IMPORTANT INFORMATION FOR NDA EXAMINATION
Tentative Vacancies Per Course 
Approx 400+ (Twice a year)
For 2021, there are 418 Vacancies:
 National Defence Academy: 370 to include 208 for Army, 42 for Navy and 120 for Air Force (including 28 for ground Duties)
 Naval Academy (10+2 Cadet Entry Scheme): 48

Notification in Employment News/ leading daily news Paper/ UPSC website 
Jun and Dec 
ELIGIBILITY CRITERIA 
Age and Marital Status 
Between 16 ½ to 19 ½ yrs as of first day of the month in which course is due to commence.
For 2021, NDA 1
 Only unmarried male candidates born not earlier than 02nd July, 2001 and not later than 1st July, 2004 are eligible.

Qualification 
 For Army Wing of National Defence Academy: 12th Class pass of the 10+2 pattern of School Education or equivalent examination conducted by a State Education Board or a University.
 For Air Force and Naval Wings of National Defence Academy and for the 10+2 Cadet Entry Scheme at the Indian Naval Academy :12th Class pass of the 10+2 pattern of School Education or equivalent with Physics and Mathematics conducted by a State Education Board or a University.
 Candidates who are appearing in the 12th Class under the 10+2 pattern of School Education or equivalent examination can also apply

Likely SSB Date 
Sep to Oct and Jan to Apr 
Date Commencement of Training 
Jan and Jul of every year 
Training Academy 
National Defence Academy, Khadakvasla, Pune 
Duration of Training 
3 Yrs at NDA.
After completion of NDA Training Cadets undergo training at respective Academies: 1 Yr at IMA (For Army cadets)/ 1 Yr at Naval Academy (for Naval cadets)/ 1½ Yrs at AFA Hyderabad (For AF cadets) 
NDA Exam Pattern
The Competitive examination comprises:
 Written examination
 Interview for intelligence and personality test – SSB interview at one of the Services Selection Centres
The subjects of the written examination, the time allowed and the maximum marks allotted to each subject is as follows
Subject

Code

Duration

Maximum Marks

Mathematics 
01 
2½ Hours 
300 
General Ability Test 
02 
2½ Hours 
600 
Total 


900 
SSB Test/Interview 


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
PAPERI MATHEMATICS (Code No. 01) (Maximum Marks300)
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 viceversa.
 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, ApplicationsSolution 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 Submultiple angles. Inverse trigonometric functions. ApplicationsHeight 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 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.
PAPERII 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.
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 Nonconductors, Ohm’s Law, Simple Electrical Circuits, Heating, Lighting and Magnetic effects of Current, Measurement of Electrical Power, Primary and Secondary Cells, Use of XRays.
 General Principles in the working of: 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 GunPowder. Elementary ideas about the structure of Atom, Atomic Equivalent and Molecular Weights, Valency.
Section ‘C’ (General Science)
 Difference between the living and nonliving. 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, Cooperatives 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. Latitudes 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 Anticyclones; 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 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 approximately 25%, 15%, 10%, 20%, 20% and 10% weightages respectively.