# Syllabus

Syllabus

## Engineering Agriculture and Medicine Common Entrance Test (EAMCET)

## :: EAMCET Exam Syllabus ::

## Indian Institutes of Technology

## Joint Entrance Examination (IIT-JEE)

## B. Arch. Aptitude Test Syllabus

**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.

## Indian Institutes of Technology

## Joint Entrance Examination (IIT-JEE)

## Mathematics Syllabus

**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.

## Indian Institutes of Technology

## Joint Entrance Examination (IIT-JEE)

## Chemistry Syllabus

### 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 ΔG and ΔG° 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 ΔG; 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, α, β, γ), 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 determination 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).

## Indian Institutes of Technology

## Joint Entrance Examination (IIT-JEE)

## Physics Syllabus

**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

## Indian Institutes of Technology

## Joint Entrance Examination (IIT-JEE)

## Syllabus :

## WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

## JEM 2012 - SYLLABUS

## MATHEMATICS

**Algebra**

**A.P., G.P., H.P. : **Definitions of A. P. and G.P.; General term;
Summation of first n-terms; A.M.and G.M.; Definitions of H.P. (only 3 terms) and
H.M.; Finite arithmetico-geometric series.

**Logarithms :**Definition; General properties; Change of base.

**Complex Numbers: **Definition and properties of complex numbers; Complex
conjugate; Triangle inequality; Square root of complex numbers; Cube roots of
unity; D’Moivre’s theorem (statement only) and its elementary applications.

**Quadratic Equations : **Quadratic equations with real coefficients;
Relations between roots and coefficients; Nature of roots; Formation of a
quadratic equation, sign and magnitude of the quadratic expression ax^{2}+bx+c
(a,b,c are rational numbers and a≠0).

**Permutation and combination : **Permutation of n different things taken
r at a time (r ≤ n). Permutation of n things not all different. Permutation with
repetitions (circular permutation excluded). Combinations of n different things
taken r at a time (r ≤ n). Combination of n things not all different. Basic
properties.

Problems involving both permutations and combinations.

**Principle of Mathematical Induction : **Statement of the principle.
Proof by induction for the sum of squares, sum of cubes of first n natural
numbers, divisibility properties like 2 2n – 1 is divisible by 3 (n ≥ 1), 7
divides 3^{2n+1}+2 ^{n+2}(n ≥ 1).

**Binomial theorem (positive integral index) :**Statement of the theorem,
general term, middle term, equidistant terms, properties of binomial co-efficients.

## WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

## JEM 2012 - SYLLABUS

## PHYSICS

**Mechanics & General properties of matter**

(i) Units and dimensions : Units of measurement, system of units, fundamental
and derived units, S I units, dimensional analysis. Methods of
measurement: Vernier scale, screw gauge, analysis of errors, significant
figures.

(ii) Scalars and vectors: Addition, subtraction, multiplication of vectors.

(iii) Kinematics in one, two and three dimensions, projectiles, uniform circular
motion,centripetal force, centrifigual force, relative velocity.

(iv) Dynamics: Newton's laws of motion; inertial frames, uniformly accelerated
frame (pseudoforces), conservation of linear momentum, rocket motion, centre of
mass, impulsive forces, friction.

(v) Work, Power and Energy , conservative and non-conservative forces,
conservation of energy, collision(elastic and inelastic)

(vi) .Rotational motion : Torque, angular momentum and conservation of angular
momentum, moment of inertia, radius of gyration, moment of inertia of objects
with simple geometrical shapes, rotational kinetic energy and rolling on
horizontal surface.

**Gravitation: **Laws of gravitation, gravitational field and potential,
acceleration due to gravity and its variation, escape velocity, Kepler's laws
and planetary motion, motion of satellites, Geostationary orbit.

**Elasticity: **Hooke's law, elastic modulii, Poisson's ratio, elastic
energy. Hydrostatics and fluid mechanics: Pressure in a fluid, Pascal's law,
Archimedes' principle, hydraulic press.

