**AUCET Syllabus** for Entrance Test in Science, Arts, Commerce and Engineering is given below.

### 101 – Life Sciences

**Cell Biology :** Ultrastructure of prokaryotic and eukaryotic cell, Structure and function of cell organelles. Cell division – Mitosis and Meiosis. Chromosomes structure, Karyotype.

**Genetics :** Mendelian principles, Gene Interaction, Linkage and Crossing over, Sex determination, Sex linkage, Mutations – Genic and chromosomal (Structural and numerical); Chromosomal aberrations in humans. Recombination in prokaryotes transformation, conjugation, transduction, sexduction. Extra genomic inheritance

**Molecular Biology and Genetic Engineering :** Structure of eukaryotic gene, DNA and RNA structure, DNA replication in pro and eukaryotes, Transcription and translation in pro and eukaryotes, genetic code. Regulation of gene expression in prokaryotes, Principles of recombinant DNA technology. DNA vectors, Transgenesis. Applications of genetic engineering.

**Biotechnology :** Plant and animal cell culture, cloning, Fermentors types and process, Biopesticides, biofertilizers, Bioremediation, Renewable and non – renewable energy resources, Non-conventional fuels.

**Biomolecules :** Carbohydrates, proteins, amino acids, lipids, vitamins and porphyrins. Enzymes – classification and mode of action, enzyme assay, enzyme units, enzyme inhibition, enzyme kinetics, Factors regulating enzyme action.

**Immunology :** Types of immunity, cells and organelles of immune system, Antigen – antibody reaction. Immunotechniques, Hypersensitivity, Vaccines.

**Techniques :** Microscopy – Light and Electron, Centrifugation, Chromatography, Eletrophoresis, Calorimetric and Spectrophotometric techniques, Blotting techniques, PCR, DNA finger printing.

**Ecology, Environment and Evolution :** Theories and evidences of organic evolution, Hardy – Weinberg law. Components of an ecosystem, Ecological pyramids, Biogeochemical cycles, Ecological adaptations. Climatic and edaphic and biotic factors. Ecological sucession – Hydrosere and xerosere, Natural resources, Biodiversity, current environmental issues, Environmental pollution, Globla warming and climate change.

**Physiology :** Structure and function of liver, kidney and heart, composition of blood, blood types, blood coagulation, Digestion and absorption, Endocrinology, Muscle and Nervous system

**Metabolism :** Metabolism of carbohydrates, lipids, proteins, aminoacids and nucleic acids. Biological oxidation and bioenergetics.

**Animal Science :** Biology of invertebrates and chordates, Embryology of chordates, Classification of marine environment – Physical and chemical parameters, Marine, estuarine, reservoir and riverine fisheries, Cultivation of fin and shell fish. Culture practices

**Plant Science :** Classification of cryptogams and phanerogams. General characteristics of taxonomic groups at class and family level Water relations and mineral nutrition of plants, Plant growth regulators, Ethnobotany and medicinal plants, Biology of plant seed, Photosynthesis.

**Microbiology :** Microbes – Types, distribution and biology. Isolation and cultivation of bacteria and virus. Staining techniques. Bacterial growth curve, Microbial diseases – food and water borne, insect borne, contact diseases in humans. Microbial diseases in plants – by bacteria, fungi and virus, Plant microbe – interactions.

**Nutrition :** Biological value of proteins, protein malnutrition, disorders, Chemistry and physiological role of vitamins and minerals in living systems.

### 102 – Physical Sciences

**Electricity, Magnetism and Electronics**

**1.Electrostatics :** Gauss law and its applications-Uniformly charged sphere, charged cylindrical conductor and an infinite conducting sheet of charge. Deduction of Coulmb’s law from Gauss law Mechanical force on a charged conductor Electric potential – Potential due to a charged spherical conductor, electric field strength from the electric dipole and an infinite line of charge. Potential of a uniformly charged circular disc

**2. Dielectrics :** An atomic view of dielectrics, potential energy of a dipole in an electric field. Polarization and charge density, Gauss’s law for dielectric medium- Relation between D,E, and P. Dielectric constant, susceptibility and relation between them. Boundary conditions at the dielectric surface. Electric fields in cavities of a dielectric-needle shaped cavity and disc shaped cavity.

**3. Capacitance :** Capacitance of concentric spheres and cylindrical condenser, capacitance of parallel plate condenser with and without dielectric. Electric energy stored in a charged condenser – force between plates of condenser, construction and working of attracted disc electrometer, measurement of dielectric constant and potential difference.

**4. Magnetostatics :** Magnetic shell – potential due to magnetic shell – field due to magnetic shell -equivalent of electric circuit and magnetic shell – Magnetic induction (B) and field (H) -permeability and susceptibility – Hysteresis loop.

**5. Moving charge in electric and magnetic field :** Hall effect, cyclotron, synchrocyclotron and synchrotron – force on a current carrying conductor placed in a magnetic field, force and torque on a current loop, Biot -Savart’s law and calculation of B due to long straight wire, a circular current loop and solenoid

**6. Electromagnetic induction :** Faraday’s law -Lenz’s law – expression for induced emf – time varying magnetic fields -Betatron -Ballistic galvanometer – theory – damping correction – self and mutual inductance, coefficient of coupling, calculation of self inductance of a long solenoid -toroid – energy stored in magnetic field – transformer – Construction, working, energy losses and efficiency.

**7. Varying and alternating currents :** Growth and decay of currents in LR, CR and LCR circuits – Critical damping. Alternating current relation between current and voltage in pure R,C and L-vector diagrams -Power in ac circuits. LCR series and parallel resonant circuit – Q-factor. AC & DC motors-single phase, three phase (basics only).

**8. Maxwell’s equations and electromagnetic waves :** A review of basic laws of electricity and magnetism – displacement current – Maxwell’s equations in differential form – Maxwell’s wave equation, plane electromagnetic waves -Transverse nature of electromagnetic waves, Poynting theorem, production of electromagnetic waves (Hertz experiment).

**9. Basic Electronics :** Formation of electron energy bands in solids, classification of solids in terms of forbidden energy gap. Intrinsic and extrinsic semiconductors, Fermi level, continuity equation – p-n junction diode, Zener diode characteristics and its application as voltage regulator. Half wave and full wave, rectifiers and filters, ripple factor (quantitative) – p n p and n p n transistors, current components in transistors, CB.CE and CC configurations – transistor hybrid parameters – determination of hybrid parameters from transistor characteristics -transistor as an amplifier — concept of negative feed back and positive feed back – Barkhausen criterion, RC coupled amplifier and phase shift oscillator (qualitative).

**10. Digital Principles :** Binary number system, converting Binary to Decimal and vice versa. Binary addition and subtraction (1’s and 2’s complement methods). Hexadecimal number system. Conversion from Binary to Hexadecimal – vice versa and Decimal to Hexadecimal vice versa.

**Logic gates:** OR,AND,NOT gates, truth tables, realization of these gates using discrete components. NAND, NOR as universal gates, Exclusive – OR gate,De Morgan’s Laws – statement and proof, Half and Full adders. Parallel adder circuits.

**Modern Physics**

**1. Atomic Spectra** : Introduction – Drawbacks of Bohr’s atomic model – Sommerfeld’s elliptical orbits – relativistic correction (no derivation). Stern & Gerlach experiment Vector atom model and quantum numbers associated with it. L-S and j-j coupling schemes. Spectral terms, selection rules, intensity rules. Spectra of alkali atoms, doublet fine structure. Alkaline earth spectra, singlet and triplet fine structure. Zeeman Effect, Paschen-Back Effect and Stark Effect.

**2. Molecular Spectroscopy:** Types of molecular spectra, pure rotational energies and spectrum of diatomic molecule, determination of internuclear distance. Vibrational energies and spectrum of diatomic molecule. Raman effect, Classical theory of Raman effect. Experimental arrangement for Raman effect and its applications.

**3. Quantum MechanicsInadequacy of classical Physics:** (Discussion only)Spectral radiation – Planck’s law. Photoelectric effect – Einstien’s photoelectric equation. Compton’s effect (quantitative) experimental verification. Stability of an atom – Bohr’s atomic theory. Limitations of old quantum theory.

**4. Matter Waves: **de Broglie’s hypothesis – wavelength of matter waves, properties of matter waves. Phase and group velocities. Davisson and Germer experiment. Double slit experiment. Standing de Brogile waves of electron in Bohr orbits.

**5. Uncertainity Principle:** Heisenberg’s uncertainty principle for position and momentum (x and px), Energy and time (E and t). Gamma ray microscope. Diffraction by a single slit. Position of electron in a Bohr orbit. Particle in a box. Complementary principle of Bohr..

**6. Schrodinger Wave Equation: **Schrodinger time independent and time dependent wave equations. Wave function properties – Significance. Basic postulates of quantum mechanics. Operators, eigen functions and eigen values, expectation values. Application of Schrodinger wave equation to particle in one and three dimensional boxes, potential step and potential barrier.

**7. Nuclear PhysicsNuclear Structure:** Basic properties of nucleus – size, charge, mass, spin, magnetic dipole moment and electric quadrupole moment. Binding energy of nucleus, deuteron binding energy, p-p and n-p scattering (concepts), nuclear forces. Nuclear models – liquid drop model, shell model.

