INTRODUCTION
The Indian
Institutes of Technology are institutions of national importance established
through an Act of Parliament. These institutes play a leading role in
technological manpower development and have research programmes comparable
to the best in the world. The admissions to the Undergraduate Programmes at
these institutions for all Indian and Foreign nationals are made through the
Joint Entrance Examination (JEE).
Institute of
Technology, Banaras Hindu University, Varanasi, is one of the oldest
institutions devoted to education in various engineering disciplines.
Indian School of Mines University, Dhanbad, is the oldest institution of its
kind in India. The admissions to the Undergraduate Programmes at these
institutions are also made through JEE.
All these
institutions are known for providing quality education in science and
technology and for research in frontier areas. The environment at these
institutions is highly conducive for
-
building
a solid foundation of knowledge,
-
development of personality, confidence building, self-discipline,
pursuit of excellence and
-
enhancement of creativity, motivation and drive.
All of the
above help to prepare the students admitted to these institutions for
successful professional and social lives. Today, alumni of these
institutions occupy key positions in industry and academia in India and
abroad.
Each
institute has well-equipped modern laboratories, state-of-the-art computer
network, and well stocked technical library. Teaching methods rely on direct
personal contact between the teachers and the students, and the use of
traditional and modern instructional techniques. Students live in a pleasant
and intellectually stimulating environment with people having similar goals
and aspirations, which is an exciting and unique experience.
Credit-based
academic programmes offer flexibility to students to progress at their own
pace. A minimum level of performance is necessary for satisfactory
progress. The medium of instruction is English. These institutions offer
courses leading to Bachelor’s degree in a number of engineering,
technological, and scientific disciplines.
M.Sc.
Integrated courses in pure and applied sciences and M.Tech. Integrated
courses in a few disciplines are also offered by some of these
Institutions. In addition, some IITs offer Dual-Degree M.Tech. programmes,
wherein both B.Tech. and M.Tech. degrees are awarded.
SYLLABUS
CHEMISTRY
Physical Chemistry
General topics: Concept of atoms and molecules; Dalton’s atomic theory; Mole concept;
Chemical formulae; Balanced chemical equations; Calculations (based on mole
concept) involving common oxidation-reduction, neutralisation, and
displacement reactions; Concentration in terms of mole fraction, molarity,
molality and normality.
Gaseous and liquid
states: Absolute scale of
temperature, ideal gas equation; Deviation from ideality, van der Waals
equation; Kinetic theory of gases, average, root mean square and most
probable velocities and their relation with temperature; Law of partial
pressures; Vapour pressure; Diffusion of gases.
Atomic structure and
chemical bonding:
Bohr model, spectrum of hydrogen atom, quantum numbers; Wave-particle
duality, de Broglie hypothesis; Uncertainty principle; Qualitative quantum
mechanical picture of hydrogen atom, shapes of s, p and d orbitals;
Electronic configurations of elements (up to atomic number 36); Aufbau
principle; Pauli’s exclusion principle and Hund’s rule; Orbital overlap and
covalent bond; Hybridisation involving s, p and d orbitals only; Orbital
energy diagrams for homonuclear diatomic species; Hydrogen bond; Polarity
in molecules, dipole moment (qualitative aspects only); VSEPR model and
shapes of molecules (linear, angular, triangular, square planar, pyramidal,
square pyramidal, trigonal bipyramidal, tetrahedral and octahedral).
Energetics: First law of thermodynamics; Internal energy, work and heat, pressure-volume
work; Enthalpy, Hess’s law; Heat of reaction, fusion and vapourization;
Second law of thermodynamics; Entropy; Free energy; Criterion of
spontaneity.
Chemical equilibrium: Law of
mass action; Equilibrium constant, Le Chatelier’s principle (effect of
concentration, temperature and pressure); Significance of DG and DGo
in chemical equilibrium; Solubility product, common ion effect, pH and
buffer solutions; Acids and bases (Bronsted and Lewis concepts); Hydrolysis
of salts.
Electrochemistry: Electrochemical cells and cell reactions; Standard electrode potentials;
Nernst equation and its relation to DG;
Electrochemical series, emf of galvanic cells; Faraday’s laws of
electrolysis; Electrolytic conductance, specific, equivalent and molar
conductivity, Kohlrausch’s law; Concentration cells.