**Surface energy and surface tension, capillary rise. **Viscosity,
streamline and turbulent motion, critical velocity, Reynold's number, Stoke's
law, Bernoulli's theorem.

**Vibrations: **Simple Harmonic Motion, equation of motion, damped and
forced vibrations, resonance, superposition of SHM.

**Wave motion: **Elastic waves, longitudinal and transverse waves.
progressive waves, superposition of waves: interference, stationary waves,
beats, vibration of strings, air columns, velocity of elastic waves in different
media, Doppler effect.

## WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

## JEM 2012 - SYLLABUS

## CHEMISTRY

**Atoms, Molecules and Chemical Arithmetic:**

Dalton’s atomic theory; Gay Lussac’s law of gaseous volume; Avogadro’s
Hypothesis and its applications. Atomic mass; Molecular mass; Equivalent weight;
Valency; Gram atomic weight; Gram molecular weight; Gram equivalent weight and
mole concept; Chemical formulae; Balanced chemical equations; Calculations
(based on mole concept) involving common oxidation-reduction, neutralization,
and displacement reactions; Concentration in terms of mole fraction, molarity,
molality and normality. Percentage composition, empirical formula and molecular
formula; Numerical problems.

**Atomic Structure: **Concept of Nuclear Atom – electron,
proton and neutron (charge and mass), atomic number; Rutherford’s model and its
limitations; Extra nuclear structure; Line spectra of hydrogen atom.
Quantization of energy (Planck’s equation E = hv); Bohr’s model of hydrogen atom
and its limitations, Sommerfelds modifications (elementary idea); The four
quantum numbers, ground state electronic configurations of many electron atoms
and mono-atomic ions; The Aufbau Principle; Pauli’s Exclusion Principle and
Hund’s Rule.

**Uncertainty principle; **The concept of atomic orbitals,
shapes of s, p and d orbitals (pictorial approach)

**Radioactivity and Nuclear Chemistry
**Radioactivity – α-, β-, γ-rays and their properties; Artificial
transmutation; Rate of radioactive decay, decay constant, half-life and average
life period of radio-elements; Units of radioactivity; Numerical problems.
Stability of the atomic nucleus – effect of neutron–proton (n/p) ratio on the
modes of decay, group displacement law, radioisotopes and their uses (C, P, Co
and I as examples) isobars and isotones (definition and examples), elementary
idea of nuclear fission and fusion reactions.

**The Periodic Table and Chemical Families**

## WEST BENGAL JOINT ENTRANCE EXAMINATIONS BOARD

## JEM 2012 - SYLLABUS

## BIOLOGY

**Unit of Life : **Definition of life, Cell as the basic unit of life.
Cell theory, Prokaryotic and Eukaryotic cell – structure and differences.

**Ultrastructure and functions of cellular components : **Cell wall,
Plasma membrane, Plastid, Endoplasmic reticulum, Golgi bodies, Mitochondria,
Ribosomes, Lysosomes, Nucleus, Centrosomes, Cilia, Flagella.

**Microscopy : **Components and principles of Simple and Compound
Microscope; Electron Microscope : Basic functional principles.

**Physical and chemical principles involved in maintenance of life processes
:**Diffusion, Osmosis, Absorption, Osmoregulation. Biomolecules :
Classification and structural properties of carbohydrates, lipids, aminoacids,
proteins and nucleic acids.

**Carbohydrates :** Monosaccharides, digosaccharides, and polysaccharides
(starch, glycogen, cellulose).

**Proteins :**Simple (albumins, globulins, collagen) and conjugated
proteins (only examples).

**Nucleic acids : **Structure of DNA, RNA, types of RNA.

**Enzymes : **Definition & properties, Examples; Mechanism of Action,
Allosterism and Regulation. Chromosomes and Cell Division : Morphology of
chromosomes; Euchromatin and Heterochromatin. Nucleic acid as genetic material
(Examples: Bacterial Transformation and Viral Transduction). Brief idea of
Polytene chromosomes:Cell cycle and phases (excluding control mechanism).
Characters of malignant cell; Process & significance of Meiosis.