**8. Alpha and Beta Decays:** Range of alpha particles, Geiger – Nuttal law, Gammow’s theory of alpha decay. Geiger – Nuttal law from Gammow’s theory. Beta spectrum – neutrino hypothesis, Fermi’s theory of p-decay (qualitative).

**9. Nuclear Reactions:** Types of nuclear reactions, channels, nuclear reaction kinematics. Compound nucleus, direct reactions (concepts).Nuclear Detectors – GM counter, proportional counter, scintillation counter, Wilson cloud chamber and solid state detector Solid State Physics

**10. Crystal Structure:** Crystalline nature of matter. Cystal lattice, Unit Cell, Elements of symmetry. Crystal systems, Bravais lattices. Miller indices. Simple crystal structures (S.C., BCC, CsCI, FCC, NaCI diamond and Zinc Blends).

**11. X-ray Diffraction:** Diffraction of X -rays by crystals, Bragg’s law, Experimental techniques – Laue’s method and powder method

**12. Nanomaterials:** Introduction, Nan particles, metal nanoclusters, semiconductor nanoparticles, carbon clusters, carbon nanotubes, quantum nanostructures – nanodot, nanowire and quantum well. Fabrication of quantum nanostructures.

**13. Bonding in Crystals:** Types of bonding in crystals – characteristics of crystals with different bindings. Lattice energy of ionic crystals – determination of Medelung constant for NaCI crystal, calculation of Born coefficient and repulsive exponent. Born – Haber cycle.

**14. Magnetism:** Magnetic properties of dia, para and ferromagnetic materials. Langevin’s theory of paramagnetism. Weiss’ theory of ferromagnetism -Concepts of magnetic domains, antiferromagnetism and ferrimagnetism ferrites and their applications

**15. Superconductivity:** Basic experimental facts – zero resistance, effect of magnetic field, Meissner effect, persistent current, Isotope effect Thermodynamic properties, specific heat, entropy. Type I and Type II superconductors.Elements of BCS theory-Cooper pairs. Applications. High temperature superconductors (general information).

**Thermodynamics and Optics**

**1. Kinetic theory of gases:** Introduction – Deduction of Maxwell’s law of distribution of molecular speeds, Experimental verification Toothed Wheel Experiment, Transport Phenomena – Viscosity of gases – thermal conductivity – diffusion of gases.

**2. Thermodynamics:** Introduction – Reversible and irreversible processes – Carnot’s engine and its efficiency – Carnot’s theorem – Second law of thermodynamics, Kelvin’s and Claussius statements – Thermodynamic scale of temperature – Entropy, physical significance – Change in entropy in reversible and irreversible processes – Entropy and disorder – Entropy of universe – Temperature- Entropy (T-S) diagram – Change of entropy of a perfect gas-change of entropy when ice changes into steam.

**3. Thermodynamic potentials and Maxwell’s equations:** Thermodynamic potentials – Derivation of Maxwell’s thermodynamic relations -Clausius-Clayperon’s equation – Derivation for ratio of specific heats – Derivation for difference of two specific heats for perfect gas. Joule Kelvin effect – expression for Joule Kelvin coefficient for perfect and Vanderwaal’s gas.

**4. Low temperature Physics:** Introduction – Joule Kelvin effect – liquefaction of gas using porous plug experiment. Joule expansion – Distinction between adiabatic and Joule Thomson expansion -Expression for Joule Thomson cooling – Liquefaction of helium, Kapitza’s method -Adiabatic demagnetization – Production of low temperatures – Principle of refrigeration, vapour compression type. Working of refrigerator and Air conditioning machines. Effects of Chloro and Fluro Carbons on Ozone layer; applications of substances at low-temperature.

**5. Quantum theory of radiation**: Black body-Ferry’s black body – distribution of energy in the spectrum of Black body -Wein’s displacement law, Wein’s law, Rayleigh-Jean’s law – Quantum theory of radiation – Planck’s law – deduction of Wein’s law, Rayleigh-Jeans law, from Planck’s law -Measurement of radiation – Types of pyrometers – Disappearing filament optical pyrometer – experimental determination – Angstrom pyroheliometer – determination of solar constant, effective temperature of sun.

**6. Statistical Mechanics:** Introduction to statistical mechanics, concept of ensembles, Phase space, MaxwellBoltzmann’s distribution law, Molecular energies in an ideal gas, Bose-Einstein Distribution law, FermiDirac Distribution law, comparison of three distribution laws, Black Body Radiation, Rayleigh-Jean’s formula, Planck’s radiation law, Weins Displacement, Stefan’s Boltzmann’s law from Plancks formula. Application of Fermi-Dirac statistics to white dwarfs and Neutron stars.

**7. The Matrix methods in paraxial optics:** Introduction, the matrix method, effect of translation, effect of refraction, imaging by a spherical refracting surface. Imaging by a co-axial optical system. Unit planes. Nodal planes. A system of two thin lenses.

**8. Aberrations:** Introduction – Monochromatic aberrations, spherical aberration, methods of minimizing spherical aberration, coma, astigmatism and curvature of field, distortion. Chromatic aberration – the achromatic doublet – Removal of chromatic aberration of a separated doublet.

**9. Interference:** Principle of superposition – coherence – temporal coherence and spatial coherence -conditions for Interference of light Interference by division of wave front: Fresnel’s biprism – determination of wave length of light. Determination of thickness of a transparent material using Biprism -change of phase on reflection – Lloyd’s mirror experiment.Interference by division of amplitude: Oblique incidence of a plane wave on a thin film due to reflected and transmitted light (Cosine law) – Colours of thin films – Non reflecting films – interference by a plane parallel film illuminated by a point source – Interference by a film with two nonparallel reflecting surfaces (Wedge shaped film) – Determination of diameter of wire-Newton’s rings in reflected light with and without contact between lens and glass plate, Newton’s rings in transmitted light (Haidinger Fringes) -Determination of wave length of monochromatic light – Michelson Interferometer – types of fringes – Determination of wavelength of monochromatic light, Difference in wavelength of sodium 0^2 lines and thickness of a thin transparent plate.

**10. Diffraction**: Introduction – Distinction between Fresnel and Fraunhoffer diffraction Fraunhoffer diffraction:- Diffraction due to single slit and circular aperture – Limit of resolution – Fraunhoffer diffraction due to double slit – Fraunhoffer diffraction pattern with N slits (diffraction grating) Resolving Power of grating – Determination of wave length of light in normal and oblique incidence methods using diffraction grating.Fresnel diffraction:- Fresnel’s half period zones – area of the half period zones -zone plate – Comparison of zone plate with convex lens – Phase reversal zone plate – diffraction at a straight edge – difference between interference and diffraction.

**11. Polarization :** Polarized light : Methods of Polarization, Polarizatioin by reflection, refraction, Double refraction, selective absorption , scattering of light – Brewsters law – Malus law – Nicol prism polarizer and analyzer – Refraction of plane wave incident on negative and positive crystals (Huygen’s explanation) – Quarter wave plate, Half wave plate -Babinet’s compensator – Optical activity, analysis of light by Laurent’s half shade polarimeter.

**12. Laser, Fiber Optics and Holography :** Lasers: Introduction – Spontaneous emission – Stimulated emission – Population inversion . Laser principle – Einstein coefficients – Types of Lasers – He-Ne laser -Ruby laser – Applications of lasers.Fiber Optics : Introduction – Optical fibers – Types of optical fibers – Step and graded index fibers – Rays and modes in an optical fiber – Fiber material – Principles of fiber communication (qualitative treatment only) and advantages of fiber communication. Holography: Basic Principle of Holography – Gabor hologram and its limitations, Holography applications.

**Mechanics and Waves and Oscillations**

**1. Vector Analysis:** Scalar and vector fields, gradient of a scalar field and its physical significance. Divergence and curl of a vector field and related problems. Vector integration, line, surface and volume integrals. Stokes, Gauss and Greens theorems- simple applications.\

**2. Mechanics of Particles :** Laws of motion, motion of variable mass system, motion of a rocket, multi-stage rocket, conservation of energy and momentum. Collisions in two and three dimensions, concept of impact parameter, scattering cross-section, Rutherford scattering

**3. Mechanics of rigid bodies :** Definition of Rigid body, rotational kinematic relations, equation of motion for a rotating body, angular momentum and inertial tensor. Eulers equation, precession of a top, Gyroscope, precession of the equinoxes.

**4. Mechanics of continuous media** : Elastic constants of isotropic solids and their relation, Poisson’s ratio and expression for Poisson’s ratio in terms of y, n, k. Classification of beams, types of bending, point load, distributed load, shearing force and bending moment, sign conventions, simple supported beam carrying a concentrated load at mid span, cantilever with an end load

**5. Central forces :** Central forces – definition and examples, conservative nature of central forces, conservative force as a negative gradient of potential energy, equation of motion under a central force, gravitational potential and gravitational field, motion under inverse square law, derivation of Kepler’s laws, Coriolis force and its expressions.

**6. Special theory of relativity** : Galilean relativity, absolute frames, Michelson-Morley experiment, Postulates of special theory of relativity. Lorentz transformation, time dilation, length contraction, addition of velocities, mass-energy relation. Concept of four vector formalism.

