# BEEE Syllabus

Bharath Engineering Entrance Examination (BEEE) is conducted by Bharath University for admission to various B-Tech courses.

## BEEE Syllabus

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### Physics Syllabus

#### Unit 1 : Units and Measurement

Units for measurement, system of Units ; S.I., fundamental and derived Units, measurements -; errors in measurement -; significant figures, dimensions -; dimensional analysis - applications.

#### Unit 2 : Mechanics

Motion in one dimension - uniform and non - uniform motion - uniformly accelerated motion - scalar and vector quantities-Newton’s laws of motion - force and inertia -impulse and momentum- law of conservation of linear momentum -applications - motions in two dimension - projectile motion -uniform circular motion- friction- laws of friction applications - centripetal force - centre of mass - torque - angular momentum and its conservation - moment of inertia -theorems of moment of inertia - work- energy - potential energy and kinetic energy - power - collision - elastic and inelastic collisions.

#### Unit 3 : Gravitation, Mechanics of Solids and Fluids

The universal law of gravitation, acceleration due to gravity-variation of - with altitude, latitude and depth - gravitation potential - escape velocity and orbital velocity - geostationary satellites - Kepler's laws of planetary motion. Solids-elastic behaviour, stress- strain -Hooke's law -Modulli of elasticity -relation between them - surface tension - capillarity - applications - viscosity - Poiseuille's formula- Stokes law -applications -streamline and turbulent flow - Reynolds number - Bemoulli's theorem - applications.

#### Unit 4 : Oscillations and Wave Motion

Periodic motion- simple harmonic motion- equations of motion - oscillations of spring - simple pendulum -free, forced and damped oscillations - resonance - applications - wave motions - longitudinal and transverse waves - velocity of wave motion in different media - Newton's formula -Laplace's correction-super position of waves - progressive and standing waves- sonometer- air columns- Doppler effect and its applications.

#### Unit 5 : Heat and Thermodynamics

Kinetic theory of gases-postulates - pressure of a gas - specific heat capacity - relation between Cp and Cv - first law of thermodynamics themodynamical processes - isothermal adiabatic-reversible and irreversible process-second law of thermodynamics - Carnot's engine - Heat transfer - conduction - convection- radiation -thermal conductivity of solids - black body radiations -Kirchoffs law- Wien's displacement law Stefan's law - Newton's law of cooling

#### Unit 6 : Ray and Wave Optics and Magnetism

Wavefront – Huygens principle – wave nature of light – interference – young’s double slit expriment – diffraction and polarization – reflection and refraction of light – total internal reflection – velocity of light determination – deviation and dispersion of light by a prism – lens.

#### Unit 7 : Electricity and Magnetism

Magnetism : Earth's magnetic field and magnetic elements- magnetic field due to a magnetic dipole- torque on a magnetic dipole - magnetic properties of a material - dia, para and ferro magnetic materials - application. Biot savart law - force on a moving charge in an uniform magnetic field. Electrostatic - coulomb's inverse square law - dielectric constant - electric field - electric lines of force - electric dipole - electric potential - potential difference - electric flux - gauss theorem - electrostatic inclusion - capacitor capritor in parallel and series - drift. Velocity of electrons - ohm's law - electrical resistivity and conductivity - super conductivity - kirchoffs law - what's tone’s bridge - principle potentiometer - electric power - faraday's law -lenz law at electromagnetic inclusion - self inductances mutual inductance - flemming's right hand rule - methods of inducing emf - eddy current, transformer.

#### Unit 8 : Atomic Physics and Relativity

Relativity - Einstien's mass energy relation - variation of mass with velocity. Atomic structure - properties of cathode rays and positive rays - specific charge of an electron- atom model - Thomson atom model - Rutherford atom model - Bohr atom model - merits and demerits - quantum numbers - X - rays-production- properties & Bragg's law- Bragg's- X -ray Spectrometer - Photoelectric effect - laser - spontaneous and stimulated emission - laser action - characteristics of laser light - ruby laser - applications of laser

#### Unit 9 : Dual Nature of Matter and Nuclear Physics

Nuclear properties : radius, mass, binding energy, density, isotopes, mass defect- Bainbridge mass spectrometer -nuclear forces. Newton discovery, matter coaves ; wave nature of particles Debroglie wavelength - electron microscope - radioactivity α, β and γ decay - half life and mean life- artificial radio activity -; radio isotopes - radio carbon dating - radiation hazards-; nuclear fission -nuclear reactor- nuclear fusion - hydrogen bomb- cosmic rays - elementary particles.

