IP University Biotechnology Entrance Syllabus

Hi buddy here I am looking for IP University Biotechnology Entrance Syllabus, so would you plz provide me same here ??

[pawan]

As you are asking for IP University Biotechnology Entrance Syllabus, so here I am telling Syllabus for IP University CET Code 128, for the prescribed subjects shall be of Diploma level. Syllabi for CET Code 130 and 131, for the subjects of Physics, Chemistry, Mathematics, Biology ( Botany & Zoology ) or Biotechnology shall be as specified by CBSE for class 11th and 12th under the 10+2 Scheme for the students passing class 12th in the year 2016.

(i) Food Microbiology

Characteristics of microorganisms : Morphology, structure and detection of bacteria, yeast and mold in food, Spores and vegetative cells; Microbial growth in food: Intrinsic and extrinsic factors, Growth and death kinetics, serial dilution method for quantification; Food spoilage : Contributing factors, Spoilage bacteria, Microbial spoilage of milk and milk products, meat and meat PRODUCTS; FOODBORNE disease : Toxins produced by Staphylococcus, Clostridium and Aspergillus; Bacterial pathogens : Salmonella, Bacillus, Listeria, Escherichia coli, Shigella, Campylobacter; Fermented food : Buttermilk, yoghurt, cheese, sausage, alcoholic beverage, vinegar, sauerkraut and soya sauce.

(ii) Molecules and their Interaction Relevant to Biology

Structure of atoms, molecules and chemical bonds. Composition, structure and function of biomolecules ( carbohydrates, lipids, proteins, nucleic acids and vitamins ). Stablizing interactions ( Van der Waals, electrostatic, hydrogen bonding, hydrophobic interaction, etc. ). Principles of biophysical chemistry ( pH, buffer, reaction kinetics, thermodynamics, colligative properties ).

Bioenergetics, glycolysis, oxidative phosphorylation, coupled reaction, group transfer, biological energy transducers. Principles of catalysis, enzymes and enzyme kinetics, enzyme regulation, mechanism of enzyme catalysis, isozymes Conformation of proteins ( Ramachandran plot, secondary structure, domains, motif and folds ). Conformation of nucleic acids ( helix ( A, B, Z ), t-RNA, micro-RNA ). Stability of proteins and nucleic acids. Metabolism of carbohydrates, lipids, amino acids nucleotides and vitamins.


(iii) Cellular Organization

Membrane structure and function ( Structure of model membrane, lipid bilayer and membrane protein diffusion, osmosis, ion channels, active transport, membrane pumps, mechanism of sorting and regulation of intracellular transport, electrical properties of membranes ). Structural organization and function of intracellular organelles ( Cell wall, nucleus, mitochondria, Golgi bodies, lysosomes, endoplasmic reticulum, peroxisomes, plastids, vacuoles, chloroplast, structure & function of cytoskeleton and its role in motility ).

Organization of genes and chromosomes ( Operon, unique and repetitive DNA, interrupted genes, gene families, structure of chromatin and chromosomes, heterochromatin, euchromatin, transposons ). Cell division and cell cycle ( Mitosis and meiosis, their regulation, steps in cell cycle, regulation and control of cell cycle ). Microbial Physiology ( Growth yield and characteristics, strategies of cell division, stress response ).

(iv) System Physiology – Plant

Photosynthesis – Light harvesting complexes; mechanisms of electron transport; photoprotective mechanisms; CO2 fixation-C3, C4 and CAM pathways. Respiration and photorespiration – Citric acid cycle; plant mitochondrial electron transport and ATP synthesis; alternate oxidase; photorespiratory pathway. Nitrogen metabolism – Nitrate and ammonium assimilation; amino acid biosynthesis. Plant hormones – Biosynthesis, storage, breakdown and transport; physiological effects and mechanisms of action. Sensory photobiology – Structure, function and mechanisms of action of phytochromes, cryptochromes and phototropins; stomatal movement; photoperiodism and biological clocks.