Chemical kinetics:
Rates of chemical reactions; Order of reactions; Rate constant; First order
reactions; Temperature dependence of rate constant (Arrhenius equation).
Solid state: Classification of solids, crystalline state, seven crystal systems (cell
parameters a, b, c,
 ),
close packed structure of solids (cubic), packing in fcc, bcc and hcp
lattices; Nearest neighbours, ionic radii, simple ionic compounds, point
defects.
Solutions: Raoult’s law; Molecular weight determ- ination from lowering of vapour
pressure, elevation of boiling point and depression of freezing point.
Surface chemistry:
Elementary concepts of adsorption (excluding adsorption isotherms);
Colloids: types, methods of preparation and general properties; Elementary
ideas of emulsions, surfactants and micelles (only definitions and
examples).
Nuclear chemistry:
Radioactivity: isotopes and isobars; Properties of
 rays;
Kinetics of radioactive decay (decay series excluded), carbon dating;
Stability of nuclei with respect to proton-neutron ratio; Brief discussion
on fission and fusion reactions.
Inorganic Chemistry
Isolation/preparation
and properties of the following non-metals: Boron, silicon,
nitrogen, phosphorus, oxygen, sulphur and halogens; Properties of allotropes
of carbon (only diamond and graphite), phosphorus and sulphur.
Preparation and properties
of the following compounds: Oxides, peroxides, hydroxides, carbonates, bicarbonates, chlorides and
sulphates of sodium, potassium, magnesium and calcium; Boron: diborane,
boric acid and borax; Aluminium: alumina, aluminium chloride and alums;
Carbon: oxides and oxyacid (carbonic acid); Silicon: silicones, silicates
and silicon carbide; Nitrogen: oxides, oxyacids and ammonia; Phosphorus:
oxides, oxyacids (phosphorus acid, phosphoric acid) and phosphine; Oxygen:
ozone and hydrogen peroxide; Sulphur: hydrogen sulphide, oxides, sulphurous
acid, sulphuric acid and sodium thiosulphate; Halogens: hydrohalic acids,
oxides and oxyacids of chlorine, bleaching powder; Xenon fluorides.
Transition elements (3d
series): Definition, general characteristics, oxidation states and their stabilities,
colour (excluding the details of electronic transitions) and calculation of
spin-only magnetic moment; Coordination compounds: nomenclature of
mononuclear coordination compounds, cis-trans and ionisation
isomerisms, hybridization and geometries of mononuclear coordination
compounds (linear, tetrahedral, square planar and octahedral).
Preparation and properties
of the following compounds: Oxides and chlorides of tin and lead; Oxides, chlorides and sulphates of
Fe2+, Cu2+ and Zn2+; Potassium permanganate, potassium dichromate, silver
oxide, silver nitrate, silver thiosulphate.
Ores and minerals: Commonly occurring ores
and minerals of iron, copper, tin, lead, magnesium, aluminium, zinc and
silver.
Extractive metallurgy: Chemical principles and reactions only (industrial details excluded); Carbon
reduction method (iron and tin); Self reduction method (copper and lead);
Electrolytic reduction method (magnesium and aluminium); Cyanide process
(silver and gold).
Principles of qualitative
analysis: Groups I to V (only Ag+, Hg2+, Cu2+, Pb2+, Bi3+, Fe3+, Cr3+, Al3+, Ca2+,
Ba2+, Zn2+, Mn2+ and Mg2+); Nitrate, halides (excluding fluoride), sulphate
and sulphide.
Organic Chemistry
Concepts: Hybridisation of carbon; Sigma and pi-bonds; Shapes of simple organic
molecules; Structural and geometrical isomerism; Optical isomerism of
compounds containing up to two asymmetric centres, (R,S and E,Z nomenclature excluded); IUPAC nomenclature of simple organic compounds
(only hydrocarbons, mono-functional and bi-functional compounds);
Conformations of ethane and butane (Newman projections); Resonance and
hyperconjugation; Keto-enol tautomerism; Determination of empirical and
molecular formulae of simple compounds (only combustion method); Hydrogen
bonds: definition and their effects on physical properties of alcohols and
carboxylic acids; Inductive and resonance effects on acidity and basicity of
organic acids and bases; Polarity and inductive effects in alkyl halides;
Reactive intermediates produced during homolytic and heterolytic bond
cleavage; Formation, structure and stability of carbocations, carbanions
and free radicals.
