VTUEEE SYLLABUS 2025

VTUEEE Physics Syllabus 2025
S. NO.	UNITS
1.	Atomic Physics
2.	Heat and Thermodynamics
3.	Optics
4.	Mechanics
5.	Electricity
6.	Nuclear Physics
7.	Laser and Optic Fiber
8.	Electronic Devices
9.	Properties of Matter
10.	Magnetism

VTUEEE Exam Syllabus 2025

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VTUEEE Exam Syllabus 2025 Details of Physics:

VTUEEE Physics Syllabus (SECTION - A)

1. Atomic Physics

• Atomic structure
• discovery of the electron
• specific charge (Thomson’s method) and charge of the electron (Millikan’s oil drop method) alpha scattering
• Rutherford’s atom model
• Bohr’s model
• energy quantization
• energy and wave number expressions
• Hydrogen spectrum
• energy level diagrams
• sodium and mercury spectra
• excitation and ionization potentials
• Dual nature of radiation
• photoelectric effect
• Hertz and Lenard’s observations
• Einstein’s photoelectric equation
• particle nature of light
• matter-wave
• wave nature of particle de Broglie relation
• Davisson-Germer experiment.

2. Heat and Thermodynamics

• Zeroth law of thermodynamics
• Thermal equilibrium
• Heat, work, and internal energy
• Concept of temperature
• Reversible and Irreversible processes
• The first law of thermodynamics
• The second law of thermodynamics 
• Carnot engine and its efficiency
• Equation of state of a perfect gas
• applications to specific heat capacities of gases
• law of equipartition of energy
• RMS speed of gas molecules
• Kinetic theory of gases
• Equation of state of a perfect gas

3. Optics 

• Wave optics
• wavefront and Huygens’ principle
• Laws of reflection and refraction using
• Huygen’s principle. Interference
• Young’s double-slit experiment and expression for fringe Width.
• Diffraction due to a single slit
• width of central maximum 
• Resolving power of microscopes and astronomical telescopes
• Polarisation
• plane-polarized light
• Brewster’s law
• uses of plane-polarized light and Polaroid.
• Reflection and refraction of light at plane and spherical surfaces
• Mirror formula 
• Total internal
• Reflection and its applications
• Deviation and Dispersion of light by a prism 
• Lens Formula
• Magnification
• Power of a Lens
• Combination of thin lenses in contact 
• Microscope and
• Astronomical Telescope (reflecting and refracting) and their magnifying power

4. Mechanics

• Uniform and non-uniform motion
• Average speed and instantaneous velocity 
• Uniformly accelerated motion 
• Scalar and vectors
• Relative velocity
• Motion in a plane
• Projectile motion-uniform circular motion-force and inertia 
• Newton’s first law of motion-momentum
• Newton’s second law of motion
• Impulse
• Newton’s third law of motion-law of conservation of linear momentum and its applications equilibrium of concurrent forces-static and kinetic friction
• Law of friction
• Rolling friction
• Basic concepts of rotational motion-moment of a force-torque
• Angular momentum
• Conservation of angular momentum and its application momentum of inertia-radius of gyration values of moments of inertia for simple geometrical objects
• Parallel and perpendicular axes theorems and their applications
• Rigid body rotation
• Equations of rotational motion.