Solute transport and photoassimilate translocation – uptake, transport and translocation of water, ions, solutes and macromolecules from soil, through cells, across membranes, through xylem and phloem; transpiration; mechanisms of loading and unloading of photoassimilates. Secondary metabolites – Biosynthesis of terpenes, phenols and nitrogenous compounds and their roles. Stress physiology – Responses of plants to biotic ( pathogen and insects ) and abiotic ( water, temperature and salt ) stresses.

(v) Food Chemistry and Nutrition

Carbohydrates : Structure and functional properties of mono-oligo-polysaccharides including starch, cellulose, pectic substances and dietary fibre; Proteins : Classification and structure of proteins in food; Lipids : Classification and structure of lipids, Rancidity of fats, Polymerization and polymorphism; Pigments : Carotenoids, chlorophylls, anthocyanins, tannins and myoglobin; Food flavours : Terpenes, esters, ketones and quinones; Enzymes : Specificity, Kinetics and inhibition, Coenzymes, Enzymatic and non-enzymatic browning; Nutrition : Balanced diet, Essential amino acids and fatty acids, PER, Water soluble and fat soluble vitamins, Role of minerals in nutrition, Antinutrients, Nutrition deficiency diseases.

Syllabus for CET for M.Tech ( Nano Science and Technology ) Programme

Physics

Interference : Young’s double slit experiment, Fresnel’s biprism, Thin films, Newton’s rings, Michelson’s interferometer, Fabry Perot interferometer.

Diffraction : Fresnel Diffraction : Zone plate, circular aperture, opaque circular disc, narrow slit, Fraunhofer diffraction : Single slit, double slit, diffraction grating, resolving power and dispersive power.

Polarization : Types of polarization, Brewsters law, Malu’s Law, Nicol prism, double refraction, quarter-wave and half-wave plates, optical activity, specific rotation.

Lasers : Introduction, coherence, population inversion, basic principle and operation of a laser, Einstein A and B coefficients, type of lasers, He-Ne laser, Ruby laser, semiconductor laser, holography-theory and applications

Fibre Optics : Types of optical fibres and their characteristics, ( Attenuation and dispersion step index and graded index fibres, principle of fibre optic communication-total internal reflection, numerical aperture, fibre optical communication network ( qualitative ) – its advantages.

Theory of Relativity : Galenlian transformations, the postulates of the special theory of relativity, Lorentz transformations, time dilation, length contraction, velocity addition, mass energy equivalence.

Thermodynamics : The first law and other basic concepts: dimensions, units, work, heat, energy, the first law of thermodynamics, enthalpy, equilibrium, phase rule, heat capacity, PVT behavior of pure substances, ideal gas, real gas, heat effects.

The second law and Entropy : statements, heat engines, Kelvin-Planck and Clausious statements and their equality, reversible and irreversible processes, Carnot cycle, thermodynamic temperature scale, entropy, entropy calculations, T-S diagrams, properties of pure substances, use of steam tables and Mollier diagram.

Refrigeration and liquefaction : the Carnot refrigerator, the vapor-compression cycle, comparison of refrigeration cycles, liquefaction processes, heat pump. Rankine power cycle.

Quantum Mechanics : Wave particle duality, deBroglie waves, evidences for the wave nature of matter – the experiment of Davisson and Germer, electron diffraction, physical interpretation of the wave function and its properties, the wave packet, the uncertainty principle.

The Schrodinger wave equation ( 1 – dimensional ), Eigen values and Eigen functions, expectation values, simple Eigen value problems – solutions of the Schrodinger’s equations for the free particle, the infinite well, the finite well, tunneling effect, simple harmonic oscillator ( qualitative ), zero point energy.

