# VMRF EEE Syllabus

Engineering Entrance Exam » Vinayaka Mission »

## VMRF EEE 2021 Syllabus

Under Graduate Programs in Engineering and Technology ( BE / B Tech )

### VMRF EEE Physics Syllabus

Mensuration, units, dimensions and dimensional homogeneity

Kinematics : Motion in straight lines, speed, velocity, acceleration, relative velocity, motion in plane, projectile, circular motion.

Laws of Motion : Inertia, force and momentum, Newton’s laws, impulse, law of conservation of linear momentum, equilibrium under concurrent forces, static and kinetic friction, laws of friction, rolling friction, dynamics of uniform circular motion.

Work, energy and power : Kinetic and potential energies, power, energy of a spring, conservative forces, collision of elastic bodies.

Rotational motion and Gravitation : Moment of a force, angular momentum, its conservation, moment of iner tia, rigid body rotation, universal law of gravitation, acceleration due to gravity, Keplar’s Laws, escape velocity.

Properties of solids and liquids : Stress-strain relation, Hooke’s law, Young’s modulus, bulk modulus, rigidity modulus, fluid pressure, viscosity, surface tension, angle of contract, heat, temperature, thermal expansion, specific heat, conduction, convection and radiation, Newton’s law of cooling.

Thermodynamics and Kinetic theory of gases : Laws of thermodynamics, reversible/irreversible processes, Carnot engine, equation of state of perfect gas, kinetic energy and temperature, law of equipar tition of energy, means free path, Avagadro number. Periodic motion and waves, period, frequency, periodicity, SHM, oscillations of a spring, force constant, simple pendulum, free, forced and damped oscillations, resonance, longitudinal and transverse waves, superposition of waves, standing waves, harmonics, beats, Doppler effect in sound.

Electrostatics: Charge, Coulomb law, forces between charges, superposition principle : electric filed lines, dipole in uniform electric field. Electric flux, Gauss law, field due to charged infinitely long straight wire, plane sheet and spherical shell, electric potential dipole, equipotential surfaces, conductors and insulators, dielectrics, electric polarization, capacitors, parallel plate capacitor with/ without dielectric medium between the plates, energy in a capacitor.

Current electricity : Electric current, drift velocity, Ohm’s law, resistance, energy power, resistivity, series / parallel combinations of resistors, temperature and resistance, electric cell, internal resistance pd and emf of a cell, series/parallel combination of cell, Kirchhoff’s laws, Wheatstone bridge, Meter bridge and potentiometer.

Magnetic effects of current and magnetism : Current in circular loop, Biot-Savart law, Ampere law, infinitely long straight current carrying wire and solenoid, charge moving in uniform magnetic and electric fields. Forces on current carrying conductor in uniform magnetic field, between two parallel conductors, torque on a current loop in uniform magnetic field, moving coil galvanometer, conversion to ammeter and voltmeter, current loop as a magnetic diopole, Ear th’s magnetic field and magnetic elements, para-dia and ferro-magnetic materials, magnetic susceptibility and permeability, hysteresis, electromagnets and permanent magnet.

Electromagnetic induction, alternating current and electromagnetic waves; Faraday’s law, inducted emf and current Lenz law, eddy current, self and mutual inductance, alternating current, rms value of alternating current/voltage, reactance, alternating currents rms values of alternating current/ voltage, reactance and impedance, LCR series circuit, resonance, power in AC circuit, AC generator and transformer, electromagnetic waves and their characteristics, electromagnetic spectra, applications of electromagnetic waves.

Optics : Reflection and refraction of light at plane and spherical surface, total internal reflection, dispersion by prism, Lens formula, magnification and power, microscope, telescope.

Wave optics : Wave front, Huygens principle, reflection, refraction and interference, Young’s double slit experiment, microscopes, telescopes, polarization, Brewster’s law, plane polarized light and Polaroid’s.

Dual nature of matter and radiation : photoelectric effect, observations of Hertz and Lenard, particle, de Brogile relation.

Atomic physics : Scattering of alpha particle, Rutherford’s and Bhor’s models of atom, hydrogen spectrum, nucleous atomic masses, isotopes, isobars isotones, radioactivity: alpha, beta, gamma particles, radioactive decay, mass-energy relation, mass defect , binding energy, nuclear fission and fusion.