Preparation, properties
and reactions of alkanes: Homologous series, physical properties of alkanes (melting points, boiling
points and density); Combustion and halogenation of alkanes; Preparation of
alkanes by Wurtz reaction and decarboxylation reactions.
Preparation, properties
and reactions of alkenes and alkynes: Physical properties of alkenes and alkynes (boiling points, density and
dipole moments); Acidity of alkynes; Acid catalysed hydration of alkenes and
alkynes (excluding the stereochemistry of addition and elimination);
Reactions of alkenes with KMnO4 and ozone; Reduction of alkenes and alkynes;
Preparation of alkenes and alkynes by elimination reactions; Electrophilic
addition reactions of alkenes with X2, HX, HOX and H2O (X=halogen);
Addition reactions of alkynes; Metal acetylides.
Reactions of benzene: Structure and aromaticity; Electrophilic substitution reactions:
halogenation, nitration, sulphonation, Friedel-Crafts alkylation and
acylation; Effect of o-, m- and p-directing groups in
monosubstituted benzenes.
Phenols: Acidity, electrophilic substitution reactions (halogenation, nitration and
sulphonation); Reimer-Tieman reaction, Kolbe reaction.
Characteristic reactions
of the following (including those mentioned above): Alkyl halides:
rearrangement reactions of alkyl carbocation, Grignard reactions,
nucleophilic substitution reactions; Alcohols: esterification, dehydration
and oxidation, reaction with sodium, phosphorus halides, ZnCl2/concentrated
HCl, conversion of alcohols into aldehydes and ketones; Ethers:Preparation
by Williamson’s Synthesis; Aldehydes and Ketones: oxidation, reduction,
oxime and hydrazone formation; aldol condensation, Perkin reaction;
Cannizzaro reaction; haloform reaction and nucleophilic addition reactions (Grignard
addition); Carboxylic acids: formation of esters, acid chlorides and
amides, ester hydrolysis; Amines: basicity of substituted anilines and
aliphatic amines, preparation from nitro compounds,
reaction with nitrous acid, azo coupling reaction of diazonium salts of
aromatic amines, Sandmeyer and related reactions of diazonium salts;
carbylamine reaction; Haloarenes: nucleophilic aromatic substitution in
haloarenes and substituted haloarenes (excluding Benzyne mechanism and Cine
substitution).
Carbohydrates: Classification; mono- and di-saccharides (glucose and sucrose); Oxidation,
reduction, glycoside formation and hydrolysis of sucrose.
Amino acids and
peptides: General structure (only primary structure for peptides) and physical
properties.
Properties and uses of
some important polymers: Natural rubber, cellulose, nylon, teflon and PVC.
Practical organic
chemistry: Detection of
elements (N, S, halogens); Detection and identification of the following
functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and
ketone), carboxyl,
amino and nitro; Chemical methods of separation of mono-functional organic
compounds from binary mixtures.
MATHEMATICS
Algebra: Algebra of complex
numbers, addition, multiplication, conjugation, polar representation,
properties of modulus and principal argument, triangle inequality, cube
roots of unity, geometric interpretations.
Quadratic equations with
real coefficients, relations between roots and coefficients, formation of
quadratic equations with given roots, symmetric functions of roots.
Arithmetic, geometric and
harmonic progressions, arithmetic, geometric and harmonic means, sums of
finite arithmetic and geometric progressions, infinite geometric series,
sums of squares and cubes of the first n natural numbers.
Logarithms and their properties.
Permutations and
combinations, Binomial theorem for a positive integral index, properties of
binomial coefficients.
Matrices as a rectangular
array of real numbers, equality of matrices, addition, multiplication by a
scalar and product of matrices, transpose of a matrix, determinant of a
square matrix of order up to three, inverse of a square matrix of order up
to three, properties of these matrix operations, diagonal, symmetric and
skew-symmetric matrices and their properties, solutions of simultaneous
linear equations in two or three variables.
Addition and multiplication rules of
probability, conditional probability, Bayes Theorem, independence of events,
computation of probability of events using permutations and combinations.