**Genetics : **Laws of Heredity : (Monohybrid and dihybrid crosses;
Mendel’s laws). Back cross, Test cross, Linkage, Crossing over, Sex linked
inheritance – Colour blindness, Haemophilia. Mutation – Definition and Types;
Replication of DNA, Transcription and Translation (Brief idea).

**Origin, Evolution and Diversity of Life :** Haldane and Oparin’s concept
on origin of life. Modern concept of Natural selection, Biological Species
concept. Human evolution – an outline.

**Taxonomy and Classification :** Definition; Importance of Taxonomy,
Binomial Nomenclature, Law of Priority (Homonym & Synonym).

**Concept of Biodiversity :** Definition of Biodiversity ; Genetic
diversity; Species diversity and Ecosystem diversity. Five kingdom
classification (only distinct characters).Salient features of major animal phyla
with common examples, classification of Chordates (up to Sub Class) with
distinctive characters only.

**Population Biology :**Concept of population growth (logistic and
exponential) and population control.

## All India Engineering Entrance Examinations (AIEEE): 2012

## AIEEE 2012 Syllabus:

## CBSE: All India Engineering
Entrance Examinations (AIEEE)

Syllabus: Physics - 2012

The syllabus contains two Sections - A and B. Section - A pertains to the Theory
Part having 80% weightage, while Section - B contains Practical Component
(Experimental Skills) having 20% weightage.

## SECTION – A

## Unit 1: Physics and Measurement:

Physics, technology and society, S I units, Fundamental and derived units. Least count, accuracy and precision of measuring instruments, Errors in measurement, Dimensions of Physical quantities, dimensional analysis and its applications.

## Unit 2: Kinematics:

Frame of reference. Motion in a straight line: Position-time graph, speed and velocity. Uniform and non-uniform motion, average speed and instantaneous velocity Uniformly accelerated motion, velocity-time, position-time graphs, relations for uniformly accelerated motion. Scalars and Vectors, Vector addition and Subtraction, Zero Vector, Scalar and Vector products, Unit Vector, Resolution of a Vector. Relative Velocity, Motion in a plane, Projectile Motion, Uniform Circular Motion.

## Unit 3: Laws of Motion:

Force and Inertia, Newton’s First Law of motion; Momentum, Newton’s Second Law of motion; Impulse; Newton’s Third Law of motion. Law of conservation of linear momentum and its applications, Equilibrium of concurrent forces. Static and Kinetic friction, laws of friction, rolling friction. Dynamics of uniform circular motion: Centripetal force and its applications.

## Unit 4: Work, Energy and Power:

Work done by a constant force and a variable force; kinetic and potential energies, workenergy theorem, power. Potential energy of a spring, conservation of mechanical energy, conservative and nonconservative forces; Elastic and inelastic collisions in one and two dimensions.

## Unit 5: Rotational Motion:

Centre of mass of a two-particle system, Centre of mass of a rigid body; Basic concepts of rotational motion; moment of a force, torque, angular momentum, conservation of angular momentum and its applications; moment of inertia, radius of gyration. Values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications. Rigid body rotation, equations of rotational motion.

## Unit 6: Gravitation:

The universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. Kepler’s laws of planetary motion. Gravitational potential energy; gravitational potential. Escape velocity. Orbital velocity of a satellite. Geo-stationary satellites.

## Unit 7: Properties of Solids and Liquids:

Elastic behaviour, Stress-strain relationship, Hooke’s Law, Young’s modulus, bulk modulus, modulus of rigidity. Pressure due to a fluid column; Pascal’s law and its applications. Viscosity, Stokes’ law, terminal velocity, streamline and turbulent flow, Reynolds number. Bernoulli’s principle and its applications. Surface energy and surface tension, angle of contact, application of surface tension - drops, bubbles and capillary rise. Heat, temperature, thermal expansion; specific heat capacity, calorimetry; change of state, latent heat. Heat transfer conduction, convection and radiation, Newton’s law of cooling.

