Pattern & Syllabus

Syllabus for VITMEE 2022

Candidates have to study graduate level lessons in various academic subjects related to maths, physics, chemistry, engineering while preparing for the exam. These lessons are taught regularly at graduate level in most of the recognised educational institutions located across India. 

The study materials in connection with the above mentioned subjects can be sourced from well-known book stores located across the country. They can be obtained from online book stores and many websites also provide them on their platforms at free of cost or at low cost. Candidates can consider these sources for procuring the study material. The syllabus is provided below for the sake of the candidates:

Mathematics

• Linear Algebra: Finite dimensional vector spaces; Linear transformations and theirmatrix representations, rank; systems of linear equations, eigen values and eigen vectors, minimal polynomial, Cayley-Hamilton Theroem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram- Schmidt orthonormalization process, self-adjoint operators.
• Complex Analysis: Analytic functions, conformal mappings, bi linear transformations;complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle Taylor and Laurent’s series; residue theorem and applications for evaluating real integrals.
• Real Analysis: Sequences and series of functions, uniform convergence, power series,Fourier series, functions of several variables, maxima, minima Riemann integration, multiple integrals, line, surface and volume integrals, theorems of Green’s, Stokes and Gauss Metric spaces, completeness, Weierstrass approximation theorem, compactness; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem.
• Ordinary Differential Equations: First order ordinary differential equations, existence anduniqueness theorems, systems of linear first order ordinary differential equations, linear ordinary differential equations of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients; method of Laplace transforms for solving ordinary differential equations, series solutions; Legendre and Bessel functions and their orthogonality.
• Algebra: Normal subgroups and homomorphism theorems, automorphisms; Group actions,Sylow’s theorems and their applications; Euclidean domains, Principle ideal domains and unique factorization domains. Prime ideals and maximal ideals in commutative rings; Fields, finite fields.
• Functional Analysis: Banach spaces, Hahn-Banach extension theorem, open mapping andclosed graph theorems, principle of uniform boundedness; Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.
• Numerical Analysis: Numerical solution of algebraic and transcendental equations:bisection, secant method, Newton-Raphson method, fixed point iteration; interpolation: error of polynomial interpolation, Lagrange, Newton interpolations Numerical differentiation; numerical integration: Trapezoidal and Simpson rules, Gauss Legendre quadrature, method of undetermined parameters; least square polynomial approximation; numerical solution of systems of linear equations: direct methods (Gauss elimination, LU decomposition); iterative methods (Jacobi and Gauss-Seidel); matrix eigenvalue problems: power method. N umerical solution of ordinary differential equations: initial value problems: Taylor series methods, Euler’s method, Runge-Kutta methods.
• Partial Differential Equations: Linear and quasilinear first order partial differentialequations, method of characteristics; second order linear equations in two variables and their classification; Cauchy, Dirichlet and Neumann problems; solutions of Laplace, wave and diffusion equations in two variables; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.
• Mechanics: Virtual work, Lagrange’s equations for holonomic systems, Hamiltonianequations.
• Topology: Basic concepts of topology, product topology, connectedness, compactness, countabi lity  and separation axioms, Urysohn’s Lemma.
• Probability and  Statistics:  Probability  s pace, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem Sampling distributions, UMVU estimators, maximum likelihood estimators, Testing of hypotheses, standard parametric tests.
• Linear programming: Linear programming problem and its formulation, convex sets and theirproperties, graphical method, basic feasible solution, simplex method, big-M and two phase methods; infeasible and unbounded LPP’s, alternate optima Dual problem and duality theorems, dual simplex method and its application in post optimality analysis; Balanced and unbalanced transportation problems, Hungarian method for solving assignment problems.
• Calculus of Variation and Integral Equations: Variation problems with fixed boundaries;sufficient conditions for extremum, linear integral equations of Fredholm and Volterra type, their iterative solutions.