**7. Fundamentals of vibrations :** Simple harmonic oscillator, and solution of the differential equation- Physical characteristics of SHM, torsion pendulum, – measurements of rigidity modulus , compound pendulum, measurement of ‘g’, combination of two mutually perpendicular simple harmonic vibrations of same frequency and different frequencies, Lissajous figures

**8. Damped and forced oscillations** : Damped harmonic oscillator, solution of the differential equation of damped oscillator. Energy considerations, comparison with undamped harmonic oscillator, logarithmic decrement, relaxation time, quality factor, differential equation of forced oscillator and its solution, amplitude resonance, velocity resonance

**9. Complex vibrations** : Fourier theorem and evaluation of the Fourier coefficients, analysis of periodic wave functions-square wave, triangular wave, saw-tooth wave

**10.Vibrations of bars :**Longitudinal vibrations in bars- wave equation and its general solution. Special cases (i) bar fixed at both ends ii) bar fixed at the mid point iii) bar free at both ends iv) bar fixed at one end. Transverse vibrations in a bar- wave equation and its general solution. Boundary conditions, clamped free bar, freefree bar, bar supported at both ends, Tuning fork.

**11. Vibrating Strings :** Transverse wave propagation along a stretched string, general solution of wave equation and its significance, modes of vibration of stretched string clamped at both ends, overtones, energy transport, transverse impedance

**12. Ultrasonics :** Ultrasonics, properties of ultrasonic waves, production of ultrasonics by piezoelectric and magnetostriction methods, detection of ultrasonics, determination of wavelength of ultrasonic waves. Velocity of ultrasonics in liquids by Sear’s method. Applications of ultrasonic waves.

### 103 – Mathematical Sciences

**LINEAR ALGEBRA AND VECTOR CALCULUS**

**Linear Algebra** : Vector spaces, General properties of vector spaces, Vector subspaces, Algebra of subspaces, linear combination of vectors. Linear span, linear sum of two subspaces, Linear independence and dependence of vectors, Basis of vector space, Finite dimensional vector spaces, Dimension of a vector space, Dimension of a subspace. Linear transformations, linear operators, Range and null space of linear transformation, Rank and nullity of linear transformations, Linear transformations as vectors, Product of linear transformations, Invertible linear transformation.

The adjoint or transpose of a linear transformation, Sylvester’s law of nullity, characteristic values and characteristic vectors , Cayley- Hamilton theorem, Diagonalizable operators. Inner product spaces, Euclidean and unitary spaces, Norm or length of a vector, Schwartz inequality, Orthogonality, Orthonormal set, complete orthonormal set, Gram – Schmidt orthogonalisation process.

**Multiple integrals and Vector Calculus** : Multiple integrals : Introduction, the concept of a plane, Curve, line integral- Sufficient condition for the existence of the integral. The area of a subset of 2 R , Calculation of double integrals, Jordan curve , Area, Change of the order of integration, Double integral as a limit, Change of variable in a double integration.

Vector differentiation, Ordinary derivatives of vectors, Space curves, Continuity, Differentiability, Gradient, Divergence, Curl operators, Formulae involving these operators. Vector integration, Theorems of Gauss and Stokes, Green’s theorem in plane and applications of these theorems.

**Abstract Algebra & Real Analysis**

**Groups** :Binary operations- Definitions and properties, Groups—Definition and elementary properties, Finite groups and group composition tables, Subgroups and cyclic subgroups. Permutations—Functions and permutations ,groups of permutations, cycles and cyclic notation, even and odd permutations, The alternating groups. Cyclic groups – Elementary properties ,The classification of cyclic groups , sub groups of finite cyclic groups. Isomorphism – Definition and elementary properties, Cayley’s theorem, Groups of cosets, Applications, Normal subgroups – Factor groups , Criteria for the existence of a coset group, Inner automorphisms and normal subgroups, factor groups and simple groups, Homomorphism- Definition and elementary properties, The fundamental theorem of homomorphisms, applications.

**RINGS**: Definition and basic properties, Fields, Integral domains, divisors of zero and Cancellation laws, Integral domains, The characteristic of a ring, some non – commutative rings, Examples, Matrices over a field, The real quaternions ,Homomorphism of Rings – Definition and elementary properties, Maximal and Prime ideals, Prime fields.

**REAL NUMBERS:** The Completeness Properties of R, Applications of the Supremum Property. Sequences and Series – Sequences and their limits, limit theorems, Monotonic Sequences, Sub-sequences and the Bolzano-Weirstrass theorem,The Cauchy’s Criterion, Properly divergent sequences, Introduction to series, Absolute convergence, test for absolute convergence, test for non-absolute convergence. Continuous Functions-continuous functions, combinations of continuous functions, continuous functions on intervals, Uniform continuity.

**DIFFERENTIATION AND INTEGRATION:** The derivative, The mean value theorems, L’Hospital Rule, Taylor’s Theorem. Riemann integration – Riemann integral , Riemann integrable functions, Fundamental theorem.

**DIFFERENTIAL EQUATIONS & SOLID GEOMETRY**

**Differential equations of first order and first degree** : Linear differential equations; Differential equations reducible to linear form; Exact differential equations; Integrating factors; Change of variables; Simultaneous differential equations; Orthogonal trajectories. Differential equations of the first order but not of the first degree: Equations solvable for p; Equations solvable for y; Equations solvable for x; Equations that do not contain x (or y); Equations of the first degree in x and y – Clairaut’s equation.

** Higher order linear differential equations :** Solution of homogeneous linear differential equations of order n with constantcoefficients. Solution of the non-homogeneous linear differential equations with constant coefficients by means of polynomial operators. Method of undetermined coefficients; Method of variation of parameters; Linear differential equations with non-constant coefficients; The Cauchy-Euler equation

**System of linear differential equations:** Solution of a system of linear equations with constant coefficients; An equivalent triangular system. Degenerate Case: p_{1} (D) p_{4} (D) – p_{2} (D) p_{3} (D) = 0.

**The Line**: Equations of a line, Angle between a line and a plane, The condition that a given line may lie in a given plane, The condition that two given lines are coplanar, Number of arbitrary constants in the equations of a straight line. Sets of conditions which determine a line, The shortest distance between two lines. The length and equations of the line of shortest distance between two straight lines, Length of the perpendicular from a given point to a given line, Intersection of three planes, Triangular Prism.

**The Sphere**: Definition and equation of the sphere, Equation of the sphere through four given points, Plane sections of a sphere. Intersection of two spheres; Equation of a circle. Sphere through a given circle; Intersection of a sphere and a line. Power of a point; Tangent plane. Plane of contact. Polar plane, Pole of a plane, Conjugate points, Conjugate planes; Angle of intersection of two spheres. Conditions for two spheres to be orthogonal; Radical plane. Coaxial system of spheres; Simplified from of the equation of two spheres.

**Cones, Cylinders and conicoids**: Definitions of a cone, vertex, guiding curve, generators. Equation of the cone with a given vertex and guiding curve. Enveloping cone of a sphere. Equations of cones with vertex at origin are homogenous. Condition that the general equation of the second degree should represent a cone. Condition that a cone may have three mutually perpendicular generators Intersection of a line and a quadric cone. Tangent lines and tangent plane at a point. Condition that a plane may touch a cone. Reciprocal cones. Intersection of two cones with a common vertex. Right circular cone. Equation of the right circular cone with a given vertex, axis and semivertical angle. Definition of a cylinder. Equation to the cylinder whose generators intersect a given conic and are parallel to a given line, Enveloping cylinder of a sphere. The right circular cylinder. Equation of the right circular cylinder with a given axis and radius.

The general equation of the second degree and the various surfaces represented by it; Shapes of some surfaces. Nature of Ellipsoid. Nature of Hyperboloid of one sheet.

### 104 – Chemical Sciences

**INORGANIC CHEMISTRY**

**104 – Chemical Sciences**

**1. s-block elements**: General characteristics of groups I & II elements, diagonal relationship between Li & Mg, Be & Al.

**2. p-block elements:**

General characteristics of elements of groups 13, 14, 15, 16 and 17

Group – 13: Synthesis and structure of diborane and higher boranes (B_{4} H_{10} and B_{5} H_{9} ), boron-nitrogen compounds (B_{3} N_{3} H_{6} and BN and BN)

Group – 14: Preparation and applications of silanes and silicones, graphitic compounds.

Group – 15: Preparation and reactions of hydrazine, hydroxylamine, phosphazenes.

Group – 16: Classifications of oxides based on (i) Chemical behaviour and (ii) Oxygen content. Group – 17: Inter halogen compounds and pseudo halogens

**3. Organometallic Chemistry :** Definition and classification of organometallic compounds, nomenclature, preparation, properties and applications of alkyls of 1, 2 and 13 group elements.

**4. Chemistry of d-block elements:** Characteristics of d-block elements with special reference to electronic configuration, variable valence, magnetic properties, catalytic properties and ability to form complexes. Stability of various oxidation states and e.m.f. Comparative treatment of second and third transition series with their 3d analogues. Study of Ti, Cr and Cu traids in respect of electronic configuration and reactivity of different oxidation states.

**5. Chemistry of f-lock elements:** Chemistry of lanthanides – electronic structure, oxidation states, lanthanide contraction, consequences of lanthanide contraction, magnetic properties, spectral properties and separation of lanthanides by ion exchange and solvent extraction methods. Chemistry of actinides – electronic configuration, oxidation states, actinide contraction, position of actinides in the periodic table, comparison with lanthanides in terms of magnetic properties, spectral properties and complex formation.