## Unit 8: Thermodynamics:

Thermal equilibrium, zeroth law of thermodynamics, concept of temperature. Heat, work and internal energy. First law of thermodynamics. Second law of thermodynamics: reversible and irreversible processes. Carnot engine and its efficiency.

## Unit 9: Kinetic Theory of Gases:

Equation of state of a perfect gas, work doneon compressing a gas.Kinetic theory of gases - assumptions, concept of pressure. Kinetic energy and temperature: rms speed of gas molecules; Degrees of freedom, Law of equipartition of energy,applications to specific heat capacities of gases; Mean free path, Avogadro’s number.

## Unit 10: Oscillations and Waves:

Periodic motion - period, frequency, displacement as a function of time. Periodic functions. Simple harmonic motion (S.H.M.) and its equation; phase; oscillations of a spring -restoring force and force constant; energy in S.H.M. - kinetic and potential energies; Simple pendulum - derivation of expression for its time period; Free, forced and damped oscillations, resonance. Wave motion. Longitudinal and transverse waves, speed of a wave. Displacement relation for a progressive wave. Principle of superposition of waves, reflection of waves, Standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect in sound

## Unit 11: Electrostatics:

Electric charges: Conservation of charge, Coulomb’s law-forces between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field: Electric field due to a point charge, Electric field lines, Electric dipole, Electric field due to a dipole, Torque on a dipole in a uniform electric field. Electric flux, Gauss’s law and its applications to find field due to infinitely long uniformly charged straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell. Electric potential and its calculation for a point charge, electric dipole and system of charges; Equipotential surfaces, Electrical potential energy of a system of two point charges in an electrostatic field. Conductors and insulators, Dielectrics and electric polarization, capacitor, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, Energy stored in a capacitor.

## Unit 12: Current Electricity:

Electric current, Drift velocity, Ohm’s law, Electrical resistance, Resistances of different materials, V-I characteristics of Ohmic and nonohmic conductors, Electrical energy and power, Electrical resistivity, Colour code for resistors; Series and parallel combinations of resistors; Temperature dependence of resistance. Electric Cell and its Internal resistance, potential difference and emf of a cel l, combination of cells in series and in paral lel. Kirchhoff’s laws and their applications. Wheatstone bridge, Metre bridge. Potentiometer - principle and its applicat ions.

## Unit 13: Magnetic Effects of Current and Magnetism:

Biot - Savart law and its application to current carrying circular loop. Ampere’s law and its applications to infinitely long current carrying straight wire and solenoid. Force on a moving charge in uniform magnetic and electric fields. Cyclotron. Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel current-carrying conductors-definition of ampere. Torque experienced by a current loop in uniform magnetic field; Moving coil galvanometer, its current sensitivity and conversion to ammeter and voltmeter. Current loop as a magnetic dipole and its magnetic dipole moment. Bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements. Para-, dia- and ferro- magnetic substances. Magnetic susceptibility and permeability, Hysteresis, Electromagnets and permanent magnets.

## Unit 14: Electromagnetic Induction and Alternating Currents:

Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self and mutual inductance. Alternating currents, peak and rms value of alternating current/ voltage; reactance and impedance; LCR series circuit, resonance; Quality factor, power in AC circuits, wattless current. AC generator and transformer.

## Unit 15: Electromagnetic Waves:

Electromagnetic waves and their characteristics. Transverse nature of electromagnetic waves. Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, Xrays, gamma rays). Applications of e.m. waves.