Chemistry

Chemistry Syllabus

Atomic Structure

• Planck’s quantum theory - wave-particle duality - Heisenberg’s principle 
• Schrodinger wave equation – particle in a box and hydrogen atom - VB and MO theories

Spectroscopy

• Rotational and vibrational spectra - harmonic anharmonic oscillator and Rigid Rotor - selection rules - fundamentals, overtones and combinational bands - calculation of force constants (diatomic molecules)
• Group frequencies - electronic spectroscopy - potential energy diagram – term symbols - selection rules – L-S and J-J coupling
• Frank Condon principle - oscillator’s strength - effect of solvents on spectra

Thermodynamics

Laws of thermodynamics – First law - second law - third law (terms and their relations)

Chemical kinetics and equilibrium

The rate is constant of chemical reactions, temperature dependence, collision and transition state theories - consecutive and parallel reactions - chemical equilibrium and the response of chemical equilibrium to temperature and pressure.

d and f block elements

• General characteristics of d and f block elements
• Coordination chemistry; structure and isomerism; stability; theories of metal-ligand bonding (CFT and LFT); mechanisms of substitution and electron transfer reactions of coordination complexes
• Electronic spectra and magnetic properties of transition metal complexes, lanthanides and actinides
• Metal carbonyls, metal-metal bonds and metal atom clusters, metallocenes; transition metal complexes with bonds to hydrogen, alkyls, alkenes and arenes; metal carbenes; use of organometallic compounds as catalysts in organic synthesis
• Bioinorganic chemistry of Na, K, Mg, Ca, Fe, Co, Zn, Cu and Mo

Solid State

• Crystal systems and lattices, Miller planes, crystal packing, crystal defects
• Bragg’s law, ionic crystals, band theory, metals and semiconductors, different structures of AX, AX2, AX3 compounds, spinels

Instrumental methods of analysis

• Atomic absorption and emission spectroscopy including ICP-AES, UV-Visible spectrophotometry, NMR, Mass, Mossbauer spectroscopy (Fe and Sn)
• ESR spectroscopy, chromatography including GC and HPLC, electroanalytical methods (coulometry, cyclic voltammetry, polarography - amperometry, and ion-selective electrodes)
• Structural determination of organic and inorganic compounds using UV-Visible, IR, NMR and mass spectroscopy

Stereochemistry

• Chirality of organic molecules with or without chiral centres
• Specification of configuration in compounds having one or more stereogenic centres
• Enantiotopic and diastereotopic atoms, groups and faces
• Stereospecific synthesis
• Conformational analysis of acyclic and cyclic compounds
• Geometrical isomerism
• Configurational and conformational effects on reactivity and selectivity/specificity

Reaction Mechanism

• Electrophilic and Nucleophilic substitution reactions in aliphatic and aromatic compounds and their mechanisms
• Addition and Elimination reactions and their mechanisms
• Reaction intermediates carbocations, carbanions, carbenes, nitrenes and free radicals

Organic synthesis

• Synthesis, reactions, mechanisms and selectivity involving the following - alkenes, alkynes, arenes, alcohols, phenols, aldehydes, ketones, carboxylic acids and their derivatives, halides, nitro compounds and amines.
• Use of compounds of Mg, Li, Cu, B and Si in organic synthesis.
• Concepts in multistep synthesis - retrosynthetic analysis, disconnections, synthons, synthetic equivalents, umpolung in chemistry, selectivity, protection and deprotection of functional groups.

Heterocyclic compounds

Structure and reactions of furan, pyrrole, thiophene, pyridine, indole and their derivatives.

Biomolecules

Structure, properties and reactions of mono- and disaccharides, physicochemical properties of amino acids, chemical synthesis of peptides, structural features of proteins, nucleic acids, steroids, terpenoids, carotenoids, and alkaloids.