5. Electricity

• Electric Current
• The flow of charges in a metallic conductor, 
• drift velocity and mobility and their relation with electric current
• Ohm’s law
• Electrical resistance
• V-I characteristics 
• Electrical resistivity and conductivity
• Classification of materials in terms of conductivity
• Carbon resistors
• Color code for carbon resistors
• Combination of resistors
• Series and parallel 
• Temperature dependence of resistance
• The internal resistance of a cell
• Potential difference and emf of a cell
• Combinations of cells in series and parallel
• Kirchoff’s law, illustration by simple circuits
• Wheatstone’s Bridge and its application for temperature coefficient of resistance measurement
• Meter bridge 
• A special case of Wheatstone bridge 
• Potentiometer principle 
• Comparing the emf of two cells
• Electromagnetic induction
• Faraday’s law 
• Induced emf and current 
• Lenz’s law 
• Self-induction
• Mutual induction
• Self-inductance of a long solenoid
• Mutual inductance of two long solenoids 
• Methods of inducing emf - (i) by changing magnetic induction (ii) by changing area enclosed by the coil and (iii) by changing the orientation of the coil (quantitative treatment), AC generator, commercial generator, (Single phase, three-phase)
• Eddy current
• Applications 
• Transformer
• Long-distance transmission
• Alternating current
• Measurement of A 
• AC circuit with resistance
• AC circuit with an inductor 
• AC circuit with a capacitor
• LCR series resonance circuit
• Q factor, power in AC circuits

6. Nuclear physics

• Nuclear properties 
• Nuclear radii 
• Masses 
• Binding energy
• Density 
• Charge 
• Isotopes
• Isobars and isotones,
• Nuclear mass defect, 
• Binding energy 
• Stability of nuclei
• Bainbridge mass spectrometer 
• Nature of nuclear force 
• Neutron and its discovery Radioactivity
• Alpha
• Beta and gamma rays and their properties
• Radioactive decay law
• Mass-energy relation 
• Mass defects 
• Binding energy per nucleon and its variation with mass number
• Nuclear fission and nuclear fusion

7. Laser and Optic Fiber

• Interaction of radiation with matter
• Essentials of Laser
• Types of Laser - Ruby Laser
• He-Ne Laser 
• Semiconductor laser 
• Application of Lasers 
• Optical Fibers – Propagation of light through an optical fiber 
• Modes of Propagation 
• Types of optical fibers 
• The optical fiber communication system 
• Attenuation in fibers

8. Electronic Devices

• Semiconductors
• Semiconductor diode
• I-V characteristics in forward and reverse bias
• Diode as a rectifier
• I-V characteristics of LED
• Photodiode 
• Solar cell and Zener diode
• Zener diode as a voltage regulator 
• Junction transistor
• Transistor action
• Characteristics of a transistor
• Transistor as an amplifier (common emitter configuration)

9. Properties of Matter

• The universal law of gravitation
• acceleration due to gravity
• variation of ‘G’ with altitude
• latitude and depth
• gravitation potential – escape velocity and orbital velocity
• geostationary satellites
• Kepler’s laws of planetary motion
• Solids
• elastic behavior
• stress-strain
• Hooke’s law
• Module of elasticity
• relation between them
• surface tension
• Capillarity
• Applications
• viscosity
• Poiseuille’s formula, stokes law
• Applications
• streamline and turbulent flow
• Reynolds number
• Bernoulli’s theorem
• Application

10. Magnetism

• Biot – Savart law and its application to current carrying circular loop 
• Ampere’s law and its applications to infinitely long current carrying straight wire and solenoid Force on a moving charge in uniform magnetic and electric fields
• Cyclotron Force on a current-carrying conductor in a uniform magnetic field 
• The force between two parallel current-carrying conductors 
• Definition of ampere
• Torque experienced by a current loop in a uniform magnetic field
• Moving coil galvanometer
• Its current sensitivity and conversion to ammeter and voltmeter 
• Current loop as a magnetic dipole and its magnetic dipole moment 
• Bar magnet as an equivalent solenoid 
• Magnetic field lines
• Earth’s magnetic field and magnetic elements
• Para dia and ferromagnetic substances Magnetic susceptibility and permeability
• Hysteresis
• Electromagnets and permanent magnets

