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, 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.

PAPER-II

**GENERAL ABILITY TEST**

(Code No. 02)

(Maximum Marks-600)

**Part ‘A’ - ENGLISH (Maximum Marks 200)**

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.

**Part ‘B’ - GENERAL KNOWLEDGE**

(Maximum Marks-400)

The question paper on General Knowledge will broadly cover the subjects : Physics, Chemistry, General Science, Social Studies, Geography and Current Events. The syllabus given below is designed to indicate the scope of these subjects included in this paper. The topics mentioned are not to be regarded as exhaustive and questions on topics of similar nature not specifically mentioned in the syllabus may also be asked. Candidate’s answers are expected to show their knowledge and intelligent understanding of the subject.

**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 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.

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 the 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 appoximately 25%, 15%, 10%, 20%, 20% and 10% weightages respectively.

**Intelligence and personality test**

In addition to the interview the candidates will be put to Intelligence Tests both verbal and non-verbal, designed to assess their basic intelligence. They will also be put to Group Tests such as group discussions, group planning, outdoor group tasks, and asked to give brief lectures on specified subjects. All these tests are intended to judge the mental calibre of a candidate. In broad terms, this is really an assessment of not only his intellectual qualities but also his social traits and interests in current affairs.

For complete details visit:

http://164.100.9.113/mainmenu2.php

http://164.100.9.113/mainmenu2.php

**About National Defence Academy (NDA)**

National Defence Academy (NDA) Entrance Exam

Introduction

NDA (National Defence Academy) test is organized twice in a year for admission in Indian Army, Navy and Air Force wings. The entrance exam is conducted by the Union Public Service Commission. The course of training is for three years. The applicants joining the Indian Naval Academy would have to undergo 4 years B.Tech course and would also be given an opportunity to join Technical Branch of the Navy subject to availability of vacancies.

To enroll for the admission, one needs to go through several rounds to make it into an Indian Military force. The NDA test includes a written examination, multiple rounds of interviews, group discussions and a medical test. Applicants are invited from any part of the state across India to appear in the exam. However, to score well in the exam, one needs to put extra efforts to clear the test.

Eligibility Criteria for Admission in NDA Entrance Exam

• The candidates should be more than 16 or ½ years of age and less than 19 years at the time of appearing for the test.

• Only unmarried candidates can apply for the exam.

• You must be medically and physically fit for the program and the test as per the specification given in the application form.

Educational Qualifications:

• The candidates should clear their 10+2 level from a recognized school or board and the candidate who all is appearing for 10+2 exam can also apply.

• To get an admission into Navy and Air force wings, candidates should have Physics and Mathematics as a part of their curriculum in 10+2 level.

Examination Pattern of NDA Entrance Exam

• There will a written test examination that covered two sections - Mathematics and General Ability Test. Time frame would be 2 ½ hrs for each.

• All the questions would be an objective type of questions. Both the sections of the test will be set bilingually in National language Hindi and other language English.

• The candidates have to attempt questions related to the metric system of Weights and Measures. These questions are included wherever necessary in the test.

• The candidates are restricted to use any tech. application such as calculator or any Mathematic table while attempting objective type papers.

How to Apply

To enroll for the exam, candidates can collect the Application Form designed by the Commission for the examination, from the Designated Head Post Offices/Post Offices (specified in Appendix III of the notice) throughout the country with cash payment of Rs. 20/- (Rupees Twenty only). Each such form can be used only once and only for oneexamination.

Candidates are advised to read carefully the "Instructions for filling up theApplication Form" as per the instruction given in the form.

For further Information visit: http://upsc.gov.in/

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