Number Systems-Natural numbers, Integers, Rational and Real numbers. Fundamental operations-addition, subtraction, multiplication, division, square roots, decimal fractions.
Unitary method-time and distance, time and work. Percentage – applications to simple and compound interest, profit and loss, ratio and proportion, variation.
Elementary Number Theory, Division algorithm Prime and composite numbers. Tests of divisibility by 2, 3, 4, 5, 9 and 11. Multiples and factors. Factorization Theorem. H.C.F. and L.C.M. Euclidean algorithm. Logarithms to base 10, laws of logarithms.
Areas of squares, rectangles, parallelograms, triangle and circles. Area of figures, which can be split up into these figures (Field Book). Surface area and volume of cuboids, lateral surface and volume of right circular cones and cylinders. Surface area and volume of spheres.
Basic Operations, simple factors, Remainder Theorem, H.C.F., L.C.M. of polynomials. Solutions of quadratic equations, relation between its roots and coefficients (only real roots to be considered). Simultaneous linear equations to two unknown analytical and graphical solutions.
Practical problems leading to two simultaneous linear equations in two variables or quadratic equations in one variable and their solutions. Set language and set notation. Rational expression and conditional identities. Law of indices.
Lines and angles. Plane and plane figure. Theorems on
1. Properties of angles at a point
2. Parallel lines
3. Sides and angles of a triangle
4. Congruency of triangles
5. Similar triangles
6. Concurrence of medians and altitudes
7. Properties of angles, sides and diagonals of a parallelogram, rectangle and square
8. Circles and their properties including tangents and normals
Sine x, Cosine x, Tangent x when 0° < x < 90°
Value of sin x, cos x and tan x for x = 0°, 30°, 45°, 60° and 90°. Simple trigonometric identities.
Use of trigonometrical tables.
Simple cases of heights and distances.
Collection and tabulation of statistical data. Graphical representation, frequency polygons, histograms, bar charts, pie charts, etc. Calculation of mean of raw and grouped data.
General Ability Test
Part A -English
The question paper in English will be designed to test the candidate’s understanding of English and workmanlike use of words. The syllabus covers various aspects like: Grammar and usage, vocabulary, comprehension and cohesion in extended texts to test the candidate’s proficiency in English.
Part B -General Knowledge
The question paper on General Knowledge will broadly cover the subjects: Physics, Chemistry, General Science, Social Studies, Geography and Current Events.
The syllabus given below is designed to indicate the scope of these subjects included in the paper. The topics mentioned are not to be regarded as exhaustive and questions on topics of similar nature not specifically mentioned in the syllabus may also be asked. Candidate’s answers are expected to show their knowledge and intelligent understanding of the subject.
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: Measurements 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 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, Lightning 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 Carbon dioxide, Oxidation and Reduction.
Acids, Bases and Salts.
Carbon-different forms. Fertilizers-Natural and Artificial.
Materials used in the preparations 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 non-living.
Basis of Life-Cells, Protoplasm’s 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 Civilization.
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:Renissance, 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. Earthquake 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 the cultural activities and sports.