Giving the Full VTUEEE Syllabus 2025 Details of Chemistry

VTUEEE Exam Syllabus of Chemistry (Physical Chemistry) SECTION - A

1. 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

2. Atomic Structure

• Thomson and Rutherford atomic models and their limitations
• Nature of electromagnetic radiation 
• Photoelectric effect 
• The spectrum of the hydrogen atom 
• Bohr model of hydrogen atom-its postulates
• Derivation of the relations for the energy of the electron and radii of the different orbits limitations of Bohr's model
• Dual nature of matter 
• De-Broglie's relationship
• Heisenberg uncertainty principle
• Elementary ideas of quantum mechanics 
• A quantum mechanical model of the atom and its important features
• Concept of atomic orbitals as one-electron wave functions 
• Variation of Ψ and Ψ2 with r for 1s and 2s orbitals
• Various quantum numbers (principal, 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 
• The extra stability of half-filled and filled orbitals

3. The States of Matter

• Classification of matter into solid, liquid, and gaseous states
• 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; 
• The concept of absolute scale of temperature
• Ideal gas equation
• Gaseous state: Kinetic theory of gases (only postulates)
• Concept of average
• Root mean square and most probable velocities
• Real gases
• Deviation from ideal behavior 
• Compressibility factor, and Van der Waals equation
• Liquid State: Properties of liquids-vapor pressure, viscosity and surface tension, and effect of temperature on them (qualitative treatment only)
• 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
• Solid State: Calculations involving unit cell parameters, an imperfection in solids; electrical, magnetic, and dielectric properties

4. Chemical Bonding and Molecular Structure

• Kossel-Lewis approach to chemical bond formation, 
• the concept of ionic and covalent bonds
• Ionic bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds;
• calculation of lattice enthalpy
• Covalent bonding: Concept of electronegativity, Fagan's rule, dipole moment; valence shell electron pair repulsion (VSEPR) theory and shapes of simple molecules
• Quantum mechanical approach to covalent bonding: Valence bond theory-its important features, the concept of hybridization involving s, p, and d orbitals; resonance
• Molecular orbital theory-its important features,
• LCAOs, types of molecular orbitals (bonding, antibonding), sigma and pi-bonds, molecular orbital electronic configurations of homonuclear diatomic molecules, 
• Concept of bond order
• Molecular orbital theory-bond length and bond energy
• Elementary idea of metallic bonding
• Hydrogen bonding and its applications

5. Solutions

• Different methods for expressing the concentration of solution-molality, molarity, mole fraction, percentage (by volume and mass both)
• The vapor 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 vapor pressure
• Depression of freezing point, the elevation of boiling point, and osmotic pressure
• Determination of molecular mass using colligative properties
• Abnormal value of molar mass, Can't Hoff factor and its significance

6. Chemical Thermodynamics

• Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, state functions, types of processes
• The first law of thermodynamics-concept of work, heat internal energy and enthalpy, heat capacity, molar heat capacity 
• Hess's law of constant heat summation
• Enthalpies of bond dissociation, combustion, formation, atomization, sublimation, phase transition
• The first law of thermodynamics-hydration, ionization, and solution
• The second law of thermodynamics; the spontaneity of processes; ΔS of the universe and ΔG of the system as criteria for spontaneity, Δg° (standard Gibbs energy change) and equilibrium constant

7. Surface Chemistry

• Adsorption-physisorption and chemisorption and their characteristics, factors affecting adsorption of gases on solids-Freundlich and Langmuir adsorption isotherms, adsorption from solutions
• Colloidal state-distinction among true solutions, colloids, and suspensions
• Classification of colloids-lyophilic, lyophobic 
• Multi molecular, macromolecular, and associated colloids (micelles), preparation and properties of the colloids-Tyndall effect
• Brownian movement, electrophoresis, dialysis, coagulation, and flocculation
• Emulsions and their characteristics

8. Chemical kinetics 

• Rate of a chemical reaction, factors affecting the rate of reactions: Concentration, temperature, pressure, and catalyst; 
• Elementary and complex reactions, order and molecularity of reactions, rate law, the rate constant, and its units
• Differential and integral forms of zero and first-order reactions, their characteristics, and half-lives, the effect of temperature on the rate of reactions-Arrhenius theory, activation energy, and its calculation
• Collision theory of bimolecular gaseous reactions (no derivation)