Electronic and Communication devices: Semiconductors, semiconductor diode, I-V characteristics in forward and reverse bias , diode as rectified, LED, photodiode, solar cell, Zener diode. Junction transistor, transistor as an amplifier. Oscillator and switch, logic gates. Propagation of electromagnetic waves, need for modulation, amplitude and frequency modulation, bandwidth of signals and of transmission medium.

### VMRF EEE Chemistry Syllabus

Physical, Inorganic and Organic Chemistry

Physical Chemistry

Basic concepts : Laws of chemical combination, atomic and molecular masses, mole, molar mass, percentage composition, empirical and molecular formulae, chemical equations.

Matter and states : Solid, liquid and gaseous states of matter.

Gas: Boyle’s Law, Charle’s law, Graham’s law of diffusion, Avagadro’s law, Dalton’s law of par tial pressure, Ideal gas equation, kinetic theory of gases, average, rms and most probable velocities real gases, Vander waals equation, liquefaction of gases, critical constants

Liquid : Vapour pressure, viscosity and surface tension effect of temperature Solid: Molecular, ionic, covalent and metallic solids, amorphous and crystalline solids, Bragg’s Law, Lattices, packing are solids, voids, electric magnetic and dielectric properties.

Atom : Electron, proton and neutron, models of Thomson and Rutherford, electromagnetic radiation, photoelectric effects, hydrogen atom, Bhor model, dual nature of matter, Hessenberg uncertainty, principle, elementary ideas of quantum mechanics, atomic orbitals as one electron wave functions, quantam numbers, s,p and d orbitals, spin quantum number, Pauli’s exclusion principal, Hunde’s rule, electronic configuration of elements.

Chemical bonding and moleculer structure : Kossel-Lewis approach to chemical bond formation. Lognic Bonding, lattice enthalpy. Covalent bonding, electro-negativity, Fajan’s rule, dipole moment, VSEPR, valence Bond theory, hybridization involving s,p and d orbitals, resonance, molecular orbital theory, LCAO, types of orbitals, sigma and pi -bonds, homonuclear diatomic molecules, bond order, bond length and bond energy.

Chemical Thermodynamics : Fundamentals, extensive and intensive properties, state functions, process types, first law of thermodynamics: work heat enthalpy, heat capacity, Hess law: Second Law of thermodynamics Solutions: Molality, molality, mole fraction, vapour pressure and Rault’s law, ideal and non ideal solutions, colligative properties of dilute solutions,determination of molecular mass ,ven Hoff factor

Equilibria : Physical process equilibria, Henry’s law, Chemical process equilibiria, laws, kp and kc, DG and DGO, equilibrium concentration, pressure, temperature, effect of catalyst, LE Chatelier principle. Lonic equilibrium weak and strong electrolytes ionization ,concepts of acids and bases, ionization of water, PH scale, common ion effect, hydrolysis of salts, solubility products, buffer solutions.

Electrochemistry : Electrolytic and metallic conduction, conductance in electrolytic solutions, specific and molar conductivities, Kohlrausch law, Electrochemical cells, Galvanic cells, Nerst equation, cell potential and Gibbs energy changes

Chemical kinetics : Reaction rate, elementary and complex reactions, order and molecularity, rate constant, zero and first order reaction ,Arrhenius theory, activation energy

Surface Chemistry : Adsorption of gases on solids, Freundlic and Langmuir adsorption solid catalyst, enzyme catalysts, Colloidal State – colloids and suspensions, classifications of colloids, Tyndall effect, brownian movement, electrophoresis, diyalysis, coagulation and flocculation, emulsions

Inorganic chemistry Classification of elements and periodicity, modern periodic law, periodic table, s p d and f block elements, periodic trends in properties of elements.

Isolation of metals : Occurrence of elements in nature, extraction of metals, concentration reduction and refining of Al, Cu, Zn and Fe.

Hydrogen : Position in periodic table, isotopes, preparation properties and uses, water and heavy water, hydrogen peroxide, ionic, covalent and interstitial classification of hydrides.

s- Block elements : Group 1 and 2 elements, electronic configuration, general trends in physical and chemical properties of sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogen carbonate.

p- Block elements : Group 13 to 18 elements, group wise study, d- and f-Block elements: transition elements, inner transition, lanthanoids and actinoids

Coordination Compounts : Werner theory , ligands, coordination number ,dent city chelation, isomerism, crystal field theory, color and magnetic properties.

