Trigonometry: Trigonometrical ratios, Inverse trigonometric functions, properties of triangles, Angles and their measures in degrees and in radians, Trigonometric identities Sum and difference formulae, Applications – Height and distance, Multiple and Sub-multiple angles.
Algebra: Complex numbers – basic properties, modulus, argument, cube roots of unity, Conversion of a number in decimal system to binary system and vice-versa, Arithmetic, Geometric and Harmonic progressions, Solution of linear inequations of two variables by graphs, Binomial theorem and its application, Representation of real numbers on a line, Binary system of numbers, Quadratic equations with real coefficients, Permutation and Combination, Logarithms and their application.
Differential Calculus: Composite functions, one to one, onto and inverse functions, Continuity of functions – examples, algebraic operations on continuous functions, geometrical and physical interpretation of a derivative – applications, increasing and decreasing functions, Application of derivatives in problems of maxima and minima, Concept of a real valued function – domain, range and graph of a function, Notion of limit, Standard limits – examples, Derivative of a 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 of another function, derivative of a composite function and Second order derivatives.
Vector Algebra: Vectors in two and three dimensions, magnitude and direction of a vector, scalar multiplication of vector, scalar product or dot product of two-vectors, Applications-work done by a force and moment of a force, and in geometrical problems, Unit and null vectors, addition of vectors, Vector product and cross product of two vectors.
Integral Calculus and Differential equations: Integration by substitution and by parts, trigonometric, exponential and hyperbolic functions, Definition of order and degree of a differential equation, formation of a differential equation by examples, solution of first order and first degree differential equations of various types – examples, Integration as inverse of differentiation, standard integrals involving algebraic expressions, Evaluation of definite integrals – determination of areas of plane regions bounded by curves – applications, General and particular solution of a differential equation, Application in problems of growth and decay.
General Ability Syllabus
English: The English syllabus covers the topics like vocabulary, Grammar and usage, comprehension and cohesion in extended text to test the candidate’s proficiency in English.
General Knowledge: The question paper comprises of general knowledge and covers the subjects that include Physics, Chemistry, General Science, Social Studies, Geography and Current Events.
Section A – Physics
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, Sound waves and their properties, Simple musical instruments, Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet, 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, Physical Properties and States of Matter, Mass, Weight, Volume, Density and Specific Gravity, Principle of Archimedes, Pressure Barometer, Effects of Heat, Measurement of temperature and heat, change of State and Latent Heat, Modes of transference of Heat, Rectilinear propagation of Light, Reflection and refraction. Spherical mirrors and Lenses. Human Eye, 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.
Section B – Chemistry
Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon-Di-oxide, Oxidation and Reduction, Carbon – different forms, Material used in the preparation of substances like soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and Gun-Powder, Physical and Chemical changes. Elements, Mixtures and Compounds, Symbols, Formulas and simple Chemical Equations, Law of Chemical Combination (excluding problems). Properties of Air and Water, Acids, bases and salts, Fertilizers – Natural and Artificial, Elementary ideas about the Structure of Atom, Atomic, Equivalent and Molecular Weights, Valency.
Section C – General Science
Basis of Life – Cells, Protoplasms and Tissues, Elementary knowledge of human Body and its important organs, Food – Source of Energy for man, Constituents of food, Balanced Diet, Achievements of Eminent Scientists, Difference between the living and non-living, Growth and Reproduction in Plants and Animals, Common Epidemics, their causes and prevention, The Solar System – Meteors and Comets, Eclipses.
Section D – History
Freedom Movement in India, Elementary knowledge of Five Year Plans of India, Bhoodan, Sarvodaya, National Integration and Welfare State, Basic Teachings of Mahatma Gandhi, A broad survey of Indian History, with emphasis on Culture and Civilisation, Elementary study of Indian Constitution and Administration, Panchayati Raj, Co-operatives and Community Development, 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
Origin of Earth, Rocks and their classification; Weathering – Mechanical and Chemical, Earthquakes and volcanoes, 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, Important Sea ports and main sea, land and air routes of India. Main items of Imports and Exports of India, The Earth, its shape and size. Latitudes and Longitudes, Concept of time, International Date Line, Movements of Earth and their effects, Ocean Currents and Tides, Regional Geography of India – Climate, Natural vegetation. Mineral and Power resources; location and distribution of agricultural and industrial activities.
Section F – Current Events
Current important world events, Knowledge of Important events that have happened in India in the recent years, prominent personalities – both Indian and International including those connected with cultural activities and sports.
It is not compulsory that the topics mentioned above will surely come in the examination. The question paper does not remain consistent, it changes every year. It may happen that the question paper will consists of the topic not discussed here.