Quantum Statistics : The statistical distributions, Maxwell Boltzmann, Bose-Einstein and Fermi-Dirac statistics, their comparisons, Fermions and Bosons. Applications : Molecular speed and energies in an ideal gas. The Black-body spectrum and failure of classical statistics to give the correct explanation – the application of Bose-Einstein statistics to the Black-body radiation spectrum, Fermi-Dirac distribution to free electron theory, electron specific heats, Fermi energy and average energy – its significance.

Band theory of solids : Origin of energy bands in solids, Kronig-Penny model, Brillouin zones, effective mass, Metals, semiconductors and insulators and their energy band structure. Extrinsic and intrinsic semiconductors, p-n junction diodes- its characteristics, tunnel diode, zener diode, photodiode, LED, photovoltaic cell, Hall effect in semiconductors, transistor characteristics ( common base, common emitter, common collector ).

Digital techniques and their applications ( registers, counters, comparators and similar circuits ) A/D and D/A converters

Superconductivity : ZFC and FC, Meissner effect, Type I and II superconductors, the Josephson effect, flux quantization, Cooper pairs, BCS theory, properties and applications of superconductors.

X-rays : Production and properties, crystalline and amorphous solids, Bragg’s law, applications.

Electricity and magnetism : Electric fields, Gauss’ Law, its integral and differential form, applications. Lorentz force, fields due to moving charges, the magnetic field, Ampere’s law, motion of a charged particle in an electric and magnetic field, magnetic and electrostatic focussing, Hall effect, determination of e/m by cathode ray tube, positive rays, Thomson’s parabolic method, Isotopes, Mass spectrographs ( Aston and Bainbridge ), Electron microscope, Cyclotron and Betatron.

Overview of Electro – Magnetism : Maxwell’s Equations : The equation of continuity for Time – Varying fields, Inconsistency in ampere’s law Maxwell’s Equations, conditions at a Boundary Surface, Introduction to EM wave.



Nuclear Physics : Introduction of nucleus, Nucleus radius and density, Nuclear forces, Nuclear reactions, Cross section, Q-value and threshold energy of nuclear reactions, Basic Idea for Nuclear Reactor, Breeder reactor, The Geiger-Mullar ( G.M. ) Counter, Introduction of Accelerators and its Applications.

Numerical techniques : Interpolations, differentiation, integration; Nonlinear equations, the bisection methods, Newton’s method, root finding; Differential equations, Euler’s method, the Runge-Kutta method; Matrices-inverting, finding eigenvalues and eigenfunctions.

Mathematics

Linear Independence and dependence of vectors, Systems of linear equations – consistency and inconsistency, rank of a matrix, Gauss elimination method, Eigen values and Eigen vectors.

Successive differentiation, Leibnitz’s theorem, Lagrange’s Theorem, Cauchy Mean value theorems, Taylor’s theorem, Asymptotes, Curvature, Reduction Formulae of trigonometric functions, Properties of definite Integral, Applications to length, area, volume, surface of revolution. Partial derivatives, Method of Lagrange’s multipliers. Jacobeans of coordinates transformations. Double and Triple integrals.

Method of separation of variables, homogeneous, linear equations, exactness and integrating factors, linear equations of higher order with constant coefficients, Operator method to find particular integral.

Scalar and vector fields, Directional Derivative, Gradient of scalar field, divergence and curl of a vector field. Green’s theorem, Divergence theorem and Stoke’s theorem.

Probability : Definition of Sample Space, Event, Event Space, Conditional Probability, Additive and Multiplicative law of Probability, Baye’s Law theorem, Application based on these results.

Chemistry

Gaseous State : Kinetic theory, molecular velocity, Probable distribution of velocities, mean free path, collision frequency. Distribution of energies of molecules translational, rotational & vibrational, Law of equipartitions of energies, Equation of State of a real gas. Critical phenomenon & principle of corresponding states.

The phase rule : Derivation of phase rule, significance of various terms involved in the definition of phase rule. Phase diagrams of one component systems ( Water, Sulphur and CO2 ).