Environmental chemistry : Environmental and atmospheric pollution, troposphere, particulate and soil pollution, control strategies.

Organic Chemistry

Organic component : Purification, qualitative analysis detection of nitrogen, sulphur, phosphorus and halogens, qualitative analysis – carbon, hydrogen, nitrogen, halogens, sulphur, phosphorous.

Fundamental of organic chemistry : Tetravalency of carbon, simple molecules, hybridization, classification of organic compounds homologous series isomerism. Covalent bond fission, electronic displacement in covalent bond, common types of organi reactions.

Hydrocarbons : Classification, isomerism, IUPAC nomenclature, preparation, properties and reaction. Alkanes, alkynes, aromatic hydrocarbons.

Organic compounds with halogens : Preparation, Properties, reactions and uses, amines diazonium salts.

Organic compounds with oxygen : Preparation, Properties,reactions and uses, alcohols, phenols, ether, aldehyde and ketones, carboxylic acids.

Polymers : Classifications, methods of polymerization, rubber, vulcanization, polythene nylon, bakelite and polyster.

Bimolecular : Carbohydrates – classification, monosacchorides, oligosaccharides, polysaccharides, Proteins – aminoacids, peptide bond, polypeptides primary, secondary, tertiary and quartermary structure of proteins, denaturation, enzymes Vitamins- classification and functions.
Nucleic acids – DNA and RNA biological function

Everyday Chemistry : Chemicals in Foods, cleansing agents and medicines.

### VMRF EEE Biology Syllabus

Living World and Diversity of Life : Biology and its meaning, what is living Taxonomic categories, Systematic and Binomial System of nomenclature. Classification of living organism (Two Kingdom and five Kingdom system), major groups of Kingdom and salient features , Viruses, Lichens, Plant Kingdom-Salient features of major groups from Algae to Angiosperms Animal Kingdom- Salient features of Nonchordates up to phylum and Chordates upto class level.

Cell , Structure and Function : Cell, wall, cell membrane, Endomembrane system, Mitochondria, plastids, Ribosomes, Cystkeleton Cilia, and Flagella, Centriole, Nucleus, Microbodies, Structural differences between prokaryotic, and eukaryoticm and between plant and animal cell. Cell cycle, Mitosis, Meiosis, Lipids Bio-molecules – Structure and function of Carbohydrates, proteins lipids and Nucleic acids. Enzymes – chemical nature, Types- properties and mechanism action.

Genetic and Evolution : Mendelian inheritance, Chromosome theory, Gene interaction, Incomplete dominance, Co-dominance, Complementary genes, multiple alleles, linkage and Crossing over, inheritance patterns of hemophilia and blood groups in human.

Structure and functions of Plant: Morphology of a flowering plant, Tissues and tissue system, Anatomy and function of root, stem, leaf, inflorescence, flower fruit and seed, Types of fruit, Secondary growth, Absorption and movement of water and of nutrients, Translocation of food, transpiration and gaseous exchange, Stomatal movement.

Mineral nutrition – macro and micro-nutrient, deficiency disorders, Nitrogen fixation.

Photophosynthesis — Light reaction, cyclic and non-cyclic photophosphorylation, pathways of carbon dioxide fixation, Photophospiration, limiting factors. Respiration – anaerobic, fermentation, Aerobic, Glycol sis, TCA cycle, electron transport system, Energy relations.

Structure and function of animals : Tissue, elementary knowledge of morphology, anatomy and function of earthworm, cockroach and frog.

Human physiology – Digestic system -organs, digestion and absorption, respiratory system – organ, breathing an exchange and transport of gases, Body fluid and circulation- blood, lymph, double circulation, regulation of cardiac activity, hypertension, Coronary artery diseases.

Excretion-urine formation, regulation of kidney function

Locomotion and movement : skeletal system, joints, muscles, types of movement -control and co-ordination -central and peripheral nervous system, nervous, reflex action and sensory reception, role of types of endocrine glands, hormone action.

Reproduction and development plant : asexsual and sexual reproduction – development of male and female gametophytes.

Pollination, fertilization, Development of embryo, endosperm, seed and fruit, Growth phases, Types of growth regulators and their role in seed dormancy, germination and movement, Apical dominance, Senescence, Abscission, Photoperiodism, Vernalisation, types of movements.

