General Information Regarding Phd
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GENERAL INFORMATION REGARDING PhD ENTRANCE TEST & INTERVIEW Duration of test: 60 minutes (50 Questions) The entrance examination will be of one hour duration and each question shall carry 1 mark and 1/4 mark will be deducted for each wrong answer. Syllabus for the Ph.D entrance examination 1 School of Management and Social Sciences Ph.D. in Psychology 1. General Psychology: Nature of Psychology, psychophysics, learning, perception, memory, emotion, motivation, thinking and problem solving, personality intelligence and creativity 2. Social Psychology: Introduction, leadership, attitude, prejudice, stereotypes and discrimination, social cognition, interpersonal attraction, aggression and violence, prosocial behavior, social influence through social interaction and social identity. 3. Research Method: Types of research, variables, problem, hypotheses, designs, tools of data collection, sampling techniques. 4. Statistics: Parameter and statistics: description and inferential, normal and skewed distributions, hypothesis testing: t-test, analysis of variance, chi-square, correlation. 5. Psychopathology and Clinical Psychology: Concept of abnormality, models of abnormal behavior, classification of mental disorders (DSM IV and ICD-ID), anxiety based, unipolar and bipoplar disorders, psychoanalytic, behavioristic, cognitive and humanistic existential therapies. 6. Organization Behavior: Accident, fatigue, selection and training, work motivation, organization structure, development and change, organizational climate and leadership in organizations. 2 School of Physics and Materials Science Mathematical Physics Special functions (Hermite, Bessel, Laguerre and Legendre); Fourier series, Fourier transforms; Elements of complex analysis: Laurent series-poles, residues and evaluation of integrals; Introductory group theory, Classical Mechanics Central-force motion; Two-body collisions, scattering in laboratory and centre-of-mass frames; Rigid body dynamics, moment of inertia tensor, non-inertial frames and pseudoforces; Variational principle, Lagrangian and Hamiltonian formalisms and equations of motion Electromagnetic Theory Electrostatics: boundary value problems; Magnetostatics, Maxwell's equations in free space and linear isotropic media; boundary conditions on fields at interfaces; Scalar and vector potentials; Gauge invariance; Electromagnetic waves in free space, dielectrics, and conductors; Reflection and refraction, polarization, Transmission lines and wave guides; Dynamics of charged particles in static electromagnetic fields; Radiation from moving charges, dipoles and retarded potentials. Quantum Mechanics Matrix representation; Dirac’s bra and ket notation; Schroedinger equation (time-dependent and timeindependent); Eigenvalue problems such as particle-in-a-box, harmonic oscillator, etc.; Tunneling through a barrier; Motion in a central potential; Orbital angular momentum, Angular momentum algebra, spin; Addition of angular momenta; Hydrogen atom, spin-orbit coupling, fine structure; Time-independent perturbation theory and applications; Statistical Physics Phase space, micro- and macrostates; Microcanonical, canonical and grand-canonical ensembles and partition functions; Free Energy and connection with thermodynamic quantities; First- and second-order phase transitions; Classical and quantum statistics, ideal Fermi and Bose gases; Bose-Einstein condensation. Electronics
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Semiconductor device physics, device structure, device characteristics, frequency dependence and applications; Optoelectronic devices, including solar cells, photodetectors, and LEDs; Operational amplifiers and their applications; Digital techniques and applications. Atomic & Molecular Physics Spectrum of Hydrogen, helium and alkali atoms; Relativistic corrections for energy levels of hydrogen; Hyperfine structure and isotopic shift; width of spectral lines; LS & JJ coupling; chemical shift; Rotational, vibrational, electronic, and Raman spectra of diatomic molecules; Nuclear and Particle Physics Basic nuclear properties: Liquid drop model; Fission and fusion; Nature of the nuclear force, form of nucleonnucleon potential; Charge-independence and charge-symmetry of nuclear forces; Deuteron problem; Evidence of shell structure, single- particle shell model, its validity and limitations; Nuclear reactions, reaction mechanisms, compound nuclei and direct reactions; Classification of fundamental forces; Elementary particles Spin and parity assignments, isospin, strangeness; C, P, and T invariance Condensed Matter Physics & Materials science Bravais lattices; Reciprocal lattice, X-ray diffraction, structure determination, Bonding of solids; Bond energy, bond type and bond length, primary and secondary bonding, Elastic properties, phonons, lattice specific heat; Free electron theory and electronic specific heat; Response and relaxation phenomena; Drude model of electrical and thermal conductivity; Hall effect and thermoelectric power; Diamagnetism, paramagnetism, and ferromagnetism; Electron motion in a periodic potential, band theory of metals, insulators and semiconductors; Conductor and resistors, dielectric materials, Superconductivity, Ordered phases of matter, translational and orientational order, kinds of liquid crystalline order; Conducting polymers; Quasicrystals, Structure of solids, covalent solids, metals and alloys, ionic solids, structure of silica and silicate, polymers, classification of polymers, structure of long chain polymers, crystallinity of long chain polymers, Crystal Defects, point defects, line defects and surface defects, Phase diagrams; phase rule, single component system, binary phase diagram (isomorphous, eutectic and nd peritectic), Diffusion in solids, Fick’s first and 2 law of diffusion, Kirkendall effect, atomic model of diffusion, plastic deformations, tensile stress strain curve, plastic deformation mechanism (slip and twinning), work hardening, strengthening mechanism, creep and its mechanism, ductile and brittle fractures. 3 School of Chemistry and Bio-Chemistry Physical Chemistry: 1. Basic principles and applications of quantum mechanics – hydrogen atom, angular momentum. 2. Variational and perturbational methods. 3. Basics of atomic structure, electronic configuration, shapes of orbitals, hydrogen atom spectra. 4. Theoretical treatment of atomic structures and chemical bonding. 5. Chemical applications of group theory. 6. Basic principles and application of spectroscopy – rotational, vibrational, electronic, Raman, ESR, NMR. 7. Chemical thermodynamics. 8. Phase equilibria. 9. Statistical thermodynamics. 10. Chemical equilibria. 11. Electrochemistry – Nernst equation, electrode kinetics, electrical double layer, Debye-Hückel theory. 12. Chemical kinetics – empirical rate laws, Arrhenius equation, theories of reaction rates, determination of reaction mechanisms, experimental techniques for fast reactions. 13. Concepts of catalysis. 14. Polymer chemistry. Molecular weights and their determinations. Kinetics of chain polymerization. 15. Solids - structural classification of binary and ternary compounds, diffraction techniques, bonding, thermal, electrical and magnetic properties 16. Collids and surface phenomena. 17. Data analysis. Inorganic Chemistry 1. Chemical periodicity
