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NDA 2 - Syllabus

National Defence Academy and Naval Academy Examination 2 2021

Form Date: 09 Jun - 29 Jun 2021

Pen & Paper Mode

Updated On - January 11 2021 by Anusha Pachauri

The candidates must have the complete knowledge of NDA 2 2021 Syllabus before starting their preparation for the exam. UPSC NDA exam syllabus comprises of two papers: Mathematics (Paper 1) and General Ability Test (Paper 2).

- Concept of set, Cartesian product, operations on sets, Venn diagrams, equivalence relation, De Morgan laws, relation.
- Complex numbers—basic properties, cube roots of unity, modulus, argument, Representation of real numbers on a line, Binary system of numbers.
- Arithmetic, Harmonic, Geometric progressions, Conversion of a number in decimal system to binary system & vice-versa.
- A solution of linear inequations of two variables by graphs, Quadratic equations with real coefficients.
- Binomial theorem and its applications, Permutation and Combination, Logarithms and their applications.

- Operations on matrices, Types of matrices, Adjoint and the inverse of a square matrix, The determinant of a matrix, basic properties of determinants.
- Applications, SOS of linear equations in two or three unknowns by Matrix Method and by Cramer’s rule.

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

- Rectangular Cartesian Coordinate system, The angle between the two lines, The distance of a point from a line, Distance formula, Equation of a line in various forms.
- Equation of a circle in standard & general form, Eccentricity and axis of a conic, Standard forms of parabola, ellipse & hyperbola.
- The point in a three-dimensional space, Equation two points, distance between two points, Direction Cosines and direction ratios, Direction Cosines & direction ratios.
- Equation of a plane & a line in various form, Equation of a spheres, The angle between the two lines & the angle between the two planes.

- Concept of a real-valued function–domain, one to one, onto and inverse functions, Notion of limit, range and graph of a function, Composite functions, Standard limits—examples.
- Continuity of functions—examples, geometrical & physical interpretation of a derivative—applications, algebraic operations on continuous functions, Derivative of function at a point.
- Derivatives of sum, a derivative of a composite function, Second-order derivatives, product and quotient of functions, a derivative of a function concerning another function.
- Application of derivatives in problems of maxima & minima, Increasing and decreasing functions.

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

- Magnitude and direction of a vector, Unit and null vectors, Vectors in two and three dimensions, scalar product or dot product of two vectors, the addition of vectors, scalar multiplication of a vector.
- Cross product or the Vector product of two vectors. Applications on work done by a force and moment of a force and in geometrical problems.

(i).** Statistics:** Classification of data, cumulative frequency distribution, Frequency distribution with examples. Graphical representation of Histogram, frequency polygon, Pie Chart with examples.

- Variance & standard deviation. Measures of Central tendency—Mean, mode and median, Correlation and regression.

(ii).** Probability: **Outcomes & associated sample space, random experiment, events, mutually exclusive & exhaustive events, impossible & certain events, Union & Intersection of events.

- Complementary, elementary and composite events, Elementary theorems on probability based on simple problems, Definition of probability in classical & statistical with examples.
- Conditional probability, Binomial distribution, examples of random experiments giving rise to Binominal distribution, Bayes’ theorem based on simple problems, Random variable as function on a sample space, .

**PART A - English:**Comprehension & cohesion in extended text, Grammar and usage, vocabulary to test the candidate’s proficiency in English.**PART B - General Knowledge:**The exam paper on General Knowledge will broadly cover the following subjects :

