This exam is conducted as −
The following table illustrates the detailed syllabus −
Mathematics Syllabus (Paper I) | |
---|---|
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 vice-versa | |
Arithmetic, Geometric and Harmonic progressions | |
Quadratic equations with real coefficients | |
Solution of linear in equations of two variables by graphs | |
Permutation and Combination | |
Binomial theorem and its applications | |
Logarithms and their applications | |
Matrices & 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 | |
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 | |
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 | |
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 | |
Integral Calculus & Differential Equations | Integration as inverse of differentiation |
Integration by substitution and by parts | |
Standard integrals involving algebraic expressions | |
Trigonometric | |
Exponential | |
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 | |
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 | |
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 | |
General Ability Syllabus | |
Part ‘A’ (Paper II) | |
English | Grammar and usage |
Vocabulary | |
Comprehension and cohesion in extended text | |
Part ‘B’ General Knowledge | |
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. | |
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 | |
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 | |
General Science | Difference between the living and non-livin |
Basis of Life—Cells, Protoplasm 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 | |
History, Freedom Movement | A broad survey of Indian History, with emphasis on Culture and Civilization |
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 | |
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 Anti-cyclones | |
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 | |
Current Events | Current National events |
Current World events | |
Prominent personalities—both Indian and International | |
Current cultural activities | |
Sports |
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