Life Sciences

• Biophysics : Levels of structures in Biological macromolecules. Basic strategies in biophysics. Forces that determine protein and nucleic acid structure, Prediction of proteins structure nucleic acids, Properties of lipid bilayers, Biochemical Kinetics studies, unimolecular reactions, methods of determining macromolecular structures inclusive of the spectroscopic techniques like UV-vis absorption, IR absorption, circular dichroism fluoresence NMR and X-ray and neutron diffraction techniques.
• Biochemistry : Structure and properties, Amino acids, peptides, proteins and conjugated proteins, protein hydration, coagulation, denaturation - gelation, protein-protein interactions, cytosolic and membrane properties, purines, pyrimidines, nucleosides, nucleotides, polynucleotides, Ribonucleic acids and deoxyribonucleic acids, TCA cycle, glycolysis, pentose phosphate pathway, Embden Meyerhof pathway, urea cycle, metabolic regulation, respiratory chain, TP cycle, energy rich compounds, integrated metabolism, Carbohydrates - linear and branched carbohydrates, N containing carbohydrates, cell wall carbohydrates, metabolism of carbohydrates, Fats and oils-structure and properties of saturated and unsaturated fatty acids, glycerolipids, phospholipids, sphingolipids, glycolipids, steroids, Vitamins and minerals-types, structure and functional properties of vitamins, utility of essential minerals sources and trace elements.
• Biotechnology : Importance and economics of downstream processing in biotechnology process-problems and requirements of bioproduct purification, process design criteria, primary separation and recovery process, membrane based separations, precipitation methods, different types of purification and chromatographic techniques. Types of reactors - ideal reactors, integral method of analysis for reactions, simultaneous, consecutive and combined reactions, models for non-ideal flow. Industrial biotechnology - isolation, preservation and improvement of industrial microbes for overproduction of primary and secondary metabolites, economics of modern industrial processes, fermentation processes and biological waste treatment processes. Introduction to bioinformatics - sequence databases, search and their use, sequence alignment, ultrasonic trees, parsimony, phylogenetic alignment, connection between multiple alignment and tree construction, DNA mapping and sequencing, sequence assembly and gene prediction, molecular predictions with DNA strings.
• Cell Structure and Function of the Organelles : Eukaryotic and Prokaryotic cells, cell division, mitosis & meiosis cell cycle and molecules that control cell cycle, endocytosis and Exocytosis. Ultrastructure of cellular organelles, viz. Mitochondria, ER, Golgi, Chloroplast, plasma membrane, centriole, nuclear and membrane bound receptors, Signal Transduction, Signal Amplification Techniques of propagation of prokaryotic and Eukayotic cells, Autocrine, Paracrine and Endocrine models of action, Cell line, generation of cell lines.
• Molecular Biology : Structure of DNA and histone molecules, Replication of eukaryotic chromosomes, nucleoid the complex replication apparatus, process of transcription and, Structure of tRNA, mRNA, rRNA, Deciphering of the genetic code, Translation, Mutation. General principles of cloning.
• Recombinant DNA : Genetic elements that control gene expression, method of creating recombinant DNA molecules creating transgenic animals, plants microbes, safety guidelines of creating recombinant DNA research, restriction enzymes and mapping of DNA, plasmid and phage and other vectors. Construction of genomic and cDNA libraries, methods of nucleic acid. Patents and methods of application of patents, legal implications bioremediation. Ecosystems, energy flow, ecological succession , pollution.
• Conventional and Non-conventional sources of energy. Bio-geo chemical cycles. Biodiversity and wild life conservation. Social issues and the environment.
• Genetics : Classical genetics, Mendel’s genetics, crossing over, linkage, Chromosome maps, chromosomal theory of heredity, cytoplasmic inheritance, Sex determination, sex linked inheritance, microbial genetics, population genetics, polyploidy, pedigree analysis, eugenics, mutation. 
• Microbiology : Basic concepts of Microbiology, classification, morphology, anatomy, physiology of bacteria, viruses, fungi, parasite. Microbes of various plant and animal diseases. Indus trial microbiology, Microbial biotechnology, Mircrobial diversity and ecology.
• Immunology : Basic concepts of immunology, types of immunity, biotechnological applications; organs of immune, response Innate and adaptive immunity, clonal selection theory, hypersensitivity, hybridoma technology, vaccine development, epitope mapping and immunomics, immunological tolerance and transplantation biotechnology.
• Plant Sciences: Taxonomy and systematic botany, Plant structure and development, morphology and anato my, embryogenesis of mono and dicots. Phytohormones, respiration, nutrition, transpiration. Photosynthesis, C3 and C4, & CAM plants, photoperiodism, concepts of ecosystems and energy flow in biosphere.

Point to remember

Students have also to study the relevant lessons of their subject taught regularly at graduate level. Example: candidate who wishes to study MTech Mechanical Engineering can study lessons related to BTech Mechanical Engineering. These lessons have to studied along with the above mentioned subjects which are general in nature.