Trigonometry: Trigonometric
functions, their periodicity and graphs, addition and subtraction formulae,
formulae involving multiple and sub-multiple angles, general solution of
trigonometric equations.
Relations between sides
and angles of a triangle, sine rule, cosine rule, half-angle formula and the
area of a triangle, inverse trigonometric functions (principal value only).
Analytical geometry:
Two dimensions: Cartesian
coordinates, distance between two points, section formulae, shift of origin.
Equation of a straight
line in various forms, angle between two lines, distance of a point from a
line; Lines through the point of intersection of two given lines, equation
of the bisector of the angle between two lines, concurrency of lines;
Centroid, orthocentre, incentre and circumcentre of a triangle.
Equation of a circle in
various forms, equations of tangent, normal and chord.
Parametric equations of a
circle, intersection of a circle with a straight line or a circle, equation
of a circle through the points of intersection of two circles and those of
a circle and a straight line.
Equations of a parabola,
ellipse and hyperbola in standard form, their foci, directrices and
eccentricity, parametric equations, equations of tangent and normal.
Locus
Problems.
Three dimensions: Direction cosines and direction ratios, equation of a straight line in
space, equation of a plane, distance of a point from a plane.
Differential calculus: Real
valued functions of a real variable, into, onto and one-to-one functions,
sum, difference, product and quotient of two functions, composite functions,
absolute value, polynomial, rational, trigonometric, exponential and
logarithmic functions.
Limit and continuity of a
function, limit and continuity of the sum, difference, product and quotient
of two functions, L’Hospital rule of evaluation of limits of functions.
Even and odd functions,
inverse of a function, continuity of composite functions, intermediate value
property of continuous functions.
Derivative of a function,
derivative of the sum, difference, product and quotient of two functions,
chain rule, derivatives of polynomial, rational, trigonometric, inverse
trigonometric, exponential and logarithmic functions.
Derivatives of implicit
functions, derivatives up to order two, geometrical interpretation of the
derivative, tangents and normals, increasing and decreasing functions,
maximum and minimum values of a function, Rolle’s Theorem and Lagrange’s
Mean Value Theorem.
Integral calculus: Integration as
the inverse process of differentiation, indefinite integrals of standard
functions, definite integrals and their properties, Fundamental Theorem of
Integral Calculus.
Integration by parts,
integration by the methods of substitution and partial fractions,
application of definite integrals to the determination of areas involving
simple curves.
Formation of ordinary
differential equations, solution of homogeneous differential equations,
separation of variables method, linear first order differential equations.
Vectors: Addition of
vectors, scalar multiplication, dot and cross products, scalar triple
products and their geometrical interpretations.
PHYSICS
General: Units and
dimensions, dimensional analysis; least count, significant figures; Methods
of measurement and error analysis for physical quantities pertaining to the
following experiments: Experiments based on using Vernier calipers and screw
gauge (micrometer), Determination of g using simple pendulum, Young’s
modulus by Searle’s method, Specific heat of a liquid using calorimeter,
focal length of a concave mirror
and a convex lens using u-v method, Speed of sound using resonance column,
Verification of Ohm’s law using voltmeter and ammeter, and specific
resistance of the material of a wire using meter bridge and post office box.
Mechanics: Kinematics in
one and two dimensions (Cartesian coordinates only), projectiles; Uniform
Circular motion; Relative velocity.
Newton’s laws of motion;
Inertial and uniformly accelerated frames of reference; Static and
dynamic friction; Kinetic and potential energy; Work and power;
Conservation of linear momentum and mechanical energy.
Systems of particles;
Centre of mass and its motion; Impulse; Elastic and inelastic collisions.
Law of gravitation;
Gravitational potential and field; Acceleration due to gravity; Motion of
planets and satellites in circular orbits; Escape velocity.
Rigid body, moment of
inertia, parallel and perpendicular axes theorems, moment of inertia of
uniform bodies with simple geometrical shapes; Angular momentum; Torque;
Conservation of angular momentum; Dynamics of rigid bodies with fixed axis
of rotation; Rolling without slipping of rings, cylinders and spheres;
Equilibrium of rigid bodies; Collision of point masses with rigid bodies.
Linear and angular simple harmonic motions.