9. Redox Reactions and Electrochemistry

• Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions
• 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
• the relationship between cell potential and Gibbs energy change
• Dry cell and lead accumulator
• fuel cells

10. Equilibrium

• Meaning of equilibrium 
• The concept of dynamic equilibrium
• Equilibria involving physical processes: Solid-liquid, liquid-gas, and solid-gas equilibria Henry's law, general characteristics of equilibrium involving physical processes
• Equilibria involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, the significance of ΔG and ΔG° in chemical equilibria, factors affecting equilibrium concentration, pressure, temperature
• Equilibria involving chemical processes: Effect of catalyst; 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 multi-stage ionization), and ionization constants
• Ionic equilibrium: Ionization of water, pH scale, common ion effect, hydrolysis of salts and pH of their solutions, the solubility of sparingly, soluble salts and solubility products, buffer solutions.

VTUEEE Syllabus 2025 of Chemistry (Inorganic Chemistry) Section - B

1. General Principles and Processes of Isolation of Metals

• Modes of occurrence of elements in nature, minerals, ores; Steps involved in the extraction of metals-concentration, reduction (chemical and electrolytic methods), and refining with special reference to the extraction of Al, Cu, Zn, and Fe
• Thermodynamic and electrochemical principles involved in the extraction of metals

2. Classification of Elements and Periodicity in Properties

• Modem periodic law and present form of the periodic table, s, p, d, and f block elements, periodic trends in properties of elements atomic and ionic radii, ionization enthalpy, electron gain enthalpy, valence, oxidation states, and chemical reactivity.

3. Hydrogen

• Position of hydrogen in periodic table, isotopes, preparation, properties, and uses of hydrogen
• Physical and chemical properties of water and heavy water
• Structure, preparation, reactions, and uses of hydrogen peroxide 
• Hydrogen as a fuel

4. S-Block Elements (alkali and alkaline earth metals)

• Group-1 and 2 elements: Preparation and properties of some important compounds-sodium carbonate and sodium hydroxide
• Industrial uses of lime, limestone, plaster of Paris, and cement; Biological significance of Na, K, Mg, and Ca
• Group-1 and 2 elements: General introduction, electronic configuration, and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships

5. P-Block Elements

• Group-13 to group 18 elements: General introduction: Electronic configuration and general trends in physical and chemical properties of elements across the periods and down the groups; unique behavior of the first element in each group
• Groupwise study of the p-block elements-group-13: Preparation, properties, and uses of boron and aluminum
• Properties of boric acid, diborane, boron trifluoride, aluminum chloride, and alums
• Groupwise study of the p-block elements-group-14: Allotropes of carbon, the tendency for catenation 
• Structure and properties of silicates, and zeolites
• Groupwise study of the p-block elements-group-15: Properties and uses of nitrogen and phosphorus 
• Allotrophic forms of phosphorus
• Preparation, properties, structure, and uses of ammonia, nitric acid, phosphine, and phosphorus halides, (PCl3, PCl5)
• Groupwise study of the p-block elements-group-15: Structures of oxides and oxoacids of phosphorus
• Groupwise study of the p-block elements-group-16: Preparation, properties, structures, and uses of ozone
• Allotropic forms of sulfur; preparation, properties, structures, and uses of sulphuric acid (including its industrial preparation)
• Groupwise study of the p-block elements-group-16: Structures of oxoacids of sulfur
• Groupwise study of the p-block elements-group-17: Preparation, properties, and uses of hydrochloric acid 
• Trends in the acidic nature of hydrogen halides
• Structures of interhalogen compounds and oxides and oxoacids of halogens
• Groupwise study of the p-block elements-group-18: Occurrence and uses of noble gases
• Structures of fluorides and oxides of xenon group-1 and 2 elements: Preparation and properties of some important compounds-sodium carbonate and sodium hydroxide
• Industrial uses of lime, limestone, plaster of Paris, and cement 
• The biological significance of Na, K, Mg, and Ca