2. Structure and bonding in homo- and heteronuclear molecules, including shapes of molecules. 3. Concepts of acids and bases. 4. Chemistry of the main group elements and their compounds. Allotropy, synthesis, bonding and structure. 5. Chemistry of transition elements and coordination compounds – bonding theories, spectral and magnetic properties, reaction mechanisms. 6. Inner transition elements – spectral and magnetic properties, analytical applications. 7. Organometallic compounds - synthesis, bonding and structure, and reactivity. Organometallics in homogenous catalysis. 8. Cages and metal clusters. 9. Analytical chemistry- separation techniques. Spectroscopic electro- and thermoanalytical methods. 10. Bioinorganic chemistry – photosystems, porphyrines, metalloenzymes, oxygen transport, electron- transfer reactions, nitrogen fixation. 11. Physical characterisation of inorganic compounds by IR, Raman, NMR, EPR, Mössbauer, UV-, NQR, MS, electron spectroscopy and microscopic techniques. 12. Nuclear chemistry – nuclear reactions, fission and fusion, radio-analytical techniques and activation analysis. Organic Chemistry 1. IUPAC nomenclature of organic compounds. 2. Principles of stereochemistry, conformational analysis, isomerism and chirality. 3. Reactive intermediates and organic reaction mechanisms. 4. Concepts of aromaticity. 5. Pericyclic reactions. 6. Named reactions. 7. Transformations and rearrangements. 8. Principles and applications of organic photochemistry. Free radical reactions. 9. Reactions involving nucleophotic carbon intermediates. 10. Oxidation and reduction of functional groups. 11. Common reagents (organic, inorganic and organometallic) in organic synthesis. 12. Chemistry of natural products such as steroids, alkaloids, terpenes, peptides, carbohydrates, nucleic acids and lipids. 13. Selective organic transformations – chemoselectivity, regioselectivity, stereoselectivity, enantioselectivity. Protecting groups. 14. Chemistry of aromatic and aliphatic heterocyclic compounds. 15. Physical characterisation of organic compounds by IR, UV-, MS, and NMR. Interdisciplinary topics 1. Chemistry in nanoscience and technology. 2. Catalysis and green chemistry. 3. Medicinal chemistry. 4. Supramolecular chemistry. 5. Environmental chemistry. 4 SCHOOL OF MATHEMATICS AND COMPUTER APPLICATIONS Ph.D (Computer Applications) Number Representation and Computer Arithmetic. Computer Organization : Machine instructions and addressing modes, ALU and data-paths, hardwired and microprogrammed control pipelining , memory interface, I/O interfaces, serial communication interface, parallel processing, memory management Structured and object oriented programming concepts (with reference to “C/ C++”): Program control, functions, recursion, scope, binding, parameter passing, pointers, array handling, structures and unions, file handling, concepts of Object Oriented Programming. Data Structures: Notion of abstract data types, stacks, queues, linked lists, trees, heap,graphs, Tree and graph traversals, hashing, sorting, searching.
Operating Systems: Definition and significance of OS, OS as resource manager, Classical concepts processes, concurrency, synchronization, deadlock, threads and inter-process communication, CPU scheduling, memory management, file systems, I/O systems, protection and security, DOS, UNIX and windows. Database Management Systems: Relational model, ER diagram, relational algebra, database design, normalization, SQL, transactions management and concurrency control. Computer Networks: OSI reference model, sliding window protocols, LAN technologies (Ethernet, Token ring), TCP/UDP, IP, , Networking addresses, transmission medias, Networking devices-Hub, switches. gateways and routers. Software Engineering: Basics of s/w engineering, Software Process models, software project planning and management. Ph.D Mathematics Differential Equations: Ordinary differential equations of first order and their solutions, Linear differential equations of higher order with constant coefficients, Classification of partial differential equations, Partial differential equations of first order, Lagrange’s solution, Charpit’s method. Special Functions Analysis: Riemann integral, Integrability of continuous and monotonic functions, Mean value theorems of integral calculus, Infinite series and their convergence, Demoivre’s theorem and its applications, Functions of complex variables, Analytic function, C-R equations. Abstract Algebra: Groups, Subgroups and their properties, Lagrange’s theorem, Rings, Subrings, Integral domain and Field, Vector spaces, Subspaces and their properties, Inner product spaces, Orthogonal vectors Statistics and Probability :Measures of central tendency, Dispersion, Skewness and kurtosis, Correlation and regression, Basic concepts of probability, Conditional probability, Baye’s theorem, Discrete and continuous distributions ( Binomial , Poisson and Normal),. Metric spaces: Open and Closed Sets, Interior, Closure and limit points of a set, Subspaces, Continuous functions on metric spaces. Convergence in a metric space, Complete metric spaces, Compact metric spaces, Compactness and uniform continuity, Connected metric spaces. Topological Spaces: Definition and examples of topological spaces, Topology induced by a metric, closed set, closure, Dense subsets, Neighborhood, Interior, Exterior, boundary and Accumulation points and derived sets, Bases and subbases, Topology generated by subbases, subspaces and relative topology, Lindelof spaces, Separable spaces, Second countability and separability, separation Axioms, T0 , T1 , T2 , T3 , T4 spaces and their characterization and basic properties, Compact spaces and their basic properties, Laplace Transform: Review of Laplace transform, Applications of Laplace transform in initial and boundary value problems Fourier Series Definition, properties, Fourier integral theorem, Convolution theorem and Inversion theorem. Functional analysis : Normed Linear space: Normed Linear space Banach space and examples, Quotient spaces, equivalent norms, Bounded linear transformations, Normed linear spaces of bounded linear transformations, Hilbert Spaces: Inner product spaces Hilbert spaces, orthogonality, Orthonormal sets, Bessel’s inequality, Parseval’s theorem, orthogonal complement and projection theorem,, , Operators: Adjoint operators, Self-adjoint operators, positive operators, normal and unitary operators, projections. Numerical Techniques: Number systems, Solution of non-linear equations, Solution of system of linear equations, curve fitting, interpolation, Numerical differentiation and integration, solutions of IVP. Optimization Techniques: Linear Programming: Graphical method, Simplex method, Duality Theory and Sensitivity Analysis. Transportation and Assignment Problem: Initial Basic Feasible Solutions of Balanced and Unbalanced Problems, Optimal Solutions. Network Analysis: Shortest Path problem. Minimum Spanning Tree Problem. Maximum Flow Problem. Minimum Cost Flow Problem. 5 Department of Computer Science & Engineering Analytical and Logical reasoning, Discrete Mathematical structures, Data structures, Operating systems, Object Oriented Programming, Computer System Architecture, Computer Networks, Programming Languages, System
