AIEEE Exam Syllabus

AIEEE Mathematics Syllabus2024:

UNIT 1:SETS, RELATIONS AND FUNCTIONS:Sets and theirrepresentation; Union, intersection andcomplement ofsets and theiralgebraic properties; Power set; Relation,Types ofrelations,equivalence relations, functions;. one-one, into andontofunctions,composition of functions.

UNIT 2: COMPLEX NUMBERS ANDQUADRATICEQUATIONS: Complex numbers as ordered pairs ofreals,Representation of complexnumbers in the form a+ib andtheirrepresentation in a plane,Arganddiagram.

Algebra of complex numbers,modulusand argument (oramplitude) of a complex number, square root ofa complexnumber,triangle inequality, Quadratic equations in real andcomplexnumbersystem and their solutions.

Relationbetweenroots and co-efficients, nature of roots, formation ofquadraticequations with given roots.

UNIT 3: MATRICES ANDDETERMINANTS:Matrices, algebra of matrices, types ofmatrices,determinants andmatrices of order two and three. Propertiesofdeterminants, evaluationof determinants, area of trianglesusingdeterminants. Adjoint andevaluation of inverse of a square matrixusingdeterminants andelementary transformations, Test of consistencyandsolution ofsimultaneous linear equations in two or threevariablesusingdeterminants and matrices.

UNIT 4: PERMUTATIONSANDCOMBINATIONS: Fundamental principle ofcounting,permutation as an arrangement andcombination as selection,Meaning of P(n,r) and C (n,r),simpleapplications.

UNIT 5: MATHEMATICALINDUCTION: Principle ofMathematical Induction and itssimpleapplications.

UNIT 6: BINOMIAL THEOREM AND ITS SIMPLEAPPLICATIONS:Binomial theorem for a positive integralindex, generalterm and middleterm, properties of Binomial coefficientsand simpleapplications.

UNIT 7: SEQUENCES AND SERIES: ArithmeticandGeometric progressions, insertion of arithmetic,geometric meansbetweentwo given numbers. Relation between A.M. andG.M. Sum upto nterms ofspecial series: Sn, Sn2, Sn3. Arithmetico-Geometricprogression.

UNIT 8:LIMIT, CONTINUITY AND DIFFERENTIABILITY:Real - valuedfunctions, algebra of functions, polynomials,rational,trigonometric,logarithmic and exponential functions,inversefunctions. Graphs ofsimple functions. Limits, continuityanddifferentiability.Differentiation of the sum, difference, productandquotient of twofunctions. Differentiation of trigonometric,inversetrigonometric,logarithmic, exponential, composite andimplicitfunctions; derivativesof order upto two. Rolle's and Lagrange'sMeanValue Theorems.Applications of derivatives: Rate of changeofquantities, monotonic -increasing and decreasing functions, Maximaandminima of functions ofone variable, tangents andnormals.

UNIT9: INTEGRAL CALCULUS: Integral as ananti - derivative.Fundamental integrals involvingalgebraic,trigonometric, exponential andlogarithmic functions.Integration bysubstitution, by parts and bypartial fractions.Integration usingtrigonometric identities. Evaluationof simpleintegrals of the typeIntegral as limit of a sum. FundamentalTheoremof Calculus. Propertiesof definite integrals. Evaluation ofdefiniteintegrals, determiningareas of the regions bounded by simplecurves instandardform.

UNIT 10:DifferentialEquations: Ordinary differential equations,their order anddegree. Formation ofdifferential equations. Solution ofdifferentialequations by themethod of separation of variables,solutionofhomogeneous and lineardifferentialequations

UNIT 11: CO-ORDINATEGEOMETRY:Cartesian system ofrectangular co-ordinatesina plane, distanceformula, section formula, locus and itsequation,translation of axes,slope of a line, parallel andperpendicular lines,intercepts of a lineon the coordinate axes.

Straight lines:Variousforms of equations of a line,intersection of lines, anglesbetween twolines, conditions