Humans : Male and female reproductive systems, Menstrual cycle, Gamete production , Fertilization, Implantation, Embryo development, Pregnancy and parturition, Birth control and contraception

Ecology and Environment : Meaning of ecology, environment, Habitat and niche. Ecological levels of organization, Characteristics of Species, Population, Biotic Community and Ecosystem, Succession and climax.
Ecosystem – Biotic and obiotic components, Ecological pyramids, Food chain and Food web, Energy flow, Major types of ecosystems.

Ecological adaptations : Structural and physiological features in plants and animals of aquatic and desert habitats.

Biodiversity – Meaning types and conservation strategies.

Environmental issues : Air and Water pollution, Global warming and climate change, Ozone depletion, Noise pollution, Radioactive pollution, pollution control, Deforestation, Extinction of species.

Biology and Human Welfare : Animal husbandry – Livestock, Fisheries, Major animal diseases and control. Pathogens of major communicable diseases of humans caused by fungi, bacteria, viruses, protozoans and helminthes, and their control. Cancer and AIDS, drug / alcohol abuse, Basic concepts of immunology. Plant Breeding and Tissue Culture in crop improvement. Bio-fertilizers, Bio-spesticides, Bio-herbicides.

Microorganisms as pathogens of plant diseases rust and smut of wheat, bacterial leaf blight of rice, late blight of potato, bean mosaic, and root-knot of vegetables. Bioenergy – Hydrocarbon – rich plants as substitute of fossil fuels.

Biotechnology and Applications : Microbes and Microbial technology in food processing, industrial production, sewage treatm ent and energy generation. Steps in recombinant DNA technology – restriction enzymes. DNA insertion, regeneration of recombinants

Applications of R – DNA techonolgy : Production of Insulin, Vaccines and Growth hormones, Organ transplant, Gene therapy – Production of expensive enzymes, strain improvement to scale up bioprocesses. GM crops including Bt crops.

### VMRF EEE Mathematics Syllabus

Complex numbers : Argand diagram, algebra of complex numbers, De Moivre’s theorem and applications, complex roots of unity.

Matrices and determinants : Types of matrices, matrix algebra, determinants, properties of determinations, ad-joint and inverse matrices, inverse by ad-joint and by elementary transformation, cayleigh – Hamilton theorem, consistency and solution of linear simultaneous equations.

Permutations and combinations : Relations, simple application. Binomial theorem : positive integral index, general term, middle term, binomial coefficients.

Sequences and series : Arithmetic , geometric and harmonic progressions, sums of first, second and third powers of natural numbers, arithmetic geometric series
Limit, continuity, and differentiability : Polynomials, rational, circular, logarithmic exponential and hyperbolic functions, inverse functions, graphs, limits, continuity and differentiability.
Differentiation of standard functions, applications on derivatives as rate measurer, increasing / decreasing functions, maxima / minima / inflection, tangents, normals, angles of intersection. Partial Differentiation, homogeneous function and Euler’s result.

Integral calculus : Standard integrals, integration by parts, substitution, definite integrals, properties.
Area and volume of revolution by integration.

Differential equations : Ordinary differential equations, order and degree, formation. Solution : separation of variables, homogeneous and linear equations, integrating factors, Bernoulli type linear equations, integrating factors, Bernoulli type linear equations of higher order.

Vectors : Vector algebra, scalar and vector products, double and triple products, geometrical and physical applications

Analytical plane geometry : Rectangular Cartesian Coordinates, points, distance point of division.

Straight line : Slope, angle between lines, Perpendicular and parallel lines, centroid, orthocenter and circumcentre of triangles.

Circles : Standard forms, circle with given extremities of a diameter, tangent line to a circle.

Conics : Parabola, ellipse and hyperbola, rectangular hyperbola, standard, forms, properties, tangent line.

Analytical solid geometry : Point distance, section, direction cosines and ratios, angle between lines, skew lines, shortest distance between lines, Equation of lines, skew lines, shortest distance between lines, equation of line and plane, intersection of line and plane, coplanar lines.

Sphere : Standard equation, section of a sphere by a plane, intersection of spheres.

Statistics and Probability : Measures of central tendency and dispersion: mean, median, mode, mean deviation, standard deviation, consistency, coefficient of variation, regression, correlation. Events, probability, addition and multiplication theorems, Baye’s theorem, probability distribution, Bernoulli trials and Binomial distribution.

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