## Unit 16: Optics:

Reflection and refraction of light at plane and spherical surfaces, mirror formula, Total internal reflection and its applications, Deviation and Dispersion of light by a prism, Lens Formula, Magnification, Power of a Lens, Combination of thin lenses in contact, Microscope and Astronomical Telescope (reflecting and refracting) and their magnifyingpowers. Wave optics: wavefront and Huygens’ principle, Laws of reflection and refraction using Huygen’s principle. Interference, Young’s double slit experiment and expression for fringe width. Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescopes, Polarisation, plane polarized light; Brewster’s law, uses of plane polarized light and Polaroids.

## Unit 17: Dual Nature of Matter and Radiation:

Dual nature of radiation. Photoelectric ef fect , Hertz and Lenard’s observat ions; Einstein’s photoelectric equation; part icle nature of light . Matter waves-wave nature of part icle, de Broglie relation. Davisson-Germer experiment.

## Unit 18: Atoms and Nuclei:

Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum. Composition and size of nucleus, atomic masses, isotopes, isobars; isotones. Radioactivity- lpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number, nuclear fission and fusion.

## CBSE: All India Engineering
Entrance Examinations (AIEEE)

Syllabus: Mathematics - 2012

## Unit 1 : Sets, Relations and Functions:

Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions;. one-one, into and onto functions, composition of functions.

## Unit 2 : Complex Numbers and Quadratic Equations:

Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.

## Unit 3 : Matrices and Determinants:

Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

## Unit 4 : Permutations and Combinations:

Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.

## Unit 5 : Mathematical Induction:

Principle of Mathematical Induction and its simple applications.

## Unit 6 : Binomial Theorem and It's Simple Applications:

Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications.

## Unit 7 : Sequences and Series:

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special series: S n, S n2, Sn3. Arithmetico – Geometric progression.

## Unit 8 : Limit, Continuity and Differentiability:

Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two. Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals.

## Unit 9 : Integral Calculus:

Integral as an anti - derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Evaluation of simple integrals of the type Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

## CBSE: All India Engineering
Entrance Examinations (AIEEE)

Syllabus: Aptitude Test B. Arch./B. Planning - 2012

Part - I Awareness of persons, places, Buildings, Materials.) Objects, Texture related to Architecture and build~environment. Visualising three dimensional objects from two dimensional drawings. Visualising. different sides of three dimensional objects. Analytical Reasoning Mental Ability (Visual, Numerical and Verbal).

## CBSE: All India Engineering
Entrance Examinations (AIEEE)

Syllabus: Chemistry - 2012

## SECTION: A

PHYSICAL CHEMISTRY

## Unit 1: Some Basic Concepts in Chemistry:

Matter and its nature, Dalton’s atomic theory; Concept of atom, molecule, element and compound; Physical quantities and their measurements in Chemistry, precision and accuracy, significant figures, S.I. Units, dimensional analysis; Laws of chemical combination; Atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae; Chemical equations and stoichiometry.

## Unit 2: States of Matter:

Classification of matter into solid, liquid and gaseous states. Gaseous State: Measurable properties of gases; Gas laws - Boyle’s law, Charle’s law, Graham’s law of diffusion, Avogadro’s law, Dalton’s law of partial pressure; Concept of Absolute scale of temperature; Ideal gas equation; Kinetic theory of gases (only postulates); Concept of average, root mean square and most probable velocities; Real gases, deviation from Ideal behaviour, compressibility factor and van der Waals equation. Liquid State: Properties of liquids - vapour pressure, viscosity and surface tension and effect of temperature on them (qualitative treatment only). Solid State: Classification of solids: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea); Bragg’s Law and its applications; Unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids, calculations involving unit cell parameters, imperfection in solids; Electrical, magnetic and dielectric properties.