**6. Theories of bonding in metals:** Valence bond theory, Explanation of metallic properties and its limitations, Free electron theory, thermal and electrical conductivity of metals, limitations, Band theory, formation of bands, explanation of conductors, semiconductors and insulators

**7. Metal carbonyls and related compounds** – EAN rule, classification of metal carbonyls, structures and shapes of metal carbonyls of V, Cr, Mn, Fe, Co and Ni. Metal nitrosyls and metallocenes (only ferrocene).

**8. Coordination Chemistry:** IUPAC nomenclature, bonding theories – review of Werner’s theory and Sidgwick’s concept of coordination, Valence bond theory, geometries of coordination numbers 4-tetrahedral and square planar and 6-octahedral and its limitations, crystal filed theory, splitting of d-orbitals in octahedral, tetrahedral and square-planar complexes – low spin and high spin complexes – factors affecting crystalfield splitting energy, merits and demerits of crystal-field theory. Isomerism in coordination compounds – structural isomerism and stereo isomerism, stereochemistry of complexes with 4 and 6 coordination numbers..

**9. Spectral and Magnetic Properties of Metal Complexes:** Electronic absorption spectrum of [Ti(H_{2}O)_{6} ]^{3}+ ion. Types of magnetic behavior, spin-only formula, calculation of magnetic moments, experimental determination of magnetic susceptibility – Gouy method.

**10. Reactivity of metal complexes:** Labile and inert complexes, ligand substitution reactions – S_{N}1 and S_{N}2, substitution reactions of square planar complexes – Trans effect and applications of trans effect

**11. Stability of Metal Complexes**: Thermodynamic stability and kinetic stability, factors affecting the stability of metal complexes, chelate effect, determination of composition of complex by Job’s method and mole ratio method.

**12. Hard and soft acids bases (HSAB):** Classification, Pearson’s concept of hardness and softness, application of HSAB principles – Stability of compounds / complexes, predicting the feasibility of a reaction..

**13. Bioinorganic Chemistry:** Essential elements, biological significance of Na, K, Mg, Ca, Fe, Co, Ni, Cu, Zn and chloride (Cl- ). Metalloporphyrins – hemoglobin, structure and function, Chlorophyll, structure and role in photosynthesis..

**ORGANIC CHEMISTRY**

**1. Structural theory in Organic Chemistry :** Types of bond fission and organic reagents (Electrophilic, Nucleophilic, and free radical reagents including neutral molecules like H_{2} O, NH_{3} & AlCl_{3} ). Bond polarization : Factors influencing the polarization of covalent bonds, electronegativity – inductive effect. Application of inductive effect (a) Basicity of amines (b) Acidity of carboxylic acides (c) Stability of carbonium ions. Resonance or Mesomeric effect, application to (a) acidity of phenol, and (b) acidity of carboxylic acids. Hyper conjugation and its application to stability of carbonium ions, Free radicals and alkenes, carbanions, carbenes and nitrenes. Types of Organic reactions : Addition – electrophilic, nucleophilic and free radical. Substitution – electrophilic, nucleophilic and free radical. Elimination- Examples (mechanism not required).

**2. Acyclic Hydrocarbons : **Alkanes– IUPAC Nomenclature of Hydrocarbons. Methods of preparation: Hydrogenation of alkynes and alkenes, Wurtz reaction, Kolbe’s electrolysis, Corey- House reaction. Chemical reactivity – inert nature, free radical substitution mechanism. Halogenation example- reactivity, selectivity and orientation.

Alkenes – Preparation of alkenes (a) by dehydration of alcohols (b) by dehydrohalogenation of alkyl halides (c) by dehalogenation of 1,2 dihalides (brief mechanism), Saytzev’s rule. Properties: Addition of hydrogen – heat of hydrogenation and stability of alkenes. Addition of halogen and its mechanism. Addition of HX, Markonikov’s rule, addition of H_{2} O, H_{2}OX, H_{2} SO_{4} with mechanism and addition of HBr in the presence of peroxide (anti – Markonikov’s addition ).

Oxidation – hydroxylation by KMnO , OsO , peracids (via epoxidation ) hydroboration, Dienes – Types of dienes, reactions of conjugated dines – 1,2 and 1,4 addition of HBr to 1,3 – butadiene and Diel’s – Alder reaction.

Alkynes – Preparation by dehydrohalogenation of dihalides, dehalogenation of tetrahalides, Properties; Acidity of acetylenic hydrogen (formation of Metal acedtylides). Preperation of higher acetylenes, Metal ammonia reductions Physical properties. Chemical reactivity – electrophilic addition of X_{2} , HX, H_{2} O (Tautomerism), Oxidation with KMnO_{4} , OsO_{4} , reduction and Polymerisation reaction of acetylene.

**3. Alicyclic hydrocarbons (Cycloalkanes) :** Nomenclature, Preparation by Freunds methods, heating dicarboxylic metal salts. Properties – reactivity of cyclopropane and cyclobutane by comparing with alkanes, Stability of cycloalkanes – Baeyer’s strain theory, Sachse and Mohr predictions and Pitzer’s strain theory. Conformational structures of cyclobutane, cyclopentane, cyclohexane.

**4. Benzene and its reactivity :** Concept of resonance, resonance energy. Heat of hydrogenation, heat of combustion of Benezene, mention of C-C bond lengths and orbital picture of Benzene. Concept of aromaticity – aromaticity (definition), Huckel’s rule – application to Benzenoid (Benzene, Napthalene) and Non – Benzenoid compounds (cyclopropenyl cation, cyclopentadienyl anion and tropylium cation) Reactions – General mechanism of electrophilic substitution, mechanism of nitration. Friedel Craft’s alkylation and acylation. Orientation of aromatic substitution – Definition of ortho, para and meta directing groups. Ring activating and deactivating groups with examples (Electronic interpretation of various groups like NO and Phenolic). Orientation of (i). Amino, methoxy and methyl groups (ii). Carboxy, nitro, nitrile, carbonyl and Sulfonic acid groups. (iii). Halogens (Explanation by taking minimum of one example from each type).

**5. Polynuclear Hydrocarbons** – Structure of naphthalene and anthracene (Molecular Orbital diagram and resonance energy) Any two methods of preparation of naphthalene and reactivity. Reactivity towards electrophilic substitution. Nitration and sulfonation as examples.

**6. Halogen compounds** : Nomenclature and classification of alkyl (into primary, secondary, tertiary), aryl, aralkyl, allyl, vinyl, benzyl halides. Chemical Reactivity, formation of RMgX Nucleophilic aliphatic substitution reaction- classification into S_{n}1 and S_{n}2. Energy profile diagram of S_{n}1 and S_{n}2 reactions. Stereochemistry of S_{n}2 (Walden Inversion) S_{n}1 (Racemisation). Explanation of both by taking the example of optically active alkyl halide – 2 bromobutane. Ease of hydrolysis – comparision of alkyl, benzyl, alkyl, vinyl and aryl halides.

**7. Hydroxy compounds :** Nomenclature and classification of hydroxy compounds. Alcohols: Preparation with hydroboration reaction, Grignard synthesis of alcohols. Phenols: Preparation i) from diazonium salt, ii) from aryl sulphonates, iii) from cumene. Physical properties- Hydrogen bonding (intermolecular and intramolecular). Effect of hydrogen bonding on boiling point and solubilitiy in water. Chemical properties:

a. acidic nature of phenols.

b. formation of alkoxides/phenoxides and their reaction with RX.

c. replacement of OH by X using PCl_{5}, PCl_{3}, PBr_{3}, SOCl_{2} and wit HX/ZnCl_{2}.

d. esterification by acids ( mechanism).

e. dehydration of alcohols.

f. oxidation of alcohols by CrO_{3} , KMnO_{2
}g. special reaction of phenols: Bromination, Kolb-Schmidt reaction, Riemer-Tiemann reaction, Fries rearrangement, azocoupling. Identification of alcohols by oxidation with KMnO , ceric ammonium nitrate, lucas reagent and phenols by reaction with FeCl . Polyhydroxy compounds: Pinacol-Pinacolone rearrangement.

**8. Carbonyl compounds :** Nomenclature of aliphatic and aromatic carbonyl compounds, structure of the carbonyl group. Synthesis of aldehydes from acid chlorides, synthesis of aldehydes and ketones using 1,3- dithianes, synthesis of ketones from nitriles and from carboxylic acids. Physical properties: absence of hydrogen bonding, keto-enol tautomerism, reactivity of carbonyl group in aldehydes and ketones. Nucleophilic addition reaction with

a) NaHSO3

b) HCN,

c) RMgX,

d) NH2OH,

e)PhNHNH2 ,

f) 2,4 DNPH,

g) Alcoholsformation of hemiacetal and acetal. Halogenation usingPCl_{5} with mechanism. Base catalysed reactions:

- a) Aldol,
- b) Cannizzaro reaction,
- c) Perkin reaction,
- d) Benzoin condensation,
- e) Haloform reaction,
- f) Knoevenagel reaction. Oxidation of aldehydes- Baeyer-Villiger oxidation of ketones.

** Reduction**: Clemmensen reduction, Wolf-Kishner reduction, MPV reduction, reduction with LiAlH4 and NaBH4 . Analysis of aldehydes and ketones with

- a) 2,4-DNT test,
- b) Tollen’s test,
- c) Fehling text,
- d) Schiff test,
- e) Haloform test (with equation).