Two component system : Eutectic, congruent and incongruent systems with examples : Partial miscible liquids: Lower and upper consolute point.

Chemical thermodynamics : Intensive and extensive variables; state and path functions; isolated, closed and open systems; zeroth law of thermodynamics.

First law : Concept of heat, q, work, w, internal energy U and statement of first law; enthalpy, H, relation between heat capacities, calculations of q, w, U and H for reversible, irreversible and free expansion of gases ( ideal and van der Waals ) under isothermal and adiabatic conditions.

Thermochemistry : Heats of reactions: standard states; enthalpy of formation of molecules and ions and enthalpy of combustion and its applications; calculation of bond energy, bond dissociation energy and resonance energy from thermochemical data, effect of temperature ( Kirchoff’s equations ) and pressure on enthalpy of reactions. Adiabatic flame temperature, explosion temperature.

Second Law : Concept of entropy; thermodynamic scale of temperature, statement of the second law of thermodynamics; molecular and statistical interpretation of entropy. Calculation of entropy change for reversible and irreversible processes.

Third Law : Statement of third law, concept of residual entropy, calculation of absolute entropy of molecules.

Free Energy Functions : Gibbs and Helmholtz energy; variation of S, G, A with T, V, P; Free energy change and spontaneity. Relation between Joule-Thomson coefficient and other thermodynamic parameters; inversion temperature; Gibbs-Helmholtz equation; Maxwell relations; thermodynamic equation of state.

Chemical Kinetics : Rate, mechanism, steady state concept, Kinetics of complex reactions, concept of energy barrier / energy of activation. Theories of reaction rates, Lindemann theory of unimolecular reaction and reactions in flow system.

Electrochemistry : Concept of electrolysis, Electrical current in ionic solutions. Kohlrausch’s law and migration of ions. Transference number. Hittroff and moving boundary methods. Applications of conductance measurements.

Strong electrolytes : Onsager equation: Activity and activity coefficients of strong electrolyte.

Surface Chemistry : Adsorption, adsorbate and adsorbents. Types of adsorption. Freundlich adsorption isotherm, Langmuir adsorption isotherms. B.C.T. Isotherm: Surface area of the adsorbent. Changes in entropy, enthalpy and free energy on adsorption. Gibbs adsorption equation.

Catalysis : Types of catalysis, homogenous / heterogeneous, enzyme catalysis, acid / base catalysis and their kinetics. Mechanism of heterogeneous catalysis. Kinetics of surface reactions : unimolecular and bimolecular. pH-dependence of rate constants of catalysed reactions. Autocatalysis.

Autocatalysis Colloids : Colloidal state, classification of colloidal solution, true solution, colloidal solution and suspensions, preparation of sol, Purification of colloidal solutions. viscosity & plasticity General and optical properites, stability f colloids, coagulation of lyphobic sols, electrical properties of sols, kinetic properties of colloids :- Brownion movement, size of colloidal particle, emulsions, gels, colloidal electrolytes and applications of colloids. Emulsions, emulsifiers, theory of emulsification

Polymers : Basic concepts & Terminology, such as monomers, Polymers, Functionality, Thermoplastics, Thermosets Linear, Branched, cross linked polymers etc. different definitions of molecular weight viz., Mw, Mn, Mv and then determinations. Industrial applications of polymers, Addition, condensation and Ionic polymerization’s, solutions of polymers, good solvents, & bad solvent, solubility parameter, solutions viscosity and determination of intrinsic viscosity.

Atomic Structure : Introduction to wave mechanics, the Schrodinger equation as applied to hydrogen atom, origin of quantum numbers, Long form of periodic table on the basis of Electronic configuration s, p, d, f block elements periodic trends, Ionisation potential, atomic and ionic radii electron affinity & electro-negativity.