(i).** Section A (Physics)**

- Physical Properties and States of Matter, Principle of Archimedes, Pressure Barometer, The motion of objects, Velocity and Acceleration, Mass, Weight, Volume, Density and Specific Gravity, Stability and Equilibrium of bodies, Gravitation, elementary ideas of work, Power and Energy , Newton’s Laws of Motion, Force and Momentum, Parallelogram of Forces.
- Effects of Heat, Modes of transference of Heat, Measurement of Temperature and Heat, change of State and Latent Heat, Sound waves and their properties, Reflection and refraction, Simple musical instruments, Rectilinear propagation of Light, Spherical mirrors and Lenses, Human Eye.
- Natural and Artificial Magnets, conductors and Non-conductors, Ohm’s Law, Simple Electrical Circuits, Properties of a Magnet, Earth as a Magnet, Static and Current Electricity, Heating, Measurement of Electrical Power, Primary and Secondary Cells, Lighting and Magnetic effects of Current, Use of X-Rays.
- General Principles in the working of the following: Balloon, Pumps, Hydrometer, Simple Pendulum, Thermos Flask, Gramophone, Telegraphs, Simple Pulleys, Siphon, Levers, , Pressure Cooker Microscope, Telephone, Periscope, Telescope,, Mariner’s Compass, Lightening Conductors, Safety Fuses.

(ii).** Section B (Chemistry)**

- Physical and Chemical changes, Law of Chemical Combination (excluding problems), Elements, Mixtures and Compounds, Symbols, Formulae and simple Chemical Equations, Properties of Air and Water.
- Preparation and Properties of NitrogenHydrogen, Oxygen, and Carbon dioxide, Oxidation and Reduction, Carbon & its different forms, Natural and Artificial fertilizers, Acids, bases and salts, The material used in the preparation of substances like Soap, Safety Matches, Glass, Ink, Paper, Cement, Paints and Gun-Powder.
- Elementary ideas about the structure of Valency, Atomic Equivalent, Atom and Molecular Weights.

(iii).** Section C (General Science) **

- Growth and Reproduction in Plants and Animals, Basis of Life of Cells, Protoplasms & Tissues, Difference between the living & non-living.
- Common Epidemics and their causes & prevention, Elementary knowledge of Human Body and its important organs.
- The Solar System: Meteors and Comets, Eclipses, Food: Constituents of food, Source of Energy for man, Balanced Diet, Achievements of Eminent Scientists.

(iv). **Section D (History, Freedom Movement etc.)**

- A broad survey of Indian History, with emphasis on Civilisation and Culture.
- Elementary study of Indian Constitution & Administration, Freedom Movement in India, Panchayati Raj, Community and Co-operatives Development, Bhoodan, National Integration, Sarvodaya and Welfare State, Basic Teachings of Mahatma Gandhi, Elementary knowledge of Five Year Plans of India.
- Forces shaping the modern world, War of American Independence, Renaissance, Exploration and Discovery, Industrial Revolution, Russian Revolution and French Revolution.
- Socialism and Communism, Concept of one World, Impact of Science & Technology on Society, United Nations, Panchsheel, Democracy, Role of India in the present world.

(v).** Section E (Geography)**

- The Earth, its shape and size, Movements of Earth, their effects, Origin of Earth, Lattitudes and Longitudes, Concept of time, International Date Line.
- Weathering—Mechanical and Chemical, Earthquakes and Volcanoes, Rocks and their classification, Temperature and Atmospheric Pressure, Cyclones, Planetary Winds and Anti-cyclones, Humidity, Ocean Currents and Tides Atmosphere and its composition, Condensation and Precipitation, Types of Climate, Regional Geography of India—Climate, Natural vegetation, Major Natural regions of the World.
- Mineral and Power resources, Important Sea ports and main sea, location and distribution of agricultural and Industrial activities, Main items of Imports and Exports in India, land and air routes of India.

(vi). **Section F (Current Events)**

Current important world events, Prominent personalities—both Indian and International including those connected with cultural activities and sports, Knowledge of Important events that have happened in India in recent years.

The SSB(Service Selection Board) organised Intelligence and Personality test consists of the two-stage Selection process - Stage 1 and Stage 2. Only those aspirants who clear stage 1 are allowed to appear for stage 2. The details are :

**STAGE 1:**This stage comprises of OIR(Officer Intelligence Rating) test and PP&DT(Picture Perception Description Test) test. The candidates will be selected based on the combination of performance in PP&DT and OIR Test.**STAGE 2:**This stage consists of Interview, Psychology Tests, Group Testing Officer Tasks and the Conference. These Stages are conducted over 4 days. The details of all these tests are given on the website (joinindianarmy.nic.in).

09 Jun 2021

29 Jun 2021

6

05 Sep 2021

₹ 100

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