SYLLABUS OF THE EXAMINATION
PAPER-I MATHEMATICS
(Code No. 01)
(Maximum Marks-300)
1. 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.
2. MATRICES AND 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.
3. 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.
4. 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 of a plane and a line
in various forms. Angle between two lines and angle between two planes.
Equation of a sphere.
5. 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.
6. INTEGRAL CALCULUS AND DIFFERENTIAL EQUATIONS: Integration as inverse of differentiation,
integration by substitution and by parts, standard integrals involving
algebraic expressions, trigonometric, exponential and 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.
7. 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.
8. STATISTICS AND PROBABILITY: Statistics: Classification of data, Frequency
distribution, And 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.
PAPER-II
GENERAL ABILITY TEST
(Code No. 02)
(Maximum Marks—600)
Part ‘A’ – ENGLISH (Maximum
Marks 200)
The question paper in English
will be designed to test the candidate’s understanding of English and workman
like use of words. The syllabus covers various aspects like: Grammar and usage,
vocabulary, comprehension and cohesion in extended text to test the candidate’s
proficiency in English.
Part ‘B’ – GENERAL KNOWLEDGE (Maximum Marks-400)
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 this 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, 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.
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 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.
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 Civilizations. 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.
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, 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.
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 cultural activities and sports.
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