Chemical Bonding : Ionic bond-energy changes, lattice energy Born Haber Cycle, Covalent bond-energy changes, Potential energy curve for H2 Molecule, characteristics of covalent compound. Co-ordinate bond – Werner’s Theory, effective atomic numbers, isomerism in coordinate compounds. Hydrogen bonding. Concept of hybridisation and resonance, Valance Shell Electron Repulsion theory ( VSEPR ). Discussion of structures of H2O, NH3, SiF4. Molecular orbital theory, Linear combination of atomic orbitals ( LCAO ) method. Structure of simple homo nuclear diatomic molecule like H2, N2, O2, F2.

Acids & Bases : Basics of acidities and basicities, electrolytic dissociation, concept of strengths of acids and bases, ionization of water, concept of pH and its scale, Buffer solutions, Buffer solution of weak acid and its salt, calculation of pH of buffer solution, Henderson equation, acid-base indicators and theory of indicators.

Classification of Organic compounds IUPAC nomenclature, Structural isomerism, Cis-trans isomerism, shapes and molecular orbital structures of compounds containing C, N and O conformation of alkanes, structures of dienes, pyridine, pyrrole, aromatic compounds, delocalisation, concept of aromaticity, stability of cycloalkanes, resonance concept, inductive and mesomeric effects, directive effects, activating and deactivating groups, hydrogen-bonding, organic reagents and reaction intermediates.

Chemistry of hydrocarbons House synthesis halogenation of alkanes, free radical mechanism, cracking effect of structure on Physical properties of compounds, alkenes catalytic hydrogenation, dehydration of alcohols, dehydrogenation, Saytzeff rule, electrophilic addition reactions, peroxide effect, mechanism of allylic substitution, acidity of 1-alkynes, conjugated dienes, 1, 2 and 1, 4 additions, free radical and ionic mechanisms of addition polymerisation reactions.

Ring opening reactions of cyclopropane and cyclobutane, chemistry of benzene and alkyl benzenes. Aromatic electrophillic substitution reaction, Friedel-Crafts reaction. Chemistry of functional groups Alkyl and aryl halides, nucleophilic substitution, synthetic utility of Grignard reagents and alkallithiums, Mechanism of Gringnartion of alcohols, Benzyl alcohol, acidity of phenols, Epoxy compounds, Anisole nucleophilic addition, Benzaldehyde, acetophene, benzophenone, aldol condensation, acidity of acids, alkyl and aryl amines.


Biology

Origin of Life : History of earth, theories of origin of life nature of the earliest organism. Basic rules of classification and nomenclature, Classification-two kingdom, five kingdom – brief introduction to kingds, three domain introduction and structure of viriods, prions and virus ( HIV, TMV, Bacteriophage ), Prokaryote ( Bacteria-cell structure, nutrition, reproduction ), Protista, Fungi, Plantae and Animalia. Structure and reproduction of bacteria and their economic importance

Chemicals of life : Definition, Properties, Types, Mechanism of action, factors affecting kinetics and their industrial applications, ( Biomolecules )- Biomolecules-carbohydrates, proteins, fats and lipids, nucleic acids ( DNA and RNA ) and identification of biomolecules in tissues.

Cell : The cell concept, structure of prokaryotic and eukaryotic cells, plant cells and animal cells, cell membrances, cell organelles and their function. Structure and use of compound microscope.

Histology : Maritimes ( apical, intercalary, lateral ) and their function; simple tissue ( parenchyma, collenchymas, sclerenchyma ); Complex tissue ( xylem and phloem ); Tissue systems ( epidermal, ground, vascular ); primary body and growth ( root, stem, leaf ); Secondary growth. Animal Epithelial tissue, connective tissue, muscle tissue and nervous tissue and their function in body.