## Unit 3: Atomic Structure:

Thomson and Rutherford atomic models and their limitations; Nature of electromagnetic radiation, photoelectric effect; Spectrum of hydrogen atom, Bohr model of hydrogen atom - its postulates, derivation of the relations for energy of the electron and radii of the different orbits, limitations of Bohr’s model; Dual nature of matter, de-Broglie’s relationship, Heisenberg uncertainty principle. Elementary ideas of quantum mechanics, quantum mechanical model of atom, its important features, ?? and ??2, concept of atomic orbitals as one electron wave functions; Variation of ?? and ??2 with r for 1s and 2s orbitals; various quantum numbers (principal, angular momentum and magnetic quantum numbers) and their significance; shapes of s, p and d - orbitals, electron spin and spin quantum number; Rules for filling electrons in orbitals – aufbau principle, Pauli’s exclusion principle and Hund’s rule, electronic configuration of elements, extra stability of half-filled and completely filled orbitals.

## Unit 4: Chemical Bonding and Molecular Structure:

Kossel - Lewis approach to chemical bond formation, concept of ionic and covalent bonds. Ionic Bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds; calculation of lattice enthalpy. Covalent Bonding: Concept of electronegativity, Fajan’s rule, dipole moment;Valence Shell Electron Pair Repulsion (VSEPR) theory and shapes of simple molecules. Quantum mechanical approach to covalent bonding: Valence bond theory - Its important features, concept of hybridization involving s, p and d orbitals; Resonance. Molecular Orbital Theory - Its important features, LCAOs, types of molecular orbitals (bonding, antibonding), sigma and pi-bonds, molecular orbital electronic configurations of homonuclear diatomic molecules, concept of bond order, bond length and bond energy. Elementary idea of metallic bonding. Hydrogen bonding and its applications.

## Unit 5: Chemical Thermodynamics:

Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, state functions, types of processes. First law of thermodynamics - Concept of work, heat internal energy and enthalpy, heat capacity, molar heat capacity; Hess’s law of constant heat summation; Enthalpies of bond dissociation, combustion, formation, atomization, sublimation, phase transition, hydration, ionization and solution. Second law of thermodynamics; Spontaneity of processes; DS of the universe and DG of the system as criteria for spontaneity, Dgo (Standard Gibbs energy change) and equilibrium constant.

## Unit 6: Solutions:

Different methods for expressing concentration of solution - molality, molarity, mole fraction, percentage (by volume and mass both), vapour pressure of solutions and Raoult’s Law – Ideal and non-ideal solutions, vapour pressure - composition, plots for ideal and non-ideal solutions; Colligative properties of dilute solutions - relative lowering of vapour pressure, depression of freezing point, elevation of boiling point and osmotic pressure; Determination of molecular mass using colligative properties; Abnormal value of molar mass, van’t Hoff factor and its significance.

## Unit 7: Equilibrium:

Meaning of equilibrium, concept of dynamic equilibrium. Equilibria involving physical processes: Solid -liquid, liquid - gas and solid – gas equilibria, Henry’s law, general characterics of equilibrium involving physical processes. Equilibria involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, significance of DG and DGo in chemical equilibria, factors affecting equilibrium concentration, pressure, temperature, effect of catalyst; Le Chatelier’s principle. Ionic equilibrium: Weak and strong electrolytes, ionization of electrolytes, various concepts of acids and bases (Arrhenius, Br??nsted - Lowry and Lewis) and their ionization, acid - base equilibria (including multistage ionization) and ionization constants, ionization of water, pH scale, common ion effect, hydrolysis of salts and pH of their solutions, solubility of sparingly soluble salts and solubility products, buffer solutions.

## Unit 8: Redox Reactions and Electrochemistry

Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions. Eectrolytic and metallic conduction, conductance in electrolytic solutions, specific and molar conductivities and their variation with concentration: Kohlrausch’s law and its applications. Electrochemical cells - Electrolytic and Galvanic cells, different types of electrodes, electrode potentials including standard electrode potential, half - cell and cell reactions, emf of a Galvanic cell and its measurement; Nernst equation and its applications; Relationship between cell potential and Gibbs’ energy change; Dry cell and lead accumulator; Fuel cells.