**9. Carboxylic acids and derivatives :** Nomenclature, classification and structure of carboxylic acids. Methods of preparation by a) hydrolysis of nitriles, amides and esters. b) carbonation of Grignard reagents. Special methods of preparation of aromatic acids by a) oxidation of side chain. b) hydrolysis by benzotrichlorides. c) Kolbe reaction. Physical properties: Hydrogen bonding, dimeric association, acidity- strength of acids with examples of trimethyl acetic acid and trichloroacetic acid. Relative differences in the acidities of aromatic and aliphatic acids. Chemical properties: Reactions involving H, OH and COOH groups- salt formation, anhydride formation, acid chloride formation, amide formation and esterification (mechanism). Degradation of carboxylic acids by Huns-Diecker reaction, decarboxylation by Schimdt reaction, Arndt-Eistert synthesis, halogenation by Hell-Volhard- Zelinsky reaction. Derivatives of carboxylic acids: Reaction of acid chlorides, acid anhydrides, acid amides, esters (mechanism of the hydrolysis of esters by acids and bases).

10.Active methylene compounds : Acetoacetic esters: preparation by Claisen condensation, keto-enol tautomerism. Acid hydrolysis and ketonic hydrolysis. Preparation of a) monocarboxylic acids. b) dicarboxylic acids. Reaction with urea Malonic ester: preparation from acetic acid. Synthetic applications: Preparation of

- a) monocarboxylic acids (propionic acid and n-butyric acid).
- b) dicarboxylic acids (succinic acid and adipic acid).
- c) unsaturated carboxylic acids (crotonic acid). Reaction with urea.

**11. Exercises in interconversion**

**12. Nitrogen compounds :** Nitro hydrocarbons: Nomenclature and classification – nitro hydrocarbons – structure. Tautomerism of nitroalkanes leading to aci and keto form. Preparation of Nitroalkanes. Reactivity – halogenation, reaction with HONO (Nitrous acid), Nef reaction and Mannich reaction leading to Michael addition and reduction. Amines (Aliphatic and Aromatic): Nomenclature, Classification into 1^{0} , 2^{0} , 3^{0 }Amines and Quarternary ammonium compounds. Preparative methods -1. Ammonolysis of alkyl halides 2. Gabriel synthesis 3. Hoffman’s bromamide reaction (mechanism). 4. Reduction of Amides and Schmidt reaction. Physical properties and basic character – Comparative basic strength of Ammonia, methyl amine, dimethyl amine, trimethyl amine and aniline – comparative basic strength of aniline, N-methylaniline and N,N-dimethyl aniline (in aqueous and non-aqueous medium), steric effects and substituent effects. Use of amine salts as phase transfer catalysts. Chemical properties: a) Alkylation b) Acylation c) Carbylamine reaction d) Hinsberg separation e) Reaction with Nitrous acid of 1^{0} , 2^{0} , 3^{0} (Aliphatic and aromatic amines). Electrophilic substitutions of Aromatic amines – Bromination and Nitration. oxidation of aryl and 3^{0} Amines. Diazotization Cyanides and isocyanides: Nomenclature (aliphatic and aromatic) structure. Preparation of cyanides from a) Alkyl halides b) from amides c) from aldoximes. Preparation of isocyanides from Alkyl halides and Amines. Properties of cyanides and isocyanides, a) hydrolysis b) addition of Grignard reagent iii) reduction iv) oxidation.

**13. Heterocyclic Compounds :** Introduction and definition: Simple 5 membered ring compounds with one hetero atom Ex. Furan. Thiophene and pyrrole. Importance of ring system – presence in important natural products like hemoglobin and chlorophyll. Numbering the ring systems as per Greek letter and Numbers. Aromatic character – 6- electron system (four-electrons from two double bonds and a pair of non-bonded electrons from the hetero atom). Tendency to undergo substitution reactions. Resonance structures: Indicating electron surplus carbons and electron deficient hetero atom. Explanation of feebly acidic character of pyrrole, electrophillic substitution at 2 or 5 position, Halogenation, Nitration and Sulphonation under mild conditions. Reactivity of furan as 1,3-diene, Diels Alder reactions (one example). Sulphonation of thiophene purification of Benzene obtained from coal tar). Preparation of furan, Pyrrole and thiophene from 1,4,- dicarbonyl compounds only, Paul-Knorr synthesis, structure of pyridine, Basicity – Aromaticity – Comparison with pyrrole – one method of preparation and properties – Reactivity towards Nucleophilic substitution reaction – chichibabin reaction.

**14. Carbohydrates :** Monosaccharides: All discussion to be confined to (+) glucose as an example of aldo hexoses and (-) fructose as example of ketohexoses. Chemical properties and structureal elucidation: Evidences for straight chain pentahydroxy aldehyde structure (Acetylation, reduction to n-hexane, cyanohydrin formation, reduction of Tollen’s and Fehling’s reagents and oxidation to gluconic and saccharic acid). Number of optically active isomers possible for the structure, configuration of glucose based on Dglyceraldehyde as primary standard (no proof for configuration is required). Evidence for cyclic structure of glucose (some negative aldehydes tests and mutarotation). Cyclic structure of glucose. Decomposition of cyclic structure (Pyranose structure, anomeric Carbon and anomers). Proof for the ring size (methylation, hydrolysis and oxidation reactions). Different ways of writing pyranose structure (Haworth formula and chair conformationa formula). Structure of fructose: Evidence of 2 – ketohexose structure (formation of penta acetate, formation of cyanohydrin its hydrolysis and reduction by HI to give 2-Carboxy-n-hexane). Same osazone formation from glucose and fructose, Hydrogen bonding in osazones, cyclic structure for fructose (Furanose structure and Haworth formula). Interconversion of Monosaccharides: Aldopentose to aldo hexose – eg: Arabinose to D-Glucose, D-Mannose (Kiliani – Fischer method). Epimers, Epimerisation – Lobry de bruyn van Ekenstein rearrangement. Aldohexose to Aldopentose eg: D-glucose to D-arabinose by Ruff’f degradation. Aldohexose (+) (glucose) to ketohexose (-) (Fructose) and Ketohexose (fructose) to aldohexose (Glucose)

**15. Amino acids and proteins :** Introduction: Definition of Amino acids, classification of Amino acids into alpha, beta, and gama amino acids. Natural and essential amino acids – definition and examples, classification of alpha amino acids into acidic, basic and neutral amino acids with examples. Methods of synthesis: General methods of synthesis of alpha amino acids (specific examples – Glycine, Alanine, valine and leucene) by following methods: a) from halogenated carboxylic acid b) Malonic ester synthesis c) strecker’s synthesis. Physical properties: Optical activity of naturally occurring amino acids: L-configuration, irrespective of sign rotation, Zwitterion structure – salt like character – solubility, melting points, amphoteric character , definition of isoelectric point. Chemical properties: General reactions due to amino and carboxyl groups – lactams from gamma and delta amino acids by heating peptide bond (amide linkage). Structure and nomenclature of peptides and proteins.

**16. Mass Spectrometry:** Basic principles – Molecular ion / parent ion, fragment ions / daughter ions. Theory – formation of parent ions. Representation of mass spectrum. Identification of parent ion, (M+1), (M+2), base peaks (relative abundance 100%) Determination of molecular formula – Mass spectra of ethylbenzene, acetophenone, n-butyl amine and 1- proponal.

**PHYSICAL CHEMISTRY**

**1. Gaseous state :** Compression factors, deviation of real gases from ideal behavior. Van der Waal’s equation of state. P-V Isotherms of real gases, Andrew’s isotherms of carbon dioxide, continuity of state. Critical phenomena. The van der Waal’s equation and the critical state. Relationship between critical constants and van der Waal’s constants. The law of corresponding states and reduced equation of states. Joule Thomson effect. Liquefaction of gases: i) Linde’s method and ii) Claude’s method.

**2. Liquid state :** Intermolecular forces, structure of liquids (qualitative description). Structural differences between solids, liquids and gases. Liquid crystals, the mesomorphic state. Classification of liquid crystals into Smectic and Nematic. Differences between liquid crystal and solid/liquid. Application of liquid crystals as LCD devices.

**3. Solid state :** Symmetry in crystals. Law of constancy of interfacial angles. The law of rationality of indices. The law of symmetry. Definition of lattice point, space lattice, unit cell. Bravis lattices and crystal systems. X-ray diffraction and crystal structure. Bragg’s law. Determination of crystal structure by Bragg’s method and the powder method. Indexing of planes and structure of NaCl and KCl crystals. Defects in crystals. Stoichiometric and non-stoichiometric defects. Band theory of semoconductors. Extrinsic and intrinsic semiconductors, nand p-type semiconductors and their applications in photo electrochemical cells.

**4. Solutions :** Liquid-liquid – ideal solutions, Raoult’s law. Ideally dilute solutions, Henry’s law. Non-ideal solutions. Vapour pressure – composition and vapour pressure-temperature curves. Azeotropes-HCl-H2O, ethanol-water systems and fractional distillation. Partially miscible liquids-phenol-water, trimethylaminewater, nicotine-water systems. Effect of impurity on consulate temperature. Immiscible liquids and steam distillation. Nernst distribution law. Calculation of the partition coefficient. Applications of distribution law.