Nutrition : Autotrophic ( Photosynthesis ) Pigment systems, Chloroplast, light absorption by chlorophyll and transfer of energy, two pigment systems, photosynthetic unit, phosphorylation and electron transport system, Calvin-Benson Cycle ( C3 ), Hatch Slack Pathway ( C4 ), Crassulacan Acid Metabolism ( CAM ), factors affecting photosynthesis; Mineral Nutrition in plants. Heterotrophic – Forms of heterotrophic nutrition, elementary canal in humans, nervous and hormonal control of digestive systems, fate of absorbed food materials; Nutrition in humans, Reference values.

Energy Utilization : ( Respiration ) - Structure of mitochondria, cellular respiration, relationship of carbohydrate metabolism to other compounds, Glycolysis, fermentation, formation of acetyl co-A, Kreb cycle, Electron Transport System and Oxidative Phosphorylation, ATP, factors affecting respiration.

Transport : Plant water relationships, properties of water, diffusion, osmosis, imbibition, movement of water in flowering plants, uptake of water by roots, the ascent of water in xylem, apoplast symplast theory, Transpiration-structure of leaf and stomata in plants opening and closing mechanism of stomata factors affecting transpiration significance of transpiration General characteristics of blood vascular system, development of blood systems in animals, Composition of blood, circulation in blood vessels, formation of tissue fluids, the heart, functions of mammalian blood, the immune system.

Food – Cereals ( wheat, rice, maze ), Beverages ( tea, coffee, cocoa ), sugarcane, medicinal plants ( Taxus, Catharanthus, Salix, Azadirachta ) and rubber ( Hevea ), Apiculture, Sericulture, Vermiculture and Leather.

Syllabus for CET for M.Tech ( Engineering Physics ) Programme

Physics

Interference : Young’s double slit experiment, Fresnel’s biprism, Thin films, Newton’s rings, Michelson’s interferometer, Fabry Perot interferometer.

Diffraction : Fresnel Diffraction: Zone plate, circular aperture, opaque circular disc, narrow slit, Fraunhofer diffraction : Single slit, double slit, diffraction grating, resolving power and dispersive power.

Polarization : Types of polarization, Brewsters law, Malu’s Law, Nicol prism, double refraction, quarter-wave and half-wave plates, optical activity, specific rotation.

Lasers : Introduction, coherence, population inversion, basic principle and operation of a laser, Einstein A and B coefficients, type of lasers, He-Ne laser, Ruby laser, semiconductor laser, holography-theory and applications

Fibre Optics : Types of optical fibres and their characteristics, ( Attenuation and dispersion step index and graded index fibres, principle of fibre optic communication-total internal reflection, numerical aperture, fibre optical communication network ( qualitative )-its advantages.

Theory of Relativity : Galenlian transformations, the postulates of the special theory of relativity, Lorentz transformations, time dilation, length contraction, velocity addition, mass energy equivalence.

Thermodynamics : The first law and other basic concepts: dimensions, units, work, heat, energy, the first law of thermodynamics, enthalpy, equilibrium, phase rule, heat capacity, PVT behavior of pure substances, ideal gas, real gas, heat effects.



The second law and Entropy : statements, heat engines, Kelvin-Planck and Clausious statements and their equality, reversible and irreversible processes, Carnot cycle, thermodynamic temperature scale, entropy, entropy calculations, T-S diagrams, properties of pure substances, use of steam tables and Mollier diagram.

Refrigeration and liquefaction : The Carnot refrigerator, the vapor–compression cycle, comparison of refrigeration cycles, liquefaction processes, heat pump. Rankine power cycle.

Quantum Mechanics : Wave particle duality, deBroglie waves, evidences for the wave nature of matter – the experiment of Davisson and Germer, electron diffraction, physical interpretation of the wave function and its properties, the wave packet, the uncertainty principle.

The Schrodinger wave equation ( 1 – dimensional ), Eigen values and Eigen functions, expectation values, simple Eigen value problems – solutions of the Schrodinger’s equations for the free particle, the infinite well, the finite well, tunneling effect, simple harmonic oscillator ( qualitative ), zero point energy.