#### Unit 10 : Electronics and Communication

Communication : Space communication - propagation of electromagnetic waves in atmosphere- sky and space wave propagation.

Electronics : Semiconductor-; doping - types - PN junction diode - biasing - amplifier- gain - feedback in amplifier's-logic gates - NOT, OR, AND, N OR, NAND -; Universal gates -; De Morgan's theorem.

### Chemistry Syllabus

#### Unit 1 : Some Basic Concepts in Chemistry

Matter and its nature, Dalton's atomic theory; concept of atom, molecule, element and compound; physical quantities and their measurements in chemistry, precision and accuracy, significant figures, S.I. Units, dimensional analysis; laws of chemical combination;atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae; chemical equations and stoichiometry.

#### Unit 2 : States of Matter

Classification of matter into solid, liquid and gaseous states. Solid State: Classification of solids : molecular, ionic, covalent and metallic solids, amorphous and crystalline solids ( elementary idea ); Bragg's Law and its applications; Unit cell and lattices, packing in solids ( fcc, bcc and hcp lattices ), voids, calculations involving Unit cell parameters, imperfection in solids; electrical, magnetic and dielectric properties. Liquid State : Properties of liquids - vapour pressure, viscosity and surface tension and effect of temperature on them ( qualitative treatment only ). Gaseous State : Measurable properties of gases; Gas laws - Boyle's law, Charle's law, Graham's law of diffusion, Avogadro's law, Dalton's law of partial pressure; concept of absolute scale of temperature; ideal gas equation, kinetic theory of gases ( only postulates ); concept of average, root mean square and most probable velocities; real gases, deviation from ideal behaviour, compressibility factor, Van der Waals equation, liquefaction of gases, critical constants.

#### Unit 3 : Chemical Families - Periodic Properties

Modem periodic law and present form of the periodic table, s - p block elements, periodic trends in properties of elements, atomic and ionic radii, ionization enthalpy, electron gain enthalpy, valence, oxidation states and chemical reactivity. Transition elements - d - block elements, inner transition elements ' f ' block elements. Ionization energy, lanthanides and actinides-general characteristics. Coordination Chemistry: Coordination compounds, nomenclature : terminology ' Wemer's coordination theory. Applications of coordination compounds.

#### Unit 4 : Atomic Structure

Discovery of sub- atomic particles ( electron, proton and neutron ); Thomson and Rutherford atomic models and their limitations; nature of electromagnetic radiation, photoelectric effect; spectrum of hydrogen atom, Bohr model of hydrogen atom - its postulates, derivation of the relations for energy of the electron and radii of the different orbits, limitations of Bohr's model; dual nature of matter, De-Broglie's relationship, ( Angular momentum and magnetic quantum numbers ) and their significance; shapes of s, p and d - orbitals, electron spin and spin quantum number; rules for filling electrons in orbitals - Aufbau principle, Pauli’s exclusion principle and Hund's rule, electronic configuration of elements, extra stability of half – filled and completely filled orbitals.

#### Unit 5 : Chemical Bonding and Molecular Structure

Covalent bonding : Concept of electronegativity, Fajan's rule, dipole moment; Valence Shell Electron Pair Repulsion ( VSEPR ) theory and shapes of simple molecules. Valence bond theory - Its important features, concept of hybridization involving s, p and d orbitals; resonance, types of molecular orbitals ( bonding, anti - bonding ), sigma and pi - bonds, molecular orbital electronic configurations of homonuclear diatomic molecules, concept of bond order, bond length and bond energy. Elementary idea of metallic bonding. Hydrogen bonding and its applications. Extractive metallurgy of sodium, lithium, properties of alkali metals, basic nature of oxides and hydroxides, compounds of alkaline earth metals, compounds of boron. Oxides, carbides, halides and sulphides of carbon group.

#### Unit 6 : Solutions

Different methods for expressing concentration of solution - Molality, molarity, mole fraction, percentage ( by volume and mass both ), vapour pressure of solutions and Raoult's law - ideal and non - ideal solutions, vapour pressure-composition plots for ideal and non - ideal solutions; colligative properties of dilute solutions - relative lowering of vapour pressure, depression of freezing point, elevation of boiling point and osmotic pressure; determination of molecular mass using colligative properties; abnormal value of molar mass, Vant Hoff factor and its signi_cance.