Analysis and Design, Database Management Systems, Software Engineering, Algorithm Analysis and Design, Software Project Management, Web Technologies, System Software, Compiler Construction, Computer Graphics, Artificial Intelligence 6 Department of Electronics and Communication Engineering Discrete Time Signal Processing, Optical Communication Networks, Information and Communication Theory, Antenna Systems, Advanced Communication Systems, Embedded Systems, RF Devices and Circuits, Advanced Wireless Communication Systems, Soft Computing, Passive Optical Networks, Audio and Speech Processing, Advanced Wireless Networks, Fractional Transforms and Applications, VLSI Signal Processing, Detection and Estimation Theory, Advanced Computer Networks and Protocols, Microstrip Antennas, Advanced Optical Technologies, Video and Image Processing, Error Coding Theory, Space-Time Wireless Communication, Wireless Broadband Networks, Optoelectronics, IP over WDM, Adaptive Signal Processing, Wireless Sensor Networks, Next Generation Wireless Systems and Networks, Digital Signal Processors, Logic Synthesis using HDLs, Physics of Semiconductor Devices, IC Fabrication Technology, Digital VLSI Design, CAD Systems Environment, Analog IC Design, VLSI Architectures, Physical Design Automation, VLSI Subsystem Design, ASICs and FPGAs, VLSI Testing and Verification, MOS Device Modeling, Memory Design and Testing, Mixed Signal Circuit Design and High Speed VLSI Design. 7 Department of Chemical Engineering Process Calculations and Thermodynamics: Laws of conservation of mass and energy; degree of freedom analysis, first and second laws of thermodynamics and their applications, phase equilibria; chemical reaction equilibrium. Fluid Mechanics and Mechanical Operations. Fluid statistics, bernoulli equation, macroscopic friction factors, dimensional analysis, flow through pipeline systems, flow meters pumps and compressors, packed and fluidized beds, size reduction and size separation. Heat Transfer: Conduction, convection, radiation, heat exchangers, evaporators. Mass Transfer: Ficks’ law, molecular diffusion in fluids, distillation, absorption and drying. Chemical Reaction Engineering: Kinetics of homogeneous reactions, interpretation of kinetic data, residence time, kinetics of heterogeneous catalytic reactions; diffusion effects in catalysis. Instrumentation and Process Control: Dynamics of simple systems, controller modes (P, PI and PID). Plant Design and Economics: Design and sizing of chemical engineering equipment, principles of process economics and cost estimation. Chemical Technology: Inorganic chemical industries; sulfuric acid, NaOH, fertilizers (Ammonia, Urea, SSP and TSP); organic chemical industries (Pulp and Paper, Sugar, Oil and Fats); petroleum refining and petrochemicals: polymerization industries; polypropylene, PVC and polyester synthetic fibers., Process Modeling and Simulation: Equation of continuity, momentum, energy, CSTR, exchangers, distillation. Mathematics: Algebra, calculus, and differential equations: first order (linear and nonlinear). Numerical Methods: Numerical solutions of linear and non linear algebraic equations, integration by trapezoidal and Simpson’s rule, single and multi-step methods of differential equations Probability and Statistics: Mean, median, mode and standard deviation, random variables, Poisson, normal and binominal distributions. Chemistry: Kinetics, spectroscopy, colligative properties, organic synthesis Biotechnology: Biochemical kinetics, bioreactors, transport phenomena in bioprocess systems Environment: The physical environment: land, water, air and climate environments, sustainability, analysis of natural resource base management practices, analysis of agricultural and industrial systems Energy Technology: Primary and secondary fuels, solar, wind, biomass, geothermal and nuclear energy. 8 Department of Electrical and Instrumentation Engineering a) Electrical Engineering Introduction to circuits and networks analysis of circuits; Fundamentals of AC: single phase, 3−phase; Network Analysis and synthesis; Basic electronics (Diode, Transistor, FETs, Op-Amp); Elements of power systems: Transmission line, modeling and performance, Load flow analysis , fault analysis, ALFC and AVR control, Switchgear and protection, HVDC transmission; Electrical machines: construction and working of DC machines, induction and
synchronous machines, fractional horse power machine, Generalized theory of electrical machines; Control Engineering : Open loop and closed loop control, signal flow graphs, stability, controllers, state space representation; Power Electronics : Power electronic devices and their applications; AC and DC drives; Fundamentals of instrumentation; Fundamentals of computer programming; Intelligent techniques. b) Electronic Instrumentation and Control Engineering: Fundamentals of Measurement and Instrumentation systems, Static and dynamic characteristics of Measurement Systems, Measurement of various physical quantities; Introduction to circuits and networks analysis; Digital Electronics: Boolean functions and their minimization, Combinational and Sequential circuits, IC families, A/D , D/A; Microprocessors and Microcontrollers; Analog Electronics: Characteristics of diode, BJT, JFET and MOSFET, OpAmp and its applications; Digital signal processing techniques; Analytical, Optical and Biomedical Instrumentation: Spectrometry, X-ray and nuclear radiation measurements, Laser, fiber optics, Elements of Biomedical instruments, EEG, ECG and EMG. Clinical measurements; Control Engineering : Feedback principles, Transient Response, Steadystate-errors, Stability, Routh and Nyquist criteria, Bode plot, Root locus, State space representation, PID controllers; Intelligent Algorithms: Fuzzy Systems, Artificial Neural Networks, Genetic Algorithm, Hybrid Systems; Power Electronics and Drives: Power electronic devices and their applications; AC and DC drives. 9 Department of Civil Engineering. Specialization: STRUCTURES Mechanics: Bending moments and shear forces in statically determinate beams -- simple stress and strain: relationship -- stress and strain in two dimensions, principal stresses, stress transformation, Mohr’s circle -- simple bending theory -- flexural shear stress -- thin-walled pressure vessels -- uniform torsion. Structural Analysis: Analysis of statically determinate trusses, arches and frames -- displacements in statically determinate structures and analysis of statically indeterminate structures by force/energy methods -- analysis by displacement methods (slope-deflection and moment-distribution methods) -- influence lines for determinate and indeterminate structures -- basic concepts of matrix methods of structural analysis. Concrete Structures: Basic working stress and limit states design concepts -- analysis of ultimate load capacity and design of members subject to flexure, shear, compression and torsion (beams, columns isolated footings) -- basic elements of prestressed concrete: analysis of beam sections at transfer and service loads. Steel Structures: Analysis and design of tension and compression members, beams and beam-columns, column bases -- connections - simple and eccentric, beam-column connections, plate girders and trusses -- plastic analysis of beams and frames. Specialization: GEOTECHNICAL ENGINEERING Soil Mechanics: Origin of soils -- soil classification -- three-phase system, fundamental definitions, relationship and inter-relationships -- permeability and seepage -- effective stress principle: consolidation, compaction -- shear strength. Foundation Engineering: Sub-surface investigation - scope, drilling bore holes, sampling, penetrometer tests, plate load test -- earth pressure theories, effect of water table, layered soils -- stability of slopes - infinite slopes, finite slopes -- foundation types - foundation design requirements -- shallow foundations -- bearing capacity, effect of shape, water table and other factors, stress distribution, settlement analysis in sands and clays -- deep foundations - pile types, dynamic and static formulae, load capacity of piles in sands and clays. Specialization: HIGHWAY AND TRANSPORTATION ENGINEERING Highway planning -- Geometric design of Highways -- Testing and specifications of paving materials -- Design of flexible and rigid pavements. Pavement Evaluation and Pavement Management Systems. Specialization: WATER RESOURCES AND HYDRAULICS Fluid Mechanics and Hydraulics: Hydrostatics applications of Bernoulli equation, Laminar and turbulent flow in pipes, pipe networks -- concept of boundary layer and its growth -- uniform flow, critical flow and gradually varied flow in channels, specific energy concept, hydraulic jump -- forces on immersed bodies -- flow measurement in channels -- tanks and pipes -- dimensional analysis and hydraulic modeling. Applications of Momentum equation, Potential flow, Kinematics of flow -- Velocity triangles and specific speed of pumps and turbines. Hydrology: Hydrologic cycle -- Rainfall -- evaporation infiltration, unit hydrographs, flood estimation, reservoir design, reservoir and channel routing, well hydraulics.
Irrigation: Duty, delta, Estimation of evapo-transpiration -- crop water requirements -- design of lined and unlined canals -- waterways -- head works, Gravity dams, Ogee spillways, Earth dams. Designs of weirs on permeable foundation, Irrigation methods 10 Department of Mechanical Engineering Section – A Solid Mechanics, Machine Design, Theory of Machines, Mechanical Vibrations, Machine Drawing, CAD CAM and Robotics, Computer Programming, Finite Element Method Section – B Thermodynamics, Steam Engineering, IC Engines and Gas Turbines, Turbo Machines, Fluid Mechanics and Machinery, Refrigeration and Air Conditioning, Heat and Mass Transfer, Power Plant Engineering, Nonconventional Source of Energy, Computational Fluid Dynamics Section – C Industrial Engineering, Plant layout, Production Management, Work Study, Inspection and Quality Control, Manufacturing Processes/Technologies, Machining Science, Measurement Techniques, Industrial Automation, Material Science and Metallurgy. 11 Department of Biotechnology and Environmental Sciences Biotechnology Biochemistry: Atoms, Molecules and chemical bonds; Structure and function of biomolecules, biophysical chemistry Bioenergetics, biological energy transducers, oxidative phosphorylation ; Enzymes and enzyme kinetics; proteins conformations, structures and functions; conformation of nucleic acids, metabolism of carbohydrates, fats, amino acids, nucleotides and vitamins. Cell structure and Organization: Membrane structure and function; organization and function of intracellular organelles; genetic information; Cell division and cell cycle; Microbial physiology. Fundamental Life processes: DNA replication, repair and recombination; RNA synthesis and processing; Protein synthesis and processing; Control of gene expression at transcription and translation level Cellular Communications: Host parasite interaction; Cell signaling; Cancer and Immune responses (innate and adaptive) Developmental Biology of Animal and Plant systems: Concepts of development, gametogenesis; fertilization; morphogenesis and organogenesis; Programmed Cell death and aeging. Plant and Animal Physiology: Photosynthesis; Respiration and photorespiration; Nitrogen metabolism; Plant hormones; Solute transport and photoassimilate translocation; Secondary metabolites; Stress physiology. Blood and circulation; Cardiovascular System, Respiratory system ; Nervous system; Sense organs; Excretory system; Thermoregulation; Stress and adaptation; Digestive system: Endocrinology and reproduction Heredity and Genetics: Mendelian principles; Concept of gene; Extensions of Mendelian principles; Gene mapping methods; Extra chromosomal inheritance; Microbial genetics; Quantitative genetics; Mutation: Structural and numerical alterations of chromosomes; recombination Biodiversity: Principles and methods of taxonomy Levels of structural organization Outline classification of plants, animals and microorganisms; Organisms of health and agricultural importance Ecology and Molecular Evolution: the Environment; Habitat and niche; Population ecology; Species interactions; Community ecology; Ecological succession; Ecosystem geography; Applied ecology; Conservation biology; Molecular Evolution Applied Biology: Microbial fermentation products, vaccines and diagnostics; genomics; biodiversity applications; plant and animal breeding – marker assisted selection; Bioremediation; phytoremediation and biosensors Methods in biology: Molecular biology and recombinant DNA methods; Histochemical and immunotechniques; Statistical Methods: Biophysical methods; Radiolabeling techniques; Microscopic techniques; computational methods Environmental Sciences Interactions between humans and environment; The physical environment- land water, and climate; Resources and their management- Natural, Technological and Human; Concept of sustainability- Natural ecosystems and sustainability; Agricultural and Industrial systems from the angles of environment protection; Environmental
Chemistry- Analytical Techniques and instrumentation; Atmospheric Chemistry; Basic Microbiology- nature and extent of microbial world; growth and energetics, Microbiology of water and wastewater; Microbial Corrosion and biofouling; Quantity of Water- per capita demand, factor affecting the demand; Quality of water- physical, chemicals and biological characteristics, Treatment of water- Sedimentation, Coagulation; filtration; Chlorination; absorption; adsorption, and Miscellaneous methods; Sewage and sewerage systems; Primary and Secondary treatment of sewage- aerobic and anaerobic processes and their applications in the wastewater treatment. 12 L M THAPAR SCHOOL OF MANAGEMENT Research Aptitude • Research: Meaning, ethics &characteristics • Type of research • ď€ Methods of research Verbal Reasoning • Verbal Speed Test- Spelling and Grammar • Verbal Power Test- Critical Reasoning Reading Comprehension • A passage to be set with questions to be answered with emphasis on major functional areas of management Logical Reasoning • Arguments, deductive & inductive research • Logical & Venn diagram • Inferences • Analogies Data Interpretation Interpretation of data • Mapping analysis of data • Analysis & Tools for data analysis • Quantitative &qualitative research
Model questions 1. The decreasing order of the first ionization energy of the following elements is (A) He > H > Be > B (B) Be > B > H > He (C) H > He > Be > B (D) B > Be > He > H 2. The solubility products (Ksp) for three salts MX, MY2 −8 and 27×10 , respectively. The solubilities of these salts follow the order (A) MX > MY2 > MZ3 (B) MZ3 > MY2 > MX (C) MZ3 > MX > MY2 (D) MY2 > MX > MZ3 and MZ3 are 1×10 ,