Quantum Statistics : The statistical distributions, Maxwell Boltzmann, Bose-Einstein and Fermi-Dirac statistics, their comparisons, Fermions and Bosons. Applications : Molecular speed and energies in an ideal gas. The Black-body spectrum and failure of classical statistics to give the correct explanation – the application of Bose-Einstein statistics to the Black-body radiation spectrum, Fermi-Dirac distribution to free electron theory, electron specific heats, Fermi energy and average energy – its significance.

Band theory of solids : Origin of energy bands in solids, Kronig-Penny model, Brillouin zones, effective mass, Metals, semiconductors and insulators and their energy band structure. Extrinsic and intrinsic semiconductors, p-n junction diodes- its characteristics, tunnel diode, zener diode, photodiode, LED, photovoltaic cell, Hall effect in semiconductors, transistor characteristics ( common base, common emitter, common collector ). Digital techniques and their applications ( registers, counters, comparators and similar circuits ) A/D and D/A converters.

Superconductivity : ZFC and FC, Meissner effect, Type I and II superconductors, the Josephson effect, flux quantization, Cooper pairs, BCS theory, properties and applications of superconductors.

X-rays : production and properties, crystalline and amorphous solids, Bragg’s law, applications.

Electricity and magnetism : Electric fields, Gauss’ Law, its integral and differential form, applications. Lorentz force, fields due to moving charges, the magnetic field, Ampere’s law, motion of a charged particle in an electric and magnetic field, magnetic and electrostatic focussing, Hall effect, determination of e/m by cathode ray tube, positive rays, Thomson’s parabolic method, Isotopes, Mass spectrographs ( Aston and Bainbridge ), Electron microscope, Cyclotron and Betatron.

Overview of Electro – Magnetism : Maxwell’s Equations : The equation of continuity for Time – Varying fields, Inconsistency in ampere’s law Maxwell’s Equations, conditions at a Boundary Surface, Introduction to EM wave.

Nuclear Physics : Introduction of nucleus, Nucleus radius and density, Nuclear forces, Nuclear reactions, Cross section, Q-value and threshold energy of nuclear reactions, Basic Idea for Nuclear Reactor, Breeder reactor, The Geiger-Mullar ( G.M. ) Counter, Introduction of Accelerators and its Applications.

Numerical Techniques : Interpolations, differentiation, integration; Nonlinear equations, the bisection methods, Newton’s method, root finding; Differential equations, Euler’s method, the Runge-Kutta method; Matrices-inverting, finding eigenvalues and eigenfunctions.

Mathematics

Linear Independence and dependence of vectors, Systems of linear equations – consistency and inconsistency, rank of a matrix, Gauss elimination method, , Eigen values and Eigen vectors.

Successive differentiation, Leibnitz’s theorem, Lagrange’s Theorem, Cauchy Mean value theorems, Taylor’s theorem, Asymptotes, Curvature, Reduction Formulae of trigonometric functions, Properties of definite Integral, Applications to length, area, volume, surface of revolution. Partial derivatives, Method of Lagrange’s multipliers. Jacobeans of coordinates transformations. Double and Triple integrals.

Method of separation of variables, homogeneous, linear equations, exactness and integrating factors, linear equations of higher order with constant coefficients, Operator method to find particular integral. Scalar and vector fields, Directional Derivative, Gradient of scalar field, divergence and curl of a vector field. Green’s theorem, Divergence theorem and Stoke’s theorem.

Probability : Definition of Sample Space, Event, Event Space, Conditional Probability, Additive and Multiplicative law of Probability, Baye’s Law theorem, Application based on these results.

Syllabus for CET for M.Tech. ( Robotics & Automation ) Programs

Engineering Mathematics

Mathematical Logic : Propositional Logic, First Order Logic.

Complex Variables : Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’ series. Residue theorem, solution integrals.