## Unit 9 : Chemical Kinetics:

Rate of a chemical reaction, factors affecting the rate of reactions: concentration, temperature, pressure and catalyst; elementary and complex reactions, order and molecularity of reactions, rate law, rate constant and its units, differential and integral forms of zero and first order reactions, their characteristics and half - lives, effect of temperature on rate of reactions – Arrhenius theory, activation energy and its calculation, collision theory of bimolecular gaseous reactions (no derivation).

## IIST: ISAT 2012 Mathematics Syllabus

## PERMUTATIONS AND COMBINATIONS:

Fundamental principle of counting. Permutations and Combinations, derivation of formulae and their connections and simple applications.

## MATHEMATICAL INDUCTION:

Principle of Mathematical Induction and its simple applications.

## BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:

Binomial theorem for positive integral indices, general term and middle term, properties of Binomial coefficients and simple applications.

## SEQUENCES AND SERIES:

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special series n, n2, n3. Arithmetico - Geometric sequence.

## TRIGONOMETRY:

Trigonometric functions. Trigonometrical identities and equations. Inverse Trigonometric functions, their properties and applications.

## COMPLEX NUMBERS AND QUADRATIC EQUATIONS:

Complex numbers as ordered pairs of reals. Representation of complex numbers in a plane. Argand plane and polar representation of complex numbers. Algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality. Quadratic equations in real and complex number system and their solutions. Relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots.

## IIST: ISAT 2012 Chemistry Syllabus

## INORGANIC CHEMISTRY:

Basic Concepts of Chemistry: particulate nature of matter, laws of chemical combination, Dalton’s atomic theory: concept of elements, atoms and molecules. atomic and molecular masses, molecular formula, stoichiometry. Structure of Atom: atomic number, isotopes and isobars. different atomic models and limitations, shells and sub-shells, dual nature of matter and light, de Broglie’s relationship, Heisenberg uncertainty principle, orbitals, quantum numbers, shapes of s, p, and d orbitals, Aufbau principle, Pauli exclusion principle and Hund’s rule, electronic configuration of atoms, stability of half filled and completely filled orbitals.

Classification of Elements and Periodicity in Properties : periodic table, periodic trends in properties of elements Chemical Bonding and Molecular Structure: valence electrons, ionic bond, covalent bond, bond parameters, Lewis structure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR theory, hybridization involving s, p and d orbitals and shapes of some simple molecules, molecular orbital theory of homonuclear diatomic molecules Hydrogen: Occurrence, isotopes, preparation, properties and uses of hydrogen and its compounds. s-Block Elements (Group 1 and Group 2 elements): electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship, trends in the variation of properties and in chemical reactivity, uses. preparation and properties of compounds of Na, Ca, Mg and their biological importance.

p-Block Elements : general Introduction to p-Block Elements Elements of Group 13, 14 15,16, 17and 18: electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group. chemical and physical properties of boron, aluminium, carbon, silicon, nitrogen, phosphorous, oxygen, sulphur, halogens and important compounds of the elements. d and f Block Elements : electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first row transition metals. General Principles and Processes of Isolation of Elements : concentration, oxidation, reduction electrolytic method and refining; occurrence and principles of extraction of aluminium, copper, zinc and iron. Lanthanides: electronic configuration, oxidation states, chemical reactivity and lanthanide contraction.

Actinides: electronic configuration, oxidation states. Coordination compounds: Ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds, bonding; isomerism, importance of coordination compounds.

## PHYSICAL CHEMISTRY:

States of Matter : three states of matter, intermolecular interactions, type of bonding, melting and boiling points, molecular, ionic, covalent and metallic solids, amorphous and crystalline solids, unit cell in two dimensional and three dimensional lattices, calculation of density of unit cell, packing in solids, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties. Boyle’s law, Charles’ law, Gay Lussac’s law, Avogadro’s law, ideal behaviour, empirical derivation of gas equation, Avogadro’s number, ideal gas equation, deviation from ideal behaviour, liquefaction of gases, critical temperature. liquid State.