Hooke’s law, Young’s
modulus.
Pressure in a fluid; Pascal’s law; Buoyancy; Surface energy
and surface tension, capillary rise; Viscosity (Poiseuille’s equation
excluded), Stoke’s law; Terminal velocity, Streamline flow, equation of
continuity, Bernoulli’s theorem and its applications.
Wave motion (plane waves
only), longitudinal and transverse waves, superposition of waves;
Progressive and stationary waves; Vibration of strings and air
columns;Resonance; Beats; Speed of sound in gases; Doppler effect (in
sound).
Thermal physics: Thermal expansion of solids,
liquids and gases; Calorimetry, latent heat; Heat conduction in one
dimension; Elementary concepts of convection and radiation; Newton’s law of
cooling; Ideal gas laws; Specific heats (Cv and Cp for monoatomic and
diatomic gases); Isothermal and adiabatic processes, bulk modulus of gases;
Equivalence of heat and work; First law of thermodynamics and its
applications (only for ideal gases); Blackbody radiation: absorptive and
emissive powers; Kirchhoff’s law; Wien’s displacement law, Stefan’s law.
Electricity and
magnetism: Coulomb’s law; Electric field and potential; Electrical
potential energy of a system of point charges and of electrical dipoles in a
uniform electrostatic field; Electric field lines; Flux of electric field;
Gauss’s law and its application in simple cases, such as, to find field due
to infinitely long straight wire, uniformly charged infinite plane sheet and
uniformly charged thin spherical shell.
Capacitance; Parallel
plate capacitor with and without dielectrics; Capacitors in series and
parallel; Energy stored in a capacitor.
Electric current; Ohm’s
law; Series and parallel arrangements of resistances and cells; Kirchhoff’s
laws and simple applications; Heating effect of current.
Biot–Savart’s law and
Ampere’s law; Magnetic field near a current-carrying straight wire, along
the axis of a circular coil and inside a long straight solenoid; Force on a
moving charge and on a current-carrying wire in a uniform magnetic field.
Magnetic moment of a
current loop; Effect of a uniform magnetic field on a current loop; Moving
coil galvano- meter, voltmeter, ammeter and their conversions.
Electromagnetic induction:
Faraday’s law, Lenz’s law; Self and mutual inductance; RC, LR and LC
circuits with d.c. and a.c. sources.
Optics: Rectilinear propagation of
light; Reflection and refraction at plane and spherical surfaces; Total
internal reflection; Deviation and dispersion of light by a prism; Thin
lenses; Combinations of mirrors and thin lenses; Magnification.
Wave nature of light:
Huygen’s principle, interference limited to Young’s double-slit experiment.
Modern physics: Atomic nucleus;
Alpha, beta and gamma radiations; Law of radioactive decay; Decay constant;
Half-life and mean life; Binding energy and its calculation; Fission and
fusion processes; Energy calculation in these processes.
Photoelectric effect;
Bohr’s theory of hydrogen-like atoms; Characteristic and continuous X-rays,
Moseley’s law; de Broglie wavelength of matter waves.
APTITUDE TEST FOR B.Arch. and B.Des. PROGRAMMES
Freehand
drawing:
This would comprise of simple drawing depicting the total object in its
right form and proportion, surface texture, relative location and details of
its component parts in appropriate scale. Common domestic or day-to-day
life usable objects like furniture, equipment, etc., from memory.
Geometrical
drawing: Exercises in geometrical drawing containing lines, angles, triangles,
quadrilaterals, polygons, circles etc. Study of plan (top view), elevation
(front or side views) of simple solid objects like prisms, cones, cylinders,
cubes, splayed surface holders etc.
Three-dimensional perception:
Understanding and appreciation of three-dimensional forms with building
elements, colour, volume and orientation. Visualization through structuring
objects in memory.
Imagination
and aesthetic sensitivity:
Composition exercise with given elements. Context mapping. Creativity check
through innovative uncommon test with familiar objects. Sense of colour
grouping or application.
Architectural
awareness: General interest and awareness of famous architectural creations – both
national and international, places and personalities (architects, designers
etc. ) in the related domain.
Candidates
are advised to bring geometry box sets, pencils, erasers and colour pencils
or crayons for the Aptitude Test.
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