#### Unit 7 : Chemical Equilibrium

Meaning of equilibrium, concept of dynamic equilibrium. Equilibria involving physical processes; Solid-liquid, liquid-gas and solid-gas equilibria, Henry's law, Equilibria involving chemical processes : Law of chemical equilibrium, equilibrium constants ( Kp and Kc ) and their significance, Le Chatelier's principle. Ionic equilibrium : Weak and strong electrolytes, ionization of electrolytes, various concepts of acids and bases ( Arrhenius, Bronsted-Lowry and Lewis ) and their ionization, acid-base equilibria ( including multistage ionization ) and ionization constants, ionization of water, pH scale, common ion effect, hydrolysis of salts and pH of their solutions, solubility of sparingly soluble salts and solubility products, buffer solutions.

#### Unit 8 : Electrochemistry

Electrolytic and metallic conduction, conductance in electrolytic solutions, specific and molar conductivities and their variation with concentration : Kohlrausch's law and its applications. Electrochemical cells- Electrolytic and Galvanic cells, different types of electrodes, electrode potentials including standard electrode potential, half-cell and cell reactions, emf of a galvanic cell and its measurement; Nernst equation and its applications; dry cell and lead accumulator; fuel cells; corrosion and its prevention.

#### Unit 9 : Surface Chemistry, Chemical Kinetics and Catalysis

Adsorption - Physisorption and chemisorption and their characteristics, factors affecting adsorption of gases on solids - Freundlich and Langmuir adsorption isotherms, adsorption from solutions. Catalysis. Tyndall effect, Brownian movement, electrophoresis, dialysis, coagulation and flocculation; emulsions and their characteristics. Factors affecting rates of reactions - factors affecting rate of collisions encountered between the reactant molecules, effect of temperature on the reaction rate, concept of activation energy, catalyst. Rate law expression. Order of a reaction ( with suitable examples ). Units of rates and specific rate constants. Nuclear Chemistry : radioactivity: isotopes and isobars : Properties of a, p and y rays; Kinetics of radioactive decay ( decay series excluded ), carbon dating.-

#### Unit 10 : Some Basic Principles of Organic Chemistry

Tetravalency of carbon; shapes of simple molecules - hybridization ( s and p ); classification of organic compounds based on functional groups : -C=C-, -C_C- and those containing halogens, oxygen, nitrogen and sulphur; homologous series; isomerism - structural and stereoisomerism. Nomenclature ( Trivial and ILJPAC ) Covalent bond fussion - Homolytic and heterolytic : free radicals, carbocations and carbanions; stability of carbocations and free radicals, electrophiles and nucleophiles. Electronic displacement in a covalent bond - inductive effect, electromeric effect, resonance and hyperconjugation.

#### Unit 11 : Hydrocarbons

Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties and reactions. Alkenes - Geometrical isomerism; mechanism of electrophilic addition : addition of hydrogen, halogens, water, hydrogen halides ( Markownikoffs and peroxide effect ); ozonolysis, oxidation, and polymerization. Mechanism of electrophilic substitution : halogenation, nitration, Friedel - Craft's alkylation and acylation, directive influence of functional group in monosubstituted benzene.

#### Unit 12 : Organic Compounds Containing Oxygen

General methods of preparation, properties, reactions and uses. Alcohols : Distinction of primary, secondary and tertiary alcohols; mechanism of dehydration. Reactions of hydroxyl derivatives. Phenols: Acidic nature, electrophilic substitution reactions : halogenation, nitration and sulphonation, Reimer-Tiemann reaction. Addition to >C=0 group, relative reactivities of aldehydes and ketones. Ethers: Structure. Aldehyde and

Ketones: Nature of carbonyl group; Nucleophilic addition reactions ( addition of HCN, NH3 and its derivatives ), Grignard reagent; oxidation; reduction ( Wolff Kishner and Clemmensen) ; acidity of - hydrogen, aldol condensation, Cannizzaro reaction, Haloform reaction; Chemical tests to distinguish between aldehydes and Ketones. Carboxyl ic acids: Reactions, Acidic strength and factors affecting it; reactions of acid derivatives.

#### Unit 13 : Organic Compounds Containing Nitrogen

General methods of preparation, properties, reactions and uses. Amines : Nomenclature, classification, structure, basic character and identification of primary, secondary and tertiary amines and their basic character.

#### Unit 14 : Polymers

General introduction and classi_cation of polymers, general methods of polymerization-addition and condensation, copolymerization; natural and synthetic rubber and vulcanization; monomers and uses - polythene, nylon, polyester and bakelite.

#### Unit 15 : Chemistry in Everyday Life

Chemicals in medicines- Analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids. Cleansing agents- Soaps and detergents, cleansing action.