**5. Colloids and surface chemistry :** Definition of colloids. Solids in liquids(sols), preparation, purification,properties -kinetic,optical,electrical. Stability of colloids, Hardy-Schulze law, protective colloid. Liquids in liquids (emulsions) preparation, properties, uses. Liquids in solids (gels) preparation, uses. Adsorption: Physical adsoption, chemisorption. Freundlich, Langmuir adsorption isotherms. Applications of adsorption

**6. Phase rule :** Concept of phase, components, degree of freedom. Derivation of Gibbs phase rule. Phase equilibrium of one component – water system. Phase equilibrium of two-component system, solid-liquid equilibrium. Simple eutectic diagram of Pb-Ag system, desilverisation of lead. Solid solutions- compound with congruent melting point- (Mg-Zn) system, compound with incongruent melting point – NaCl- water system. Freezing mixtures.

**7. Dilute solutions :** Colligative properties. Raoult’s law, relative lowering of vapour pressure, its relation to molecular weight of non-volatile solute. Elevation of boiling point and depression of freezing point. Derivation of relation between molecular weight and elevation in boiling point and depression in freezing point. Experimental methods of determination. Osmosis, osmotic pressure, experimental determination. Theory of dilute solutions. Determination of molecular weight of non-volatile solute from osmotic pressure. Abnormal Colligative properties. Van’t Hoff factor, degree of dissociation and association.

**8. Electrochemistry :** Specific conductance, equivalent conductance, measurement of equivalent conductance. Variation of equivalent conductance with dilution. Migration of ions, Kohlrausch’s law. Arrhenius theory of electrolyte dissociation and its limitations. Ostwald’s dilution law. Debye-Huckel-Onsagar’s equation for strong electrolytes (elementary treatment only). Definition of transport number, determination by Hittorf’s method. Application of conductivity measurements-determination of dissociation constant (Ka ) of an acid, determination of solubility product of sparingly soluble salt, conductometric titrations. Types of reversible electrodes- the gas electrode, metal-metal ion, metal-insoluble salt and redox electrodes. Electrode reactions, Nernst equation, single electrode potential, standard Hydrogen electrode, reference electrodes, standard electrode potential, sign convention, electrochemical series and its significance. Reversible and irreversible cells, conventional representation of electrochemical cells. EMF of a cell and its measurements. Computation of cell EMF. Applications of EMF measurements, Calculation of thermodynamic quantities of cell reactions (DG, DH and K). Determination of pH using quinhydrone electrode, Solubility product of AgCl. Potentiometric titrations.

**9. Chemical kinetics :** Rate of reaction, factors influencing the rate of a reaction-concentration, temperature, pressure, solvent, light, catalyst. Experimental methods to determine the rate of reaction. Definition of order and molecularity. Derivation of rate constants for first, second, third and zero order reactions and examples. Derivation for time half change. Methods to determine the order of reactions. Kinetics of complex reactions (first order only): opposing reactions, parallel reactions, consecutive reactions and chain reactions. Effect of temperature on rate of reaction, Arrhenius equation, concept of activation energy. Theories of reaction rates- collision theoryderivation of rate constant for bimolecular reaction. The transition state theory (elementary treatment).

**10. Photochemistry :** Difference between thermal and photochemical processes. Laws of photochemistryGrothus-Draper’s law and Stark-Einstein’s law of photochemical equivalence. Quantum yield. Ferrioxalate actinometry. Photochemical hydrogen- chlorine, hydrogen-bromine reaction. Jablonski diagram depicting various processes occurring in the excited state, qualitative description of fluorescence, phosphorescence, non-radiative processes (internal conversion, intersystem crossing). Photosensitized reactions- energy transfer processes (simple example)

**11. Thermodynamics :** The first law of thermodynamics-statement, definition of internal energy and enthalpy. Heat capacities and their relationship. Joule’s law-Joule-Thomson coefficient. Calculation of w, q, dU and dH for the expansion of perfect gas under isothermal and adiabatic conditions for reversible processes. State function. Temperature dependence of enthalpy of formation-Kirchoff’s equation. Second law of thermodynamics. Different Statements of the law. Carnot cycle and its efficiency. Carnot theorem. Thermodynamic scale of temperature. Concept of entropy, entropy as a state function, entropy changes in cyclic, reversible, and irreversible processes and reversible phase change. Calculation of entropy changes with changes in V & T and P&T. Entropy of mixing inert perfect gases. Entropy changes in spontaneous and equilibrium processes. The Gibbs (G) and Hlmholtz (A) energies. A & G as criteria for thermodynamic equilibrium and spontaneity-advantage over entropy change. Gibbs equations and the Maxwell relations. Variation of G with P, V and T.

**Chemistry and Industry Physico Chemical methods of analysis**

**1. Separation techniques**

**1. Solvent extraction:** Principle and process, Batch extraction, continuous extraction and counter current extraction. Application – Determination of Iron (III)

**2. Chromatography:** Classification of chromatography methods, principles of differential migration adsorption phenomenon, Nature of adsorbents, solvent systems, Rf values, factors effecting Rf values.

- a. Paper Chromatography: Principles, Rf values, experimental procedures, choice of paper and solvent systems, developments of chromatogram – ascending, descending and radial. Two dimensional chromatography, applications.
- b. Thin layer Chromatography (TLC): Advantages. Principles, factors effecting Rf values. Experimental procedures. Adsorbents and solvents. Preparation of plates. Development of the chromatogram. Detection of the spots. Applications.
- c. Column Chromatography: Principles, experimental procedures, Stationary and mobile Phases, Separation technique. Applications
- d. High Performance Liquid Chromatography (HPLC): Principles and Applications.
- e. Gas Liquid Chromatography (GLC): Principles and Applications

2. Spectrophotometry : General features of absorption – spectroscopy, Beer-Lambert’s law and its limitations, transmittance, Absorbance, and molar absorptivity. Single and double beam spectrophotometers. Application of Beer-Lambert law for quantitative analysis of

- Chromium in K
_{2}Cr_{2}O_{7} - Manganese in manganous sulphate Iron (III) with thiocyanate.

**3. Molecular sectorscopy**

- (i) Electronic spectroscopy: Interaction of electromagnetic radiation with molecules and types of molecular spectra. Potential energy curves for bonding and antibonding molecular orbitals. Energy levels of molecules (ó,ð, n) . Selection rules for electronic spectra. Types of electronic transitions in molecules effect of conjugation. Concept of chromophore.
- (ii) Infra red spectroscopy : Energy levels of simple harmonic oscillator, molecular vibration spectrum, selection rules. Determination of force constant. Qualitative relation of force constant to bond energies. Anharmonic motion of real molecules and energy levels. Modes of vibrations in polyatomic molecules. Characteristic absorption bands of various functional groups. Finger print nature of infrared spectrum.
- (iii) Raman spectroscopy : Concept of polarizavility, selection rules, pure rotational and pure vibrational Raman spectra of diatomic molecules, selection rules.
- (iv) Proton magnetic resonance spectroscopy (1H-NMR) Principles of nuclear magnetic resonance, equivalent and non-equivalent protons, position of signals. Chemical shift, NMR splitting of signals – spin-spin coupling, coupling constants. Applications of NMR with suitable examples – ethyl bromide, ethanol, acetaldehyde, 1,1,2-tribromo ethane, ethyl acetate, toluene and acetophenone.
- (v) Spectral interpretation : Interpretation of IR, UV-Visible, 1H-NMR and mass spectral data of the following compounds 1. Phenyl acetylene 2. Acetophenone 3.Cinnamic Acid 4. para- nitro aniline.

**Drugs, formulations, pesticides and green chemistry**

**1. Drugs**

- Introduction: Drug, disease (definition), Historical evolution, Sources – Plant, Animal synthetic, Biotechnology and human gene therapy
- Terminology: Pharmacy, Pharmacology, Pharmacophore, Pharmacodynamics, Pharmacokinetics (ADME, Receptors – brief teartment) Metabolites and Anti metabolites.
- Nomenclature: Chemical name, Generic name and trade names with examples
- Classification: Classification based on structures and therapeutic activity with one example each.
- Synthesis: Synthesis and therapeutic activity of the following drugs., L-Dopa, Chloroquin, Omeprazole, Albuterol and ciprofloxacin.
- Drug Development: Pencillin, Separation and isolation, structures of different pencillins
- HIV-AIDS: Immunity – CD-4 cells, CD-8 cells Retrovirus, replication in human body. Investigation available, prevention of AIDS. Drugs available – examples with structures: PIS: Indinavir (Crixivan), Nelfinavir (Viracept), NNRTIS: Efavirenz (Susrtiva), Nevirapine (Viramune) NRTIs: Abacavir (Ziagen), Lamivudine (Epivir, 3TC) Zidovudine (Retravir, AZT, ZDV)
- Monographs of drugs: Eg Paracetamol, Sulpha methoxazole (Tablets)

**2. Formulations**

- Need of conversion of drugs into medicine. Additives and their role (brief account only)
- Different types of formulations

**3. Pesticides**

- Introduction to pesticides – types – Insecticides, Fungicides, Herbicides, Weedicides, Rodenticides plant growth regulators, Pheremones and Hormones. Brief discussion with examples, Structure and uses.
- Synthesis and presnt status of the following. DDT, BHC, Malathion, Parathion, Endrin, Baygon, 2,4-D and Endo-sulphon

**4. Green Chemistry**

Introduction: Definition of green Chemistry, need of green chemistry, basic principles of green chemistry Green synthesis: Evalution of the type of the reaction i) Rearrangements (100% atom economic), ii) Addition reaction (100% atom economic), Pericyclic reactions (no by-product).

