NATIONAL DEFENCE ACADEMY & NAVAL ACADEMY EXAMINATION (II),
NDA Syllabus:
NDA Syllabus:-
PAPER-I: MATHES (Maximum Marks- 300)
Algebra:
operations of sets, Concept of set, DE Morgan Laws, relation Venn diagrams. , Cartesian Product ., Binomial theorem and its application, equivalence relation, permutation and combination, solution of linear inequations of two variables by graphs.,Quadratic Equitation with real coefficients, Geometric and harmonic progressions. Arithmetic, Conversation of a number in the decimal system to binary and vice versa. Binary system of numbers. Cube roots of unity. Real numbers on a line REPRESENTATION BASIC PROPERTIES OF COMPLEX NUMBERS, modulus.
DETERMINANTS AND MATRICES:
Applications – By Matrix method and creamer's rule two or three unknown systems of linear Equitation
Adjoin and the inverse of a square matrix, Determinant of a matrix, basic properties of determinants. Operations on matrices.Types of matrices.
TRIGONOMETRY:
Height and distance - Applications, Inverse trigonometric functions. Trigonometric identities Sum and difference formulae. Trigonometrical ratios. , Triangles properties. , Multiple - sub-multiple angles, measures and their angles in radians and degrees.
IN TWO OR THREE DIMENSIONS ANALYTICAL GEOMETRY:
Equation of a sphere, Angle between two lines and the angle between two planes, Equation of a plane and a line in various forms., Direction ratios direction Cosines ., Between two-point Distance., Point in a three-dimensional space, Eccentricity and axis of a conic. Ellipse and hyperbola. The standard form of a parabola, Equation of a circle in standard and in general form., Distance of point form line. Between two lines angle. Equation of a line in various forms., Distance formula. Rectangular Cartesian Coordinate system.
DIFFERENTIAL CALCULUS:-
Application of derivatives in problems of maxima and minima, Increasing and decreasing functions. Second-order derivatives. The derivative of a composite function, the derivative of a function with respect to another function, product and quotient of functions, Derivatives of sum, geometrical - physical interpretation of a derivative – applications., Derivative of function at a point algebraic operations on continuous functions. Continuity of functions – examples, Standard limits – examples. The notion of limit, onto and inverse functions. One to one, Composite functions, range and graph of a function. Concept of a real-valued Domain
DIFFERENTIAL EQUATIONS AND INTEGRAL CALCULUS
Application in problems of decay and growth. The first-degree differential solution of first-order equations of various types – examples, particular and General solution of a differential equation, the formation of a differential equation by examples. Definition of the degree of a differentials equation, Evaluation of definite integrals – determination of areas of plane regions bounded by curves – applications. Standard integrals involving /algebraic expressions, trigonometric, Integration by substitution and by parts, Integration as inverse of differentiation.
VECTOR ALGEBRA:
Applications-moment of a force and work are done by a force and in geometrical problems. Cross product of two vector scalar product or dot product of two vectors, scalar multiplication of a vector, addition of vectors, Unit and null vectors, magnitude and direction of a vector.
STATISTICS AND PROBABILITY
examples of random experiments giving rise to Binomial distribution. Binomial distribution. On a sample space Random variable as function. Bayes theorem – problems. Definition of probability – statistical and classical – examples. Elementary theorems probability – simple problems. Conditional probability Intersection and Union of events. Elementary, complementary and composite events.Probability: Random experiment, impossible and certain events, mutually exclusive and exhaustive events, events, outcomes and associated sample space, Correlation and regression. Standard and Variance and deviation –comparison and determination. Measures of tendency –median, Mean, and mode. Graphical representation –Pie Chart, Histogram, frequency polygon – examples. Statistics: Classification of data, cumulative frequency distribution, Frequency distribution.
PAPER-II: GENERAL ABILITY TEST (Maximum Marks-600)
Part ‘A’ – ENGLISH (Maximum Marks 200)
English paper question will be designed to test the candidate's understanding of English workmanlike use of words. The syllabus covers various aspects like vocabulary Grammar and usage, comprehension and cohesion in extended text to test the candidate's proficiency in English.