6. D and F - Block Elements

• Transition elements: Catalytic behavior, magnetic properties, complex formation, interstitial compounds, alloy formation; preparation, properties, and uses of K2 Cr2 O7 and KMnO4
• Lanthanoids-electronic configuration, oxidation states, and lanthanide contraction
• Actinoids-electronic configuration and oxidation states
• Transition elements: General introduction, electronic configuration, occurrence and characteristics, general trends in properties of the first-row transition elements-physical properties, ionization enthalpy, oxidation states, atomic radii, color
• Inner Transition Elements

7. Environmental Chemistry

• Stratospheric pollution-formation and breakdown of ozone, depletion of ozone layer-its mechanism and effects
• Water pollution-major pollutants such as pathogens, organic wastes, and chemical pollutants; their harmful effects and prevention
• Soil pollution-major pollutants such as Pesticides (insecticides, herbicides, and fungicides), their harmful effects, and prevention
• Strategies to control environmental pollution
• Environmental pollution-atmospheric, water, and soil
• Atmospheric pollution-tropospheric and stratospheric
• Tropospheric pollutants-gaseous pollutants: Oxides of carbon, nitrogen, and sulfur, hydrocarbons; their sources, harmful effects, and prevention 
• Greenhouse effect and global warming
• Acid rain
• Particulate pollutants: Smoke, dust, smog, fumes, mist; their sources, harmful effects, and prevention

8. Coordination Compounds

• Bonding-valence bond approach and basic ideas of crystal field theory, color, and magnetic properties
• The importance of coordination compounds (in qualitative analysis, extraction of metals, and in biological systems)
• Introduction to coordination compounds, Werner's theory
• ligands, coordination number, denticity, chelation 
• IUPAC nomenclature of mononuclear coordination compounds, isomerism

VTUEEE Exam Syllabus of Chemistry (Organic Chemistry) Section - C

1. Some Basic Principles of Organic Chemistry

• Isomerism-structural and stereoisomerism
• Nomenclature (trivial and IUPAC)
• Covalent bond fission-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
• Tetravalency of carbon 
• Shapes of simple molecules-hybridization (s and p); classification of organic compounds based on functional groups: – C = C –, – C h C – and those containing halogens, oxygen, nitrogen, and sulfur
• Homologous series

2. Purification and Characterisation of Organic Compounds

• Quantitative analysis (basic principles only)-estimation of carbon, hydrogen, nitrogen, halogens, sulfur, phosphorus
• Qualitative analysis-detection of nitrogen, sulfur, phosphorus, and halogens
• Purification-crystallization, sublimation, distillation, differential extraction, and chromatography-principles and their applications
• Calculations of empirical formula and a molecular formula
• Numerical problems in organic quantitative analysis

3. Organic Compounds Containing Halogens

• Uses- Environmental effects of chloroform and iodoform
• General methods of preparation, properties, and reactions 
• Nature of C-X bond 
• Mechanisms of substitution reactions

4. Hydrocarbons

• Alkenes-geometrical isomerism; mechanism of electrophilic addition: Addition of hydrogen, halogens, water, hydrogen halides (Markownikoff's and peroxide effect)
• Ozonolysis and polymerization
• Aromatic hydrocarbons-nomenclature, benzene-structure, and aromaticity; 
• Mechanism of electrophilic substitution: Halogenation, nitration, Friedel-Craft's alkylation, and acylation, directive influence of the functional group in mono-substituted benzene
• Alkynes-acidic character
• Addition of hydrogen, halogens, water, and hydrogen halides 
• Polymerization
• Alkanes-conformations: Sawhorse and Newman projections (of ethane)
• Mechanism of halogenation of alkanes
• Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties, and reactions