Solutions : types of solutions, solubility of gases in liquids, solid solutions, colligative properties – relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic pressure, determination of molecular masses

Thermodynamics : systems, surroundings, work, heat, energy, extensive and intensive properties, state functions. first law of thermodynamics – internal energy and enthalpy, heat capacity and specific heat, measurement of ΔU and ΔH, Hess’s law of constant heat summation, enthalpy of: bond dissociation, combustion, formation, atomization, sublimation, phase transition, ionization, and dilution. entropy as a state function, free energy change for spontaneous and nonspontaneous process, equilibrium.

Equilibrium : equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium – Le Chatelier’s principle; ionic equilibrium – onization of acids and bases, strong and weak electrolytes, degree of ionization, concept of pH. Hydrolysis of salts, buffer solutions, solubility product, common ion effect. Redox Reactions : redox reactions, oxidation number, balancing redox reactions, applications of redox reactions.

## IIST: ISAT 2012 Physics Syllabus

## MECHANICS:

Units and Measurements: The international system of units, measurement of length, mass and time, accuracy, precision of instruments and errors in measurement, Significant figures, dimension of physical quantities, dimensional formulae and equations, dimensional analysis and its applications. Motion in a straight line: position, path length and displacement, average velocity and speed, instantaneous velocity and speed, acceleration, kinematic equations for uniformly accelerated motion, relative velocity.

Motion in a plane: scalars and vectors, multiplication of vectors by real numbers, addition and aubtraction of ectors- graphical method, resolution of vectors, vector addition – analytical method, motion in a plane, motion in a plane with constant acceleration, relative velocity in two dimensions, projectile motion, uniform circular motion.

Laws of motion: the law of inertia, Newton’s first, second and third law of motion, conservation of momentum, equilibrium of particle, common forces in mechanics,circular motion. Work, Power and Energy: the work energy theorem, kinetic and potential energy, work-energy theorem for variable force, the conservation of mechanical energy, Power, the potential energy of a spring, collisions.

System of particles and rotational motion: centre of mass, motion of centre of mass, linear momentum of a system of particles, vector product of two vectors, angular velocity and linear velocity relations, torque and angular momentum, equilibrium of a rigid body, Moment of Inertia, theorem of perpendicular and parallel axes, kinematics and dynamics of rotational motion about a fixed axis, angular momentum in case of rotation about a fixed axis, rolling motion Gravitation: Kepler’s laws, universal law of gravitation, gravitation constant, acceleration due to gravity of the earth, acceleration due to gravity below and above the surface of earth, gravitational potential energy.

## ELETROMAGNETISM:

Electric charges and Fields: Electric charges, conductors and insulators, basic properties of electric charge, Coulomb’s law, Force between multiple charges, electric field and flux, electric dipole, continuous charge distribution, Gauss’s law and its applications.

Electrostatic Potential and capacitance: electrostatic potential, potential due to a point charge and systems of charges, potential due to an electric dipole, equipotential surfaces, Potential energy in an external field, electrostatics of conductors, dielectric and polarization, capacitors and capacitance, the parallel plate capacitor, combination of capacitors, energy stored in a capacitor. Current Electricity: electric current, electric currents in conductors, Ohm’s law, drift of electrons and origin of resistivity, resistivity and its temperature dependence, electrical energy and power, Combination of resistors (Series and Parallel) , cells, emf, internal resistance, cells in series and parallel, Kirchoff’s laws, Wheatstone bridge, meter bridge, and potentiometer.

## Indian Institutes of Technology

Joint Entrance Examination, IIT-JEE - 2012

## Aptitude Test Syllabus

**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.

## Indian Institutes of Technology

Joint Entrance Examination, IIT-JEE - 2012

## Mathematics Syllabus

**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.