### Mathematics Syllabus

#### Unit 1 : Sets, Relations and Functions

Sets and their representations, union, intersection and complements o f sets and their algebraic properties.

#### Unit 2 : Complex Numbers

Complex numbers in the form a+ib and their representation in a plane. Argand diagram. Algebra of complex numbers, modulus and argument ( or amplitude ) of a complex number, square root of a complex number. Cube roots of Unity, triangle inequality.

#### Unit 3 : Matrices and Determinants

Determinants and matrices of order two and three, properties of determinants, evaluation of determinants. Addition and multiplication of matrices, adjoint and inverse of matrix.

#### Unit 4 : Applications of Matrices and Determinants

Computing the rank of a matrix – test of consistency and solution of simultaneous linear equations using determinants and matrices.

#### Unit 5 : Quadratic Equations

Quadratic equations in real and complex number system and their solutions. Relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots; symmetric functions of roots, equations reducible to quadratic equations.

#### Unit 6 : Permutations and Combinations

Fundamental principle of counting: permutation as an arrangement and combination as selection, meaning of P(n,r) and C(n,r). Simple applications.

#### Unit 7 : Mathematical Induction and its Applications

Stating and interpreting the principle of mathematical induction. Using it to prove formula and facts.

#### Unit 8 : Trigonometry

Trigonometrical identities and equations. Inverse trigonometric functions and their properties. Properties of triangles, including, incentre, circumcentre and orthocenter, solution of triangles.

#### Unit 9 : Sequences and Series

Arithmetic, geometric and harmonic progressions. Insertion of arithmetic, geometric and harmonic means between two given numbers. Relation between A.M., G.M. and H.M. arithmetic, geometric series, exponential and logarithmic series.

#### Unit 10 : Differential Calculus

Polynomials, rational, trigonometric, logarithmic and exponential functions. Inverse functions. Graphs of simple functions. Limits, continuity, differentiation of the sum, difference, product and quotient of two functions, differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions, derivatives of order up to two.

#### Unit 11 : Applications of Differential Calculus

Rate of change of quantities, monotonic- increasing and decreasing functions, maxima and minima of functions of one variable, tangents and normals, Rolle’s theorem and Lagrange’s theorem mean value theorem.

#### Unit 12 : Integral Calculus

Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Integral as limit of a sum. Properties of definite integrals. Evaluation of definite integrals; Determining areas of the regions bounded by simple curves.

#### Unit 13 : Differential Equations

Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables. Solution of homogeneous and linear differential equations and those of the type d2y/dx2= f(x).

#### Unit 14 : Straight Lines in Two Dimensions

Equation of family of lines passing through the point of intersection of two lines, homogeneous equation of second degree in x and y, angle between pair of lines through the origin, combined equation of the bisectors of the angles between a pair of lines, condition for the general second degree equation to represent a pair of lines, point of intersection and angle between two lines.

#### Unit 15 : Circles in Two Dimensions

Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle in the parametric form, length of the tangent, equation of the tangent, equation of a family of circles through the intersection of two circles, condition for two intersecting circles to be orthogonal.

#### Unit 16 : Conic Sections in Two Dimensions

Sections of cones, equations of conic sections ( parabola, ellipse and hyperbola ) in standard form, condition for y = mx+ c to be a tangent and point(s) of tangency.

#### Unit 17 : Vector Algebra

Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product. Application of vectors to plane geometry.

#### Unit 18 : Measures of Central Tendency and Dispersion

Calculation of mean, median and mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.

#### Unit 19 : Probability

Probability of an event, addition and multiplication theorems of probability and their applications; Conditional probability; Baye’s theorem, probability distribution of a random variate; binomial and Poisson distributions and their properties.

### Biology Syllabus

#### Unit 1 : Taxonomy of Angiosperm

Types of classifications-Artificial, Natural, Phylogenetic - Biosystematics – Binomial Nomenclature - Herbaria and their uses - Bentham and Hooker’s classification of plants - Families Malvaceae, Solanaceae - Euphorbiaceae, Musaceae and Economic Importance.

#### Unit 2 : Plant Anatomy

Tissues and Tissue System - anatomy of monocot and dicot roots – anatomy of Monocot and dicot stem and anatomy of dicot leaf.

#### Unit 3 : Cell Biology and Genetics

Chromosomes - Structure and types - genes recombination of chromosomes mutation - chromosomal aberration - DNA as genetic material - Structure of DNA -replication of DNA - Structure of RNA and its type.