5. Organic Compounds Containing Oxygen 

• General methods of preparation, properties, uses, and reactions 

6. Alcohols, Phenols, and Ethers

• Aldehyde and ketones: Nature of carbonyl group
• Nucleophilic addition to >C=O group, relative reactivities of aldehydes and ketones
• Important reactions such as-nucleophilic addition reactions (addition of HCN, NH3, and its derivatives), Grignard reagent
• Alcohols: Identification of primary, secondary, and tertiary alcohols
• Mechanism of dehydration
• Phenols: Acidic nature, electrophilic substitution reactions: Halogenation, nitration and sulphonation, Reimer-Tiemann reaction
• Ethers: Structure
• Aldehyde and ketones: Oxidation; reduction (Wolff Kishner and Clemmensen)
• The acidity of α-hydrogen, aldol condensation, Cannizzaro reaction, haloform reaction
• Chemical tests to distinguish between aldehydes and ketones

7. Carboxylic Acid

• Acidic strength and factors affecting it

8. Polymers

• General introduction and classification of polymers, general methods of polymerization-addition and condensation, copolymerization
• Natural and synthetic rubber and vulcanization
• Some important polymers with emphasis on their monomers and uses-polythene, nylon, polyester, and Bakelite

9. 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
• Diazonium salts: importance in synthetic organic chemistry

10. Biomolecules

• General introduction and importance of biomolecules
• Carbohydrates-classification: Aldoses and ketoses
• Monosaccharides (glucose and fructose) and constituent monosaccharides of oligosaccharides (sucrose, lactose, and altose)
• Proteins: Elementary idea of amino acids, peptide bond, polypeptides; proteins: Primary, secondary, tertiary, and quaternary structure (qualitative idea only), denaturation of proteins, enzymes
• Vitamins: Classification and functions
• Nucleic acids: Chemical constitution of DNA and RNA. Biological functions of nucleic acids

11. Chemistry in Everyday Life

• Chemicals in medicines-analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines-their meaning, and common examples
• Chemicals in food-preservatives, artificial sweetening agents-common examples
• Cleansing agents-soaps and detergents, cleansing action

12. Principles Related to Practical Chemistry

• Detection of extra elements (N, S, halogens) in organic compounds
• Detection of the following functional groups: Hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl, and amino groups in organic compounds
• The chemistry involved in the preparation of the following: Inorganic compounds-Mohr's salt, potash alum. Organic compounds: Acetanilide, pnitroacetanilide, aniline yellow, iodoform
• The chemistry involved in the titrimetric exercises: Acids bases and the use of indicators, oxalic-acid vs. KMnO4, Mohr's salt vs. KMnO4
• Chemical principles involved in the qualitative salt analysis: Cations-Pb2+ , Cu2+, AI3+, Fe3+, Zn2+, Ni2+, Ca2+, Ba2+, Mg2+, NH4+. Anions-CO3 2-, S2-, SO4 2-, NO2-, NO3-, CI -, Br, I (insoluble salts excluded)
• Chemical principles involved in the following experiments: 
• 1. Enthalpy of solution of CuS04 2. Enthalpy of neutralization of strong acid and strong base. 3. Preparation of lyophilic and lyophobic sols
• Chemical principles involved in the following experiments: 4. Kinetic study of the reaction of iodide ion with hydrogen peroxide at room temperature

VTUEEE Syllabus Details of Mathematics

1. Sets, Relations, and Functions

• Sets and their representation
• Union, intersection, and complement of sets and their algebraic properties 
• Power set
• Relation, Types of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions

2. Complex Numbers and Quadratic Equations

• Complex numbers as ordered pair of reals, representation of 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
• The square root of a complex number, triangle inequality, quadratic equations in real and complex number systems and their solutions
• The relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots

3. Permutations and Combinations

• The fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications

4. Matrices and Determinants

• Matrices, algebra of matrices, types of matrices, determinants, and matrices of order two and three
• Properties of determinants, evaluation of determinants, area of triangles using determinants
• Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices

5. Mathematical Induction 

• Principle of mathematical induction and its simple applications

6. Binomial Theorem and its Simple Applications

• Binomial theorem for the positive integral index, general term and middle term, properties of binomial coefficients, and simple applications