−8
4×10
−9
3. The rate of nitration of following aromatic compounds decreases in the order (i) benzene (ii) pyridine (iii) thiophene (iv) toluene (A) (iv) > (i) > (iii) > (ii) (B) (iii) > (iv) > (i) > (ii) (C) (iii) > (ii) > (i) > (iv) (D) (ii) > (i) > (iv) > (iii)
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Semiconductor device physics, device structure, device characteristics, frequency dependence and applications; Optoelectronic devices, including solar cells, photodetectors, and LEDs; Operational amplifiers and their applications; Digital techniques and applications. Atomic & Molecular Physics Spectrum of Hydrogen, helium and alkali atoms; Relativistic corrections for energy levels of hydrogen; Hyperfine structure and isotopic shift; width of spectral lines; LS & JJ coupling; chemical shift; Rotational, vibrational, electronic, and Raman spectra of diatomic molecules; Nuclear and Particle Physics Basic nuclear properties: Liquid drop model; Fission and fusion; Nature of the nuclear force, form of nucleonnucleon potential; Charge-independence and charge-symmetry of nuclear forces; Deuteron problem; Evidence of shell structure, single- particle shell model, its validity and limitations; Nuclear reactions, reaction mechanisms, compound nuclei and direct reactions; Classification of fundamental forces; Elementary particles Spin and parity assignments, isospin, strangeness; C, P, and T invariance Condensed Matter Physics & Materials science Bravais lattices; Reciprocal lattice, X-ray diffraction, structure determination, Bonding of solids; Bond energy, bond type and bond length, primary and secondary bonding, Elastic properties, phonons, lattice specific heat; Free electron theory and electronic specific heat; Response and relaxation phenomena; Drude model of electrical and thermal conductivity; Hall effect and thermoelectric power; Diamagnetism, paramagnetism, and ferromagnetism; Electron motion in a periodic potential, band theory of metals, insulators and semiconductors; Conductor and resistors, dielectric materials, Superconductivity, Ordered phases of matter, translational and orientational order, kinds of liquid crystalline order; Conducting polymers; Quasicrystals, Structure of solids, covalent solids, metals and alloys, ionic solids, structure of silica and silicate, polymers, classification of polymers, structure of long chain polymers, crystallinity of long chain polymers, Crystal Defects, point defects, line defects and surface defects, Phase diagrams; phase rule, single component system, binary phase diagram (isomorphous, eutectic and nd peritectic), Diffusion in solids, Fick’s first and 2 law of diffusion, Kirkendall effect, atomic model of diffusion, plastic deformations, tensile stress strain curve, plastic deformation mechanism (slip and twinning), work hardening, strengthening mechanism, creep and its mechanism, ductile and brittle fractures. 3 School of Chemistry and Bio-Chemistry Physical Chemistry: 1. Basic principles and applications of quantum mechanics – hydrogen atom, angular momentum. 2. Variational and perturbational methods. 3. Basics of atomic structure, electronic configuration, shapes of orbitals, hydrogen atom spectra. 4. Theoretical treatment of atomic structures and chemical bonding. 5. Chemical applications of group theory. 6. Basic principles and application of spectroscopy – rotational, vibrational, electronic, Raman, ESR, NMR. 7. Chemical thermodynamics. 8. Phase equilibria. 9. Statistical thermodynamics. 10. Chemical equilibria. 11. Electrochemistry – Nernst equation, electrode kinetics, electrical double layer, Debye-Hückel theory. 12. Chemical kinetics – empirical rate laws, Arrhenius equation, theories of reaction rates, determination of reaction mechanisms, experimental techniques for fast reactions. 13. Concepts of catalysis. 14. Polymer chemistry. Molecular weights and their determinations. Kinetics of chain polymerization. 15. Solids - structural classification of binary and ternary compounds, diffraction techniques, bonding, thermal, electrical and magnetic properties 16. Collids and surface phenomena. 17. Data analysis. Inorganic Chemistry 1. Chemical periodicity
2. Structure and bonding in homo- and heteronuclear molecules, including shapes of molecules. 3. Concepts of acids and bases. 4. Chemistry of the main group elements and their compounds. Allotropy, synthesis, bonding and structure. 5. Chemistry of transition elements and coordination compounds – bonding theories, spectral and magnetic properties, reaction mechanisms. 6. Inner transition elements – spectral and magnetic properties, analytical applications. 7. Organometallic compounds - synthesis, bonding and structure, and reactivity. Organometallics in homogenous catalysis. 8. Cages and metal clusters. 9. Analytical chemistry- separation techniques. Spectroscopic electro- and thermoanalytical methods. 10. Bioinorganic chemistry – photosystems, porphyrines, metalloenzymes, oxygen transport, electron- transfer reactions, nitrogen fixation. 11. Physical characterisation of inorganic compounds by IR, Raman, NMR, EPR, Mössbauer, UV-, NQR, MS, electron spectroscopy and microscopic techniques. 12. Nuclear chemistry – nuclear reactions, fission and fusion, radio-analytical techniques and activation analysis. Organic Chemistry 1. IUPAC nomenclature of organic compounds. 2. Principles of stereochemistry, conformational analysis, isomerism and chirality. 3. Reactive intermediates and organic reaction mechanisms. 4. Concepts of aromaticity. 5. Pericyclic reactions. 6. Named reactions. 7. Transformations and rearrangements. 8. Principles and applications of organic photochemistry. Free radical reactions. 9. Reactions involving nucleophotic carbon intermediates. 10. Oxidation and reduction of functional groups. 11. Common reagents (organic, inorganic and organometallic) in organic synthesis. 12. Chemistry of natural products such as steroids, alkaloids, terpenes, peptides, carbohydrates, nucleic acids and lipids. 13. Selective organic transformations – chemoselectivity, regioselectivity, stereoselectivity, enantioselectivity. Protecting groups. 14. Chemistry of aromatic and aliphatic heterocyclic compounds. 15. Physical characterisation of organic compounds by IR, UV-, MS, and NMR. Interdisciplinary topics 1. Chemistry in nanoscience and technology. 2. Catalysis and green chemistry. 3. Medicinal chemistry. 4. Supramolecular chemistry. 5. Environmental chemistry. 4 SCHOOL OF MATHEMATICS AND COMPUTER APPLICATIONS Ph.D (Computer Applications) Number Representation and Computer Arithmetic. Computer Organization : Machine instructions and addressing modes, ALU and data-paths, hardwired and microprogrammed control pipelining , memory interface, I/O interfaces, serial communication interface, parallel processing, memory management Structured and object oriented programming concepts (with reference to “C/ C++”): Program control, functions, recursion, scope, binding, parameter passing, pointers, array handling, structures and unions, file handling, concepts of Object Oriented Programming. Data Structures: Notion of abstract data types, stacks, queues, linked lists, trees, heap,graphs, Tree and graph traversals, hashing, sorting, searching.