Differential equations : First order equation ( linear and non – linear ), Higher order linear differential equations with constant coefficients, Methods of variation of parameters, Cauchy’s and Euler’s equations. Initial and boundary value problems, Partial Differential Equations and variable separable method.

Probability and Statistics : Sampling theorems, Conditional probability, Mean, Median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.

Set Theory & Algebra : Sets: Relations; Functions; Groups; Partial Orders; Lattice; Boolean Algebra.

Combinatorics : Permutations; Combinations; Counting; Summation; generating functions; recurrence relations, asymptotics.

Graph Theory : Connectivity : spanning trees; Cut vertices & edges; covering; matching; independent sets; Colouring; Planarity; Isomorphism.

Linear Algebra : Algebra of matrices, determinants, systems of linear equations, Eigen values and Eigen vectors.

Numerical Methods : LU decomposition for systems of linear equations; numerical solutions of nonlinear algebraic equations by Secant, Bisection and Newton- Raphson Methods; Numerical integration by trapezoidal and Simpson’s rules.

Calculus : Limit, Continuity & differentiability, Mean value Theorems, Theorems of Integral calculus, evaluation of definite & improper integrals, Partial derivatives, Total derivatives, maxima & minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.

Engineering Subjects

Network theorems : Superposition, Thevenin and Norton’s maximum power transfer.

Electric Circuits and Fields: Network graph, KCL, KVL, node and mesh analysis, transient response of dc and ac networks.

Programming in C, Functions.

Electrical Machines : Single phase transformer- equivalent circuit, phasor diagram , tests, regulations and efficiency, DC machines- types, windings, generator characteristics, armature reaction and commutation, starting and speed control of motors; three phase induction motors – principles, types, performances characteristics, starting and speed control; single phase induction motors; synchronous machines – performances, regulation and parallel operation of generators, motor starting, characteristics and application; servo and stepper motors.

Electronic Devices : Generation and recombination of carriers. P-n junction diode, Zener diode, BJT, JFET, MOS capacitor, MOSFET, LED, p – I – n and available photo diode, Basics of LASERs. Device technology.

Basics of Measurement Systems : Static and dynamic characteristics of Measurement Systems. Error and uncertainty, analysis, statistical analysis of data and curve fitting.

Transducers, Mechanical Measurement and Industrial Instrumentation : Resistive, Capacitive, Inductive and piezoelectric transducers and their signal conditioning. Measurement of displacement, velocity and acceleration ( translational and rotational ), force, torque, vibration and shock. Measurement of pressure, flow, temperature and liquid level. Measurement of pH, conductivity, viscosity and humidity.

Control System : Principles of feedback, transfer function; block diagrams; steady – state errors, Basic control system components; block diagrammatic description, reduction of block diagrams. Open loop and closed loop ( feedback ) systems and stability analysis of these systems.

Applied Mechanics : Free body diagrams and equilibrium, trusses and frames; virtual work; kinematics and dynamics of particles and of rigid bodies in plane motion, including impulse and momentum ( linear and angular ) and energy formulations, impact, strength of materials- stress, strain and their relationship, Mohr’s circle, deflection of beams, bending and shear stress, Euler’s theory of columns.

Theory of Machines : Acceleration of a point on a link, Acceleration diagram, Coroilis component of acceleration, Crank and slotted lever mechanism, Klien’s construction for Slider Crank mechanism and Four Bar mechanism, Analytical method for slider crank mechanism, Mechanisms with Lower Pairs Pantograph, Exact straight line motion mechanisms – Peaucellier’s Hart and Scott Russell mechanism, Approximate straight line motion mechanisms – Peaucellier’s, Hart and Scott Rusell mechanism.
Approximate straight line motion mechanism – Grass – Hopper, Watt and Tchebicheff mechanism, Analysis of Hooke’s joint, Davis and Ackermann steering gear mechanisms