Selection of solvent:

i) Aqueous phase reactions ii) Reactions in ionic liquids iii) Solid supported synthesis iv) Solvent free reactions (solid phase reactions)

ii) Green catalysts: i) Phase transfer catalysts (PTC) ii) Biocatalysts

**Microwave and Ultrasound assisted green synthesis:**

1. Aldol condensation

2. Cannizzaro reaction

3. Diels-Alder reactions

4. Strecker synthesis

5. Willaimson synthesis

6. Dieckmann condensation

**Macromolecules, materials Science and catalysis**

**1. Macromolecules :** Classification of polymers, chemistry of polymerization, chain polymerization, step polymerization, coordination polymerization – tacticity. Molecular weight of polymers-number average and weight average molecular weight, degree of polymerization, determination of molecular weight of polymers by viscometry, Osmometry and light scattering methods. Kinetics of free radical polymerization, derivation of rate law. Preparation and industrial application of polyethylene, PVC, Teflon, polyacrylonitrile, terelene and Nylon66. Introduction to biodegradability.

**2. Materials science :** Superconductivity, characteristics of superconductors, Meissner effect, types of superconductors and applications. Nanomaterials- synthetic techniques, bottom-up-sol-gel method, top-down- electro deposition method. Properties and applications of nano-materials. Composites- definition, general characteristics, particle reinforce and fiber reinforce composites and their applications.

**3. Catalysis** Homogeneous and heterogeneous catalysis, comparision with examples. Kinetics of specific acid catalyzed reactions, inversion of cane sugar. Kinetics of specific base catalyzed reactions, base catalyzed conversion of acetone to diacetone alcohol. Acid and base catalyzed reactions- hydrolysis of esters, mutarotation of glucose. Catalytic activity at surfaces. Mechanisms of heterogeneous catalysis. LangmuirHinshelwood mechanism. Enzyme catalysis: Classification, characteristics of enzyme catalysis. Kinetics of enzyme catalyzed reactions-Michaelis Menton law, significance of Michaelis constant (Km ) and maximum velocity (Vmax ). Factors affecting enzyme catalysis- effect of temperature, pH, concentration and inhibitor. Catalytic efficiency. Mechanism of oxidation of ethanol by alcohol dehydrogenase.

**GENERAL CHEMISTRY**

**1. Atomic Structure and elementary quantum mechanics :** Blackbody radiation, Planck’s radiation law, photoelectric effect, Compton effect, de Broglie’s hypothesis, Heisenberg’s uncertainty principle. Postulates of quantum mechanics. Schrodinger wave equation and a particle in a box, energy levels, wave functions and probability densities. Schrodinger wave equation for H-atom. Separation of variables, Radial and angular functions, hydrogen like wave functions, quantum numbers and their importance.

**2. Chemical Bonding :** Valence bond theory, hybridization, VB theory as applied to ClF , BrF , Ni(CO) , XeF . Dipole moment – orientation of dipoles in an electric field, dipole moment, induced dipole moment, dipole moment and structure of molecules. Molecular orbital theory – LCAO method, construction of M.O. diagrams for homo-nuclear and hetero-nuclear diatomic molecules (N , O , HCl, CO and NO). Comparision of VB and MO theories.

**3. Stereochemistry of carbon compounds :** Molecular representations- Wedge, Fischer, Newman and Saw-Horse formulae. Stereoisomerism, Stereoisomers: enantiomers, diastereomers- definition and examples.Conformational and configurational isomerism- definition. Conformational isomerism of ethane and n-butane. Enantiomers: Optical activity- wave nature of light, plane polarised light, interaction with molecules, optical rotation and specific rotation. Chiral molecules- definition and criteria- absence of plane, center, and Sn axis of symmetry- asymmetric and disymmetric molecules. Examples of asymmetric molecules (Glyceraldehyde, Lactic acid, Alanine) and disymmetric molecules (trans -1,2-dichloro cyclopropane). Chiral centers: definition- molecules with similar chiral carbon (Tartaric acid), definition of mesomers- molecules with dissimilar chiral carbons (2,3-dibromopentane). Number of enantiomers and mesomers- calculation. D,L and R,S configuration for asymmetric and disymmetric molecules. Cahn-Ingold-Prelog rules. Racemic mixture- racemisation and resolution techniques. Diastereomers: definition- geometrical isomerism with reference to alkenes- cis, trans and E,Z- configuration.

**4. General Principles of Inorganic qualitative analysis** : Solubility product, common ion effect, characteristic reactions of anions, elimination of interfering anions, separation of cations into groups, group reagents, testing of cations.

**5. Molecular symmetry :** Concept of symmetry in chemistry-symmetry operations, symmetry elements. Rotational axis of symmetry and types of rotational axes. Planes of symmetry and types of planes. Improper rotational axis of symmetry. Inversion centre. Identity element. The symmetry operations of a molecule form a group. Flow chart for the identification of molecular point group..

6. Theory of quantitative analysis

- a) Principles of volumetric analysis. Theories of acid-base, redox, complexometric, iodometric and precipitation titrations, choice of indicators for these titrations.
- b) Principles of gravimetric analysis: precipitation, coagulation, peptization, coprecipitation, post precipitation, digestion, filtration and washing of precipitate, drying and ignition, precipitation from homogenous solutions, requirements of gravimetric analysis.

7. Evaluation of analytical data. : Theory of errors, idea of significant figures and its importance, accuracy – methods of expressing accuracy, error analysis and minimization of errors, precision – methods of expressing precision, standard deviation and confidence limit.

8. Introductory treatment to:

- a) Pericyclic Reactions Concerted reactions, Molecular orbitals, Symmetry properties HOMO, LUMO, Thermal and photochemical pericyclic reactions. Types of pericyclic reactions – electrocyclic, cycloaddition and sigmatropic reactions – one example each.
- b) Synthetic strategies Terminology – Disconnection (dix), Symbol ( ), synthon, synthetic equivalent (SE), Functional group interconversion (FGI), Linear, Convergent and Combinatorial syntheses, Target molecule (TM). Retrosynthesis of the following molecules
- 1) acetophenone
- 2) cyclohexene
- 3) phenylethylbromide

- c) Asymmetric (Chiral) synthesis Definitions-Asymmetric synthesis, enantiomeric excess, diastereomeric excess. stereospecific reaction, definition, example, dehalogenation of 1,2-dibromides by I-. stereoselective reaction, definition, example, acid catalysed dehydration of 1-phenylproponol.

### 105 – Geology

**Palaeontology, Indian Geology and Economic Geology**

**Palaeontology :** Definition of palaeontology, conditions of fossilization, modes of preservation and uses of fossils. Phylum Echinodermata and Phylum Brachiopod, Phylum Mollusca and Phylum Arthropoda, Phylum Hemichordata, Phylum Coelenterata. Study of the following fossils with respect to their classification, morphology and geological distribution. Cidaris, Micraster, Holaster, Hemiaster, Terebratula, Spinifer, Rhynchonella, Productus, Turritella, Murex, Cypraea, Natica, Voluta, Pecten, Gryphaea, Arca, Cardita, Exogyra, Nautilus, Ammonoids, Belemnites, Calymene, Paradoxide, Corals and Graptolites. Plant fossils : Glossopteris, Gangam Operas, Ptylophyllum.

**Indian Geology :** Definition of stratigraphy, principles of stratigraphy, lithostratigraphy, standard geological timescale. Physiographic divisions of India with their stratigraphic and structural characteristics. Dharwar System, Cuddapah System, Vindhyan System, Kurnool System and Gondwana System. Triassic of Spiti, Jurssic of Kutch, Cretaceous of Tiruchirapalli, Deccan Traps and their Age, Siwaliks with vertebrate fossils. Geology of Andhra Pradesh. Stratigraphic contacts – boundaries between Archaean and Proterozoic; and Cretaceous and Tertiary.

**Economic Geology** : Definition of Economic Geology, Global tectonics and metallogeny – mineral resources and mineral deposits, Importance of economic minerals and rocks, ore minerals, gangue minerals (gangue). Ore, industrial minerals, tenor and grade; Syngenetic deposits, epigenetic deposits. Classification of mineral deposits – Bateman’s classification modified by Jenson. Processes of formation of mineral deposits; endogenetic and exogenetic processes. Study of ore deposits of gold, copper, lead, zinc, aluminium, iron, manganese, chromium, uranium and thorium with respect to their mineralogy, uses, mode of occurrence, origin and distribution in India. Distribution of industrial minerals in India for the following industries : abrasives, cement, ceramics, glass, fertilizers and chemicals, and insulators. Fossils fuels : Coal, it’s origin and types of coal – Coal deposits of India. Oil and Natural Gas : Origin, migration and entrapment and distribution in India, Use of micropaleontology in oil exploration, Gemstones and Dimensional Stones. Atomic minerals : Uraninite, pitchblende, coffenite; Beach sands : monazite, ilmenite, rutile, zircon and their uses. Mineral resources of Andhra Pradesh.