#### Unit 4 : Biotechnology

Recombinant DNA Technology- Transgenic plants with beneficial traits - plant tissue culture and its application - Protoplasmic fusion

#### Unit 5 : Plant Physiology

Photosynthesis - Significance- site of photosynthesis - photochemical and biosynthetic phases - electron transport system - cyclic and non cyclic photophosphorylation - C3 and C4 pathway - photorespiration - factor affecting photosynthesis - fermentation - plant growth - growth regulators - phytohormones - auxin - gibberellins - cytokinins - ethylene.

#### Unit 6 : Biology in Human Welfare

Food production - breeding experiments - improved varieties and role of biofertilizer - crop diseases and their control - biopesticides-genetically modi ed food - sustained agriculture and medicinal plants including microbes.

### Zoology Syllabus

#### Unit 1 : Human Physiology

Nutrition - introduction - carbohydrates - proteins - lipids -vitamins mineral - water - Balanced diet - calorie value - ( ICBM standard ) obesity - Hyperglycemia - hypoglycemia - malnutrition. Digestion - enzymes and enzyme action - Bones and Joints ( Major types ) - Arthritis - Rickets and Osteomalacia - Gout.
Muscles - muscle action - muscle tone - Rigor Mortis - aerobic exercises ( body building ) myasthenia gravis.

Respiration - Process of pulmonary respiration - inspiration Expiration - Exchange of gases at alveolar level -Circulation - Functioning of heart origin and conduction of heart beat - Artificial pacemaker - coronary blood vessels and its significance - myocardial infarction - Angina pectoria - Atherosclerosis - heart attack -Resuscitation in heart attack ( First aid ) Blood components - functions - plasma - corpuscles - blood clotting - anticoagulants - Thrombosis - embolism - blood related diseases like polycythemia - Leukemia - Lymph fluid.

Physiological Coordination System :
Brain - functioning of different regions - memory - sleep - stroke - Alzheimer’s disease - meningitis - Thyroid - parathyroid hormones - insulin and glucagon - Hormones of adrenal cortex and medulla - Reproductive hormones - problems related to secretion, non secretion of hormones.

Receptor Organs :

Eye - Focussing mechanism and photo chemistry of retina - short sightedness - Nyctalopia - Eye infection - conjunctivitis - Glaucoma - Ear - Hearing mechanism - Hearing impairments and aids - Noise pollution and its importance - skin - melanin functions - Effect of solar radiation / UV Excretion :

Ureotelism - urea - Biosynthesis ( ornithine cycle) Nephron - ultrafiltration - tubular reabsorption and tubular secretion - Renal failure - Dialysis kidney stone formation kidney transplantation - Diabetes.

Reproductive System :

Brief account of spermatogenesis and oogenesis - menstrual cycle - in vitro fertilization - Birth control

#### Unit 2 : Microbiology

Introduction - History of medical microbiology - The influence of Pasteur, Koch and Lister - Virology - structure Genetics culture and diseases - AIDS and its control - Bacteriology - structure, Genetics and diseases - protozoan microbiology - Diseases oriented - pathogenecity of micro organism - anti microbial resistance chemotherapy. Single cell protein. Microbial culture technique and its applications - Strain Isolation and Improvement - Isolation of microbial products.

#### Unit 3 : Immunology

Innate immunity ( Non specic )- anatomical Barriers - Physiological barriers - phagocytic barriers Lymphoidal organs - Thymus - Bursa of fabricius - Peripheral Lymphoid organs - Lymph nodes - Transplantation immunology - Autoimmune disorders.

#### Unit 4 : Modern Genetics and Animal Biotechnology

Introduction - scope - Human Genetics Karyotyping Chromosome gene mapping - Recombinant DNA technology and segmenting - genetic diseases - Human genome project - cloning - Transgenic organisms - Genetically modified organism ( GMO ) - Gene therapy - Animal cell culture and its applications - Stem cell technology - Bioethics of genetic engineering in animals.

#### Unit 5 : Environmental Science

Human population and explosion - issue - Global Warming Crisis - Green house effect - Ozone layer depletion - waste management -Biodiversity conservation ( Biosphere reserve )

#### Unit 6 : Applied Biology

Livestock and management - Breeds - Farming method - poultry diseases-Economic value Pisciculture - sh farming-Edible shes of Tamil Nadu.

#### Unit 7 : Theories of Evolution

Lamarckism-Darwinisin - Modern concept of natural selection - species of concept - origin of species and isolating mechanism.