Part ‘B’ – GENERAL KNOWLEDGE (Maximum Marks-400)
General Knowledge question paper will broadly cover the subjects: Chemistry, Physics, General Science, Social Studies, Geography and Current Events. Candidate's answers are expected to exhibit their knowledge and intelligent comprehension of the subject.
Section ‘A’ (Physics): States of Matter and Physical Properties, Volume, Mass, Weight, Density and Specific Gravity, Pressure Barometer, Principle of Archimedes. Velocity and Acceleration, Motion of objects, Force and Momentum, Newton's Laws of Motion, Stability and Equilibrium of bodies.
Forces Parallelogram, Gravitation, Power and Energy, elementary ideas of work. Measurement of temperature and Heat, Effects of Heat, Modes of transference of Heat, change of State and Latent Heat. Simple instruments of musical, Sound properties and their waves .refraction and Reflection, Light Rectilinear propagation. Spherical Lenses and mirrors. Human Eye. Artificial and Natural Magnets, Earth as a Magnet, Properties of a Magnet. Conductors and Non-conductors, Static and Current Electricity, Simple Electrical Circuits, Ohm's Law, Lighting, Heating, Measurement of Electrical Power, and Magnetic effects of Current.
Use of X-Rays, Primary and Secondary Cells. General Principles following: Simple Pulleys, Siphon, Simple Pendulum, Levers, Hydrometer, Balloon, Pumps, Thermos Flask, Pressure Cooker, Telegraphs, Gramophone, Telephone, Mariner's Compass, Periscope, Microscope, Telescope; Safety Fuses, Lightning Conductors.
Section ‘B’ (Chemistry): Elements, Physical and Chemical changes. Symbols, Compounds and Mixtures, Law of Chemical Combination (excluding problems), Formulae and simple Chemical Equations. Properties of Water and air. Properties and Preparation of Nitrogen, Hydrogen, Oxygen, and Carbon dioxide, Oxidation and Reduction. Bases, Acids, and salts. Fertilizers – Natural, Carbon – different forms. And Artificial Material used in the preparation of substances like soap, Paints, Glass, Ink, Cement, Safety Matches, Paper, and Gun-Powder. Equivalent and Molecular Weights, Elementary ideas about the Structure of Atom, Valency, Atomic.
Section ‘C’
(General Science): Difference between the non- living and living. Basis of Life –
Protoplasm's and Tissues, Cells. Reproduction and Growth in Animals and
Plants .knowledge of Human Body and its organs. Common Epidemics, their causes
and prevention. Constituents of food, Balanced Diet. Food – Source of Energy
for man. Achievements of Eminent Scientists. The Solar System – Meteors
and Comets, Eclipses.
Section ‘D’ (History, Freedom Movement, etc.): Freedom Movement in India. A wide survey of Indian History, with emphasis on Civilizations and Culture. An elementary understanding of Five Year Plans of India. Elementary study of Indian Constitution and Administration. Sarvodaya, Bhoodan, Welfare State and National Integration, Basic Teachings of Mahatma Gandhi. Panchayati Raj, Co-operatives and Community Development. French Revolution, the Industrial Revolution and the Russian Revolution. Forces are shaping the modern World; Exploration, Renaissance, and Discovery; War of American Independence. Concept of one World, Impact of Science and Technology on Society. Democracy, United Nations, Panchsheel. Role of India in the present World.Socialism and Communism.
Section ‘E’ (Geography): Latitudes and Longitudes, The Earth, its shape and size. Concept of International Date Line and time. Origin of Earth, Movements of Earth and their effects. Weathering – Mechanical and Chemical, Rocks and their classification; volcanoes and Earthquakes. Tides Atmosphere and Ocean Currents and its composition; Atmospheric Pressure and Temperature, cyclones and Anti-cyclones, Planetary Winds, Humidity; Types of Climate, Condensation and Precipitation. Regional Geography of India – Natural vegetation, Climate. Major Natural regions of the World. Power resources and Mineral; distribution of agricultural and location and industrial activities. And air routes of India, Important Sea ports and main sea. Main components of Imports and Exports in India.
Section ‘F’ (Current Events): Knowledge of Important events in India in recent years. Latest Current important world events. Prominent personalities – Indian and International, including connected with cultural activities and sports.