**Nature and scope of Petrology** – Definition of rock, classification of rocks into igneous, sedimentary and metamorphic. Distinguishing features of the three types of rocks. Igneous rocks : Classification into plutonic, hypabyssal and volcanic rocks; Forms – Lava flows, intrusions, sills, laccolith, lopolith, dykes, ring dykes, cone sheets, volcanic necks, phacoliths and batholiths. Structures : vescicular, amygdaloidal, block lava, ropy lava, pillow lava, flow, jointing and sheet structures. Platy, columnar and prismatic structures. Textures – Definition of texture, micro-structure, devitrification. Allotriomorphic, hypidiomorphic, panidiomorphic, porphyritic, poikilitic, ophitic, intergranular, intersertal, trachytic, graphic and micro-graphic. Reaction structures – Corona, myrmekitic, orbicular, spherulitic, perlitic. Classification of igneous rocks – CIPW and Tyrrell tabular classification. Descriptive study of the following rocks types : granite, granodiorite, syenite, nepheline syenite, diorite, pegmatite, aplite, gabbro, anorthosite, peridotite, pyroxenite, dunite, dolerite, rhyolite, obsidian, trachyte, andesite and basalt. Composition and constitution of magma – Crystallization of magma, unicomponent and binary systems, eutectic and solid solutions. Origin of igneous rocks – Bowen’s reaction principle, differentiation and assimilation.

**Sedimentary rocks**: Sources of sediments – mechanical and chemical weathering, modes of transportation, stratification. Sedimentary structures : types of bedding, surface marks, deformed bedding and solution structures. Classification of sedimentary rocks : Clastic – rudaceous, arenaceous, and argillaceous; Non-Clastic – calcareous, carbonaceous, ferruginous, phosphatic, and evaporates. Descriptive study of the following sedimentary rocks – conglomerate, breccia, sandstone, grit, arkose, greywacke, shale, limestone, and shelly limestone.

**Metamorphic rocks**: Definition of metamorphism, agencies of metamorphism, types of metamorphism, grades and zones of metamorphism. Metamorphic minerals – stress and antistress minerals – Structures of metamorohic rocks – Cataclastic, maculose, schistose, granulose and gneissose. Textures of metamorphic rocks – crystalloblastic, palimpset, xenoblastic and idioblastic. Classification of metamorphic rocks – concept of metamorphic facies. Cataclastic metamorphism of argillaceous and arenaceous rocks. Thermal metamorphism of argillaceous, arenaceous and calcareous rocks. Dynamothermal metamorphism of argillaceous, arenaceous and basic igneous rocks. Plutonic metamorphism, metasomatism and additive processes. Definition of anatexis and palingenesis. Descriptive study of the following metamorphic rocks : gneiss, schist, slate, phyllite, quartzite, marble, granulite, eclogite, amphibolite, migmatite, charnockite and khondalite.

**Structural Geology**: Definition of structural geology, aim and objectives of structural geology; Importance of study of structures, primary and secondary structures; Outcrops, attitude of beds; Strike, dip and apparent dip, and Use of clinometer. Primary structures. Folds – description, nomenclature and recognition in the field. Joints – geometrical and genetic classification. Faults – geometrical and genetic classification and recognition in the field. Effects of faults on the outcrops. Unconformities – definition, types, and recognition in the field. Distinguishing the faults from unconformities. Definitions of overlap, offlap, outlier, cleavage, schistosity, foliation and lineation.

**Physical Geology, Crystallography and Mineralogy**

**Physical Geology** : General aspects, definition of geology – Basic assumptions of Geology – Its relationship with other sciences – Branches of geology – Aim and applications of Geology.

**Earth as a planet** – It’s shape, size, density – movements and their effects. Origin and age of the earth. Geological processes – exogenic and endogenic. Definition of weathering – types of weathering of rocks – physical and chemical. Definition of erosion and denudation, cycle of erosion, transportation and deposition, agents of erosion.

**Rivers**: erosion, transportation, and deposition of river (fluvial) cycle in different stages – Development of typical landforms by river erosion and deposition. V-shaped valley, waterfall, alluvial fan, meander, ox-bow lake, floodplain, natural plane, peneplain, and delta. Types of rivers. Glaciers: Definition of a glacier – types – development of typical landforms by glacial erosion and deposition – cirque, U-shaped valley – changing valley; Rocks – monadrocks, morains, drum-line, kama, eskors and varves, characteristic features of glaciated regions. Groundwater: starage of ground water – porosity, permeability, acquifer, water table – zone of saturation, artesian well, spring, geysers – development of typical landforms by erosion and deposition by groundwater (Karst topography), sinkhole, cavern, stalactites, and stalagmites.

**Seas**: Offshore profile – landforms of the sea – marine deposits and coral reefs. Lacustrine deposits, atmospheric circulation, weather and climatic changes, land-air-sea interaction. Earth’s heat budget and global climatic changes.

**Wind**: Development of characteristic features by winds (arid cycle), erosion and deposition – pedestal rock – mushroom topography – Inselberg – Ventifacts – locus and sand dunes. Earth movements: definition of diastrophism, epirogenic and orogenic movements – mountains, geosyncline. Basic concepts of isostasy, continental drift and plate tectonics.

**Earthquakes**: causes, kinds of earthquake waves, mode of propagation, the intensity of earthquakes, Richter’s scale, seismograph, and seismogram. Effects of earthquakes, earthquake zones, the interior of the earth.

**Volcanoes**: origin and products.

**Crystallography**: Definition of crystal-amorphous and crystalline states – morphology of crystals – face, edge, solid angle and interfacial angle.

**Forms:** simple, combination, closed and open forms.

**Symmetry**: Plane, axis, centre, crystallographic axes, parameters, indices, crystallographic notation – Parameter system of Weiss, Index system of Miller.

**Classification** of Crystals into ‘7’ systems. Morphological study of the following classes of symmetry: a) Cubic system – Normal (Galena) type, b) Tetragonal system – Zircon type, c) Hexagonal system – Beryl type, d) Trigonal system – Calcite type, e) Orthorhombic system – Barytes type, f) Monoclinic system – Gypsum type, and g) Triclinic system – Axinite type.

Twinning in crystals – definition of twin, twin plane, twin axis and composition plane.

**Mineralogy** : Definition of a mineral – Classification of minerals into rock forming and ore forming minerals. Physical properties of minerals – colour, streak, play of colours, opalescence, asterism, transparency, luster, luminescence, fluorescence, form, hardness, tenacity, cleavage, parting, fracture, specific gravity, magnetic properties, electrical properties, pyro- and piezo-electricity.

**Modes of mineral formation** : Occurrence and association of minerals. Chemical properties of minerals – isomorphism – solid solution – polymorphism – allotropy, pseudomorphism, radioactivity, silicate structure.

**Descriptive Mineralogy** : Study of physical and chemical properties and mode of occurrence of the following mineral groups : Nesosilicate – Olivine, garnet and aluminium silicates; Sorosilicate – epidote; Cyclosilicate – beryl; Inosilicate – pyroxene and amphibole; Phyllosilicate – mica, hydrous magnesium silicate; Tektosilicate – feldspars, feldspathoids and quartz; Miscellaneous – staurolite, tourmaline, zircon, calcite, corundum and apatite.

Optical Mineralogy: Optical properties of minerals – Isotropic and Anisotropic – Polarized light, refractive index – Double refraction, Uniaxial and Biaxial minerals – Nicol Prism and it’s construction, Concept of crossed nicols. Petrological (Polarizing) Microscope – Its mechanical and optical p[arts – behavior of isotropic and anisotropic mineral between crossed nicols – extinction, pleochroism, interference colour. Optical properties of important minerals.

### 201. Humanities & Social Sciences

**Reasoning** : Analogy Test – Alphabet Series – Test of Direction Sense – Coding – Decoding test – Number series – Puzzle – Problem on Age Calculation – Blood Relations – Calendar – Decision Making – Number Series – Matrix – Mathematical Reasoning – Statement and Assumption – Statement and Arguments – Dice – Clock – Inserting the Mission Character – Clerical Aptitude – Word formation – Venn Diagram.

**Numerical Ability:** General aptitude with emphasis on logical reasoning, graphical analysis, analytical ability, quantitative comparisons, series formation, puzzles, etc. Time and distance – Time and work General arithmetic aptitude – Ratios, Percentage Increase/Decrease – – Numerical Logic – Arithmetic Test – Numerical Reasoning – Data Interpretation – Numerical Estimation.

**General English :** Active/Passive Voice; Parts of Speech; Time, Tense and Aspect; Phrasal Verbs; Auxiliary verbs; Use of Shall, will, For, Since; Idioms and Phrases; Common Errors; Proposition; Synonyms and Antonyms; Precis Writing and Comprehension

**Current Affairs:** Current events of national and international importance. – History of India and Indian National Movement. – Indian and World Geography-Physical, Social, Economic Geography of India and the World. – Indian Polity and Governance – Constitution, Political System, Panchayati Raj, Public Policy. – Economic and Social Development Sustainable Development, Poverty, Inclusion, Demographics, Social Sector initiatives, etc. General issues on Environmental Ecology, Bio-diversity, and Climate Change – that do not require subject specialization. General Science

### 202. English

1. Literary terms, Genres, Literary Movements and Trends, Critical concepts.

2.Verb, verb patterns, and structures, phrasal verbs concord, Active and Passive Voice, Prepositions, Question tags, Articles, synonyms and antonyms, one-word substitutes, Note taking, confusables.

3. Comprehension – unknown poem and passage, Letter writing, Idioms, and phrases.

### 203. Telugu

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