Exam pattern
Exam Syllabus
PAPER-I
MATHEMATICS (Maximum Marks- 300)
1. ALGEBRA
Concept of a 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
inequations 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, exponentialand 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. Applicationswork done by a force and moment of a force and
in geometrical problems.
8. STATISTICS
AND PROBABILITY
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.
PAPER-II GENERAL ABILITY TEST (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 Carbondioxide, 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, Protoplasms 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 Civilisation. 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. Lattitudes 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.
Intelligence and
personality test
In addition to the interview the candidates will be put
to Intelligence Tests both verbal and non-verbal, designed to assess their basic
intelligence. They will also be put to Group Tests such as group discussions, group
planning, outdoor group tasks, and asked to give brief lectures on specified subjects.
All these tests are intended to judge the mental calibre of a candidate. In broad
terms, this is really an assessment of not only his intellectual qualities but
also his social traits and interests in current affairs.