Operating Systems: Definition and significance of OS, OS as resource manager, Classical concepts processes, concurrency, synchronization, deadlock, threads and inter-process communication, CPU scheduling, memory management, file systems, I/O systems, protection and security, DOS, UNIX and windows. Database Management Systems: Relational model, ER diagram, relational algebra, database design, normalization, SQL, transactions management and concurrency control. Computer Networks: OSI reference model, sliding window protocols, LAN technologies (Ethernet, Token ring), TCP/UDP, IP, , Networking addresses, transmission medias, Networking devices-Hub, switches. gateways and routers. Software Engineering: Basics of s/w engineering, Software Process models, software project planning and management. Ph.D Mathematics Differential Equations: Ordinary differential equations of first order and their solutions, Linear differential equations of higher order with constant coefficients, Classification of partial differential equations, Partial differential equations of first order, Lagrange’s solution, Charpit’s method. Special Functions Analysis: Riemann integral, Integrability of continuous and monotonic functions, Mean value theorems of integral calculus, Infinite series and their convergence, Demoivre’s theorem and its applications, Functions of complex variables, Analytic function, C-R equations. Abstract Algebra: Groups, Subgroups and their properties, Lagrange’s theorem, Rings, Subrings, Integral domain and Field, Vector spaces, Subspaces and their properties, Inner product spaces, Orthogonal vectors Statistics and Probability :Measures of central tendency, Dispersion, Skewness and kurtosis, Correlation and regression, Basic concepts of probability, Conditional probability, Baye’s theorem, Discrete and continuous distributions ( Binomial , Poisson and Normal),. Metric spaces: Open and Closed Sets, Interior, Closure and limit points of a set, Subspaces, Continuous functions on metric spaces. Convergence in a metric space, Complete metric spaces, Compact metric spaces, Compactness and uniform continuity, Connected metric spaces. Topological Spaces: Definition and examples of topological spaces, Topology induced by a metric, closed set, closure, Dense subsets, Neighborhood, Interior, Exterior, boundary and Accumulation points and derived sets, Bases and subbases, Topology generated by subbases, subspaces and relative topology, Lindelof spaces, Separable spaces, Second countability and separability, separation Axioms, T0 , T1 , T2 , T3 , T4 spaces and their characterization and basic properties, Compact spaces and their basic properties, Laplace Transform: Review of Laplace transform, Applications of Laplace transform in initial and boundary value problems Fourier Series Definition, properties, Fourier integral theorem, Convolution theorem and Inversion theorem. Functional analysis : Normed Linear space: Normed Linear space Banach space and examples, Quotient spaces, equivalent norms, Bounded linear transformations, Normed linear spaces of bounded linear transformations, Hilbert Spaces: Inner product spaces Hilbert spaces, orthogonality, Orthonormal sets, Bessel’s inequality, Parseval’s theorem, orthogonal complement and projection theorem,, , Operators: Adjoint operators, Self-adjoint operators, positive operators, normal and unitary operators, projections. Numerical Techniques: Number systems, Solution of non-linear equations, Solution of system of linear equations, curve fitting, interpolation, Numerical differentiation and integration, solutions of IVP. Optimization Techniques: Linear Programming: Graphical method, Simplex method, Duality Theory and Sensitivity Analysis. Transportation and Assignment Problem: Initial Basic Feasible Solutions of Balanced and Unbalanced Problems, Optimal Solutions. Network Analysis: Shortest Path problem. Minimum Spanning Tree Problem. Maximum Flow Problem. Minimum Cost Flow Problem. 5 Department of Computer Science & Engineering Analytical and Logical reasoning, Discrete Mathematical structures, Data structures, Operating systems, Object Oriented Programming, Computer System Architecture, Computer Networks, Programming Languages, System
Analysis and Design, Database Management Systems, Software Engineering, Algorithm Analysis and Design, Software Project Management, Web Technologies, System Software, Compiler Construction, Computer Graphics, Artificial Intelligence 6 Department of Electronics and Communication Engineering Discrete Time Signal Processing, Optical Communication Networks, Information and Communication Theory, Antenna Systems, Advanced Communication Systems, Embedded Systems, RF Devices and Circuits, Advanced Wireless Communication Systems, Soft Computing, Passive Optical Networks, Audio and Speech Processing, Advanced Wireless Networks, Fractional Transforms and Applications, VLSI Signal Processing, Detection and Estimation Theory, Advanced Computer Networks and Protocols, Microstrip Antennas, Advanced Optical Technologies, Video and Image Processing, Error Coding Theory, Space-Time Wireless Communication, Wireless Broadband Networks, Optoelectronics, IP over WDM, Adaptive Signal Processing, Wireless Sensor Networks, Next Generation Wireless Systems and Networks, Digital Signal Processors, Logic Synthesis using HDLs, Physics of Semiconductor Devices, IC Fabrication Technology, Digital VLSI Design, CAD Systems Environment, Analog IC Design, VLSI Architectures, Physical Design Automation, VLSI Subsystem Design, ASICs and FPGAs, VLSI Testing and Verification, MOS Device Modeling, Memory Design and Testing, Mixed Signal Circuit Design and High Speed VLSI Design. 7 Department of Chemical Engineering Process Calculations and Thermodynamics: Laws of conservation of mass and energy; degree of freedom analysis, first and second laws of thermodynamics and their applications, phase equilibria; chemical reaction equilibrium. Fluid Mechanics and Mechanical Operations. Fluid statistics, bernoulli equation, macroscopic friction factors, dimensional analysis, flow through pipeline systems, flow meters pumps and compressors, packed and fluidized beds, size reduction and size separation. Heat Transfer: Conduction, convection, radiation, heat exchangers, evaporators. Mass Transfer: Ficks’ law, molecular diffusion in fluids, distillation, absorption and drying. Chemical Reaction Engineering: Kinetics of homogeneous reactions, interpretation of kinetic data, residence time, kinetics of heterogeneous catalytic reactions; diffusion effects in catalysis. Instrumentation and Process Control: Dynamics of simple systems, controller modes (P, PI and PID). Plant Design and Economics: Design and sizing of chemical engineering equipment, principles of process economics and cost estimation. Chemical Technology: Inorganic chemical industries; sulfuric acid, NaOH, fertilizers (Ammonia, Urea, SSP and TSP); organic chemical industries (Pulp and Paper, Sugar, Oil and Fats); petroleum refining and petrochemicals: polymerization industries; polypropylene, PVC and polyester synthetic fibers., Process Modeling and Simulation: Equation of continuity, momentum, energy, CSTR, exchangers, distillation. Mathematics: Algebra, calculus, and differential equations: first order (linear and nonlinear). Numerical Methods: Numerical solutions of linear and non linear algebraic equations, integration by trapezoidal and Simpson’s rule, single and multi-step methods of differential equations Probability and Statistics: Mean, median, mode and standard deviation, random variables, Poisson, normal and binominal distributions. Chemistry: Kinetics, spectroscopy, colligative properties, organic synthesis Biotechnology: Biochemical kinetics, bioreactors, transport phenomena in bioprocess systems Environment: The physical environment: land, water, air and climate environments, sustainability, analysis of natural resource base management practices, analysis of agricultural and industrial systems Energy Technology: Primary and secondary fuels, solar, wind, biomass, geothermal and nuclear energy. 8 Department of Electrical and Instrumentation Engineering a) Electrical Engineering Introduction to circuits and networks analysis of circuits; Fundamentals of AC: single phase, 3−phase; Network Analysis and synthesis; Basic electronics (Diode, Transistor, FETs, Op-Amp); Elements of power systems: Transmission line, modeling and performance, Load flow analysis , fault analysis, ALFC and AVR control, Switchgear and protection, HVDC transmission; Electrical machines: construction and working of DC machines, induction and
synchronous machines, fractional horse power machine, Generalized theory of electrical machines; Control Engineering : Open loop and closed loop control, signal flow graphs, stability, controllers, state space representation; Power Electronics : Power electronic devices and their applications; AC and DC drives; Fundamentals of instrumentation; Fundamentals of computer programming; Intelligent techniques. b) Electronic Instrumentation and Control Engineering: Fundamentals of Measurement and Instrumentation systems, Static and dynamic characteristics of Measurement Systems, Measurement of various physical quantities; Introduction to circuits and networks analysis; Digital Electronics: Boolean functions and their minimization, Combinational and Sequential circuits, IC families, A/D , D/A; Microprocessors and Microcontrollers; Analog Electronics: Characteristics of diode, BJT, JFET and MOSFET, OpAmp and its applications; Digital signal processing techniques; Analytical, Optical and Biomedical Instrumentation: Spectrometry, X-ray and nuclear radiation measurements, Laser, fiber optics, Elements of Biomedical instruments, EEG, ECG and EMG. Clinical measurements; Control Engineering : Feedback principles, Transient Response, Steadystate-errors, Stability, Routh and Nyquist criteria, Bode plot, Root locus, State space representation, PID controllers; Intelligent Algorithms: Fuzzy Systems, Artificial Neural Networks, Genetic Algorithm, Hybrid Systems; Power Electronics and Drives: Power electronic devices and their applications; AC and DC drives. 9 Department of Civil Engineering. Specialization: STRUCTURES Mechanics: Bending moments and shear forces in statically determinate beams -- simple stress and strain: relationship -- stress and strain in two dimensions, principal stresses, stress transformation, Mohr’s circle -- simple bending theory -- flexural shear stress -- thin-walled pressure vessels -- uniform torsion. Structural Analysis: Analysis of statically determinate trusses, arches and frames -- displacements in statically determinate structures and analysis of statically indeterminate structures by force/energy methods -- analysis by displacement methods (slope-deflection and moment-distribution methods) -- influence lines for determinate and indeterminate structures -- basic concepts of matrix methods of structural analysis. Concrete Structures: Basic working stress and limit states design concepts -- analysis of ultimate load capacity and design of members subject to flexure, shear, compression and torsion (beams, columns isolated footings) -- basic elements of prestressed concrete: analysis of beam sections at transfer and service loads. Steel Structures: Analysis and design of tension and compression members, beams and beam-columns, column bases -- connections - simple and eccentric, beam-column connections, plate girders and trusses -- plastic analysis of beams and frames. Specialization: GEOTECHNICAL ENGINEERING Soil Mechanics: Origin of soils -- soil classification -- three-phase system, fundamental definitions, relationship and inter-relationships -- permeability and seepage -- effective stress principle: consolidation, compaction -- shear strength. Foundation Engineering: Sub-surface investigation - scope, drilling bore holes, sampling, penetrometer tests, plate load test -- earth pressure theories, effect of water table, layered soils -- stability of slopes - infinite slopes, finite slopes -- foundation types - foundation design requirements -- shallow foundations -- bearing capacity, effect of shape, water table and other factors, stress distribution, settlement analysis in sands and clays -- deep foundations - pile types, dynamic and static formulae, load capacity of piles in sands and clays. Specialization: HIGHWAY AND TRANSPORTATION ENGINEERING Highway planning -- Geometric design of Highways -- Testing and specifications of paving materials -- Design of flexible and rigid pavements. Pavement Evaluation and Pavement Management Systems. Specialization: WATER RESOURCES AND HYDRAULICS Fluid Mechanics and Hydraulics: Hydrostatics applications of Bernoulli equation, Laminar and turbulent flow in pipes, pipe networks -- concept of boundary layer and its growth -- uniform flow, critical flow and gradually varied flow in channels, specific energy concept, hydraulic jump -- forces on immersed bodies -- flow measurement in channels -- tanks and pipes -- dimensional analysis and hydraulic modeling. Applications of Momentum equation, Potential flow, Kinematics of flow -- Velocity triangles and specific speed of pumps and turbines. Hydrology: Hydrologic cycle -- Rainfall -- evaporation infiltration, unit hydrographs, flood estimation, reservoir design, reservoir and channel routing, well hydraulics.