7. Sequences and Series

• Arithmetic and geometric progressions, insertion of arithmetic, geometric means between two given numbers
• The relation between a.m. and g.m
• Sum up to n terms of special series: Sn, Sn2, Sn3
• Arithmetic-Geometric progression

8. Limit, Continuity, and Differentiability

• Real-valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic, and exponential functions, inverse functions
• Graphs of simple functions
• 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
• Rolle's and Lagrange's mean value theorems
• Applications of derivatives: Rate of change of quantities, monotonic-increasing and decreasing functions, maxima and minima of functions of one variable, tangents, and normals

9. Integral Calculus

• Integral as an anti-derivative
• Fundamental integrals involving algebraic, trigonometric, exponential, and logarithmic functions
• Integration by substitution, by parts, and by partial fractions
• Integration using trigonometric identities
• Evaluation of simple integrals of the type
• Integral as limit of a sum
• The fundamental theorem of calculus
• Properties of definite integrals
• Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form

10. Differential Equations

• Ordinary differential equations, their order, and degree
• Formation of differential equations
• A solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type: dy/dx+p(x)y=q(x)

11. Coordinate Geometry 

• Cartesian system of rectangular coordinates 10 in a plane, distance formula, section formula, locus, and its equation, translation of axes, the slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes
• Straight lines: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, a distance of a point from a line, equations of internal and external bisectors of angles between two lines
• Straight lines: Coordinates of the centroid, orthocentre, and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines
• Circles, conic sections: Standard form of the equation of a circle, the general form of the equation of a circle, its radius and center, equation of a circle when the endpoints of a diameter are given
• Circles, conic sections: Points of intersection of a line and a circle with the center at the origin and condition for a line to be tangent to a circle, equation of the tangent
• Circles, conic sections: Sections of cones, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, condition for y = MX + c to be a tangent and point (s) of tangency

12. Three Dimensional Geometry

• Coordinates of a point in space, the distance between two points, section formula, direction ratios, and direction cosines, the angle between two intersecting lines
• Skew lines, the shortest distance between them, and its equation
• Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines

13. Vector Algebra

• Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector products, scalar, and vector triple product

14. Statistics and Probability

• Measures of dispersion: Calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance, and mean deviation for grouped and ungrouped data
• Probability: Probability of an event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a random variate, Bernoulli trials, and binomial distribution

15. Trigonometry 

• Trigonometric identities and equations
• Trigonometric functions
• Inverse trigonometric functions and their properties
• Heights and distances

16. Mathematical Reasoning 

• Statements, logical operations and, or, implies, implied by, if and only if
• Understanding of tautology, contradiction, converse, and contrapositive

Best Books For VTUEEE Examination 2025

Books For Physics

• Concepts of Physics by H. C. Verma
• Problems in General Physics by I. E. Irodov
• Fundamentals of Physics by Halliday, Resnick, and Walker
• University Physics by Freedman and Young
• Problem In Physics by SS Krotov
• Understanding JEE physics series by DC Pandey

Books For Chemistry

• Modern Approach to Chemical Calculations by RC Mukherjee
• Organic Chemistry by Solomons and Fryhle 
• Concise Inorganic by  J. D. Lee
• Organic Chemistry by Morrison and Boyd
• University Chemistry by Freedman and Young
• Physical Chemistry by N Awasthi
• Arihant's Practice Book Chemistry for JEE Main And Advanced by R.K Gupta

Books For Mathematics

• Trigonometry by S L Loney
• Problems Plus in IIT Mathematics by A Das Gupta
• Course in Mathematics for IIT-JEE by Tata McGraw Hill publication
• IIT Mathematics for JEE Main & Advanced by M.L. Khanna
• Calculus and Analytic Geometry by Thomas and Finney
• Differential and Integral Calculus by N. Piskunov
• Coordinate Geometry by S.L. Loney
• Higher Algebra by Hall and Knight