Irrigation: Duty, delta, Estimation of evapo-transpiration -- crop water requirements -- design of lined and unlined canals -- waterways -- head works, Gravity dams, Ogee spillways, Earth dams. Designs of weirs on permeable foundation, Irrigation methods 10 Department of Mechanical Engineering Section – A Solid Mechanics, Machine Design, Theory of Machines, Mechanical Vibrations, Machine Drawing, CAD CAM and Robotics, Computer Programming, Finite Element Method Section – B Thermodynamics, Steam Engineering, IC Engines and Gas Turbines, Turbo Machines, Fluid Mechanics and Machinery, Refrigeration and Air Conditioning, Heat and Mass Transfer, Power Plant Engineering, Nonconventional Source of Energy, Computational Fluid Dynamics Section – C Industrial Engineering, Plant layout, Production Management, Work Study, Inspection and Quality Control, Manufacturing Processes/Technologies, Machining Science, Measurement Techniques, Industrial Automation, Material Science and Metallurgy. 11 Department of Biotechnology and Environmental Sciences Biotechnology Biochemistry: Atoms, Molecules and chemical bonds; Structure and function of biomolecules, biophysical chemistry Bioenergetics, biological energy transducers, oxidative phosphorylation ; Enzymes and enzyme kinetics; proteins conformations, structures and functions; conformation of nucleic acids, metabolism of carbohydrates, fats, amino acids, nucleotides and vitamins. Cell structure and Organization: Membrane structure and function; organization and function of intracellular organelles; genetic information; Cell division and cell cycle; Microbial physiology. Fundamental Life processes: DNA replication, repair and recombination; RNA synthesis and processing; Protein synthesis and processing; Control of gene expression at transcription and translation level Cellular Communications: Host parasite interaction; Cell signaling; Cancer and Immune responses (innate and adaptive) Developmental Biology of Animal and Plant systems: Concepts of development, gametogenesis; fertilization; morphogenesis and organogenesis; Programmed Cell death and aeging. Plant and Animal Physiology: Photosynthesis; Respiration and photorespiration; Nitrogen metabolism; Plant hormones; Solute transport and photoassimilate translocation; Secondary metabolites; Stress physiology. Blood and circulation; Cardiovascular System, Respiratory system ; Nervous system; Sense organs; Excretory system; Thermoregulation; Stress and adaptation; Digestive system: Endocrinology and reproduction Heredity and Genetics: Mendelian principles; Concept of gene; Extensions of Mendelian principles; Gene mapping methods; Extra chromosomal inheritance; Microbial genetics; Quantitative genetics; Mutation: Structural and numerical alterations of chromosomes; recombination Biodiversity: Principles and methods of taxonomy Levels of structural organization Outline classification of plants, animals and microorganisms; Organisms of health and agricultural importance Ecology and Molecular Evolution: the Environment; Habitat and niche; Population ecology; Species interactions; Community ecology; Ecological succession; Ecosystem geography; Applied ecology; Conservation biology; Molecular Evolution Applied Biology: Microbial fermentation products, vaccines and diagnostics; genomics; biodiversity applications; plant and animal breeding – marker assisted selection; Bioremediation; phytoremediation and biosensors Methods in biology: Molecular biology and recombinant DNA methods; Histochemical and immunotechniques; Statistical Methods: Biophysical methods; Radiolabeling techniques; Microscopic techniques; computational methods Environmental Sciences Interactions between humans and environment; The physical environment- land water, and climate; Resources and their management- Natural, Technological and Human; Concept of sustainability- Natural ecosystems and sustainability; Agricultural and Industrial systems from the angles of environment protection; Environmental
Chemistry- Analytical Techniques and instrumentation; Atmospheric Chemistry; Basic Microbiology- nature and extent of microbial world; growth and energetics, Microbiology of water and wastewater; Microbial Corrosion and biofouling; Quantity of Water- per capita demand, factor affecting the demand; Quality of water- physical, chemicals and biological characteristics, Treatment of water- Sedimentation, Coagulation; filtration; Chlorination; absorption; adsorption, and Miscellaneous methods; Sewage and sewerage systems; Primary and Secondary treatment of sewage- aerobic and anaerobic processes and their applications in the wastewater treatment. 12 L M THAPAR SCHOOL OF MANAGEMENT Research Aptitude • Research: Meaning, ethics &characteristics • Type of research • ď€ Methods of research Verbal Reasoning • Verbal Speed Test- Spelling and Grammar • Verbal Power Test- Critical Reasoning Reading Comprehension • A passage to be set with questions to be answered with emphasis on major functional areas of management Logical Reasoning • Arguments, deductive & inductive research • Logical & Venn diagram • Inferences • Analogies Data Interpretation Interpretation of data • Mapping analysis of data • Analysis & Tools for data analysis • Quantitative &qualitative research
Model questions 1. The decreasing order of the first ionization energy of the following elements is (A) He > H > Be > B (B) Be > B > H > He (C) H > He > Be > B (D) B > Be > He > H 2. The solubility products (Ksp) for three salts MX, MY2 −8 and 27×10 , respectively. The solubilities of these salts follow the order (A) MX > MY2 > MZ3 (B) MZ3 > MY2 > MX (C) MZ3 > MX > MY2 (D) MY2 > MX > MZ3 and MZ3 are 1×10 ,
−8
4×10
−9
3. The rate of nitration of following aromatic compounds decreases in the order (i) benzene (ii) pyridine (iii) thiophene (iv) toluene (A) (iv) > (i) > (iii) > (ii) (B) (iii) > (iv) > (i) > (ii) (C) (iii) > (ii) > (i) > (iv) (D) (ii) > (i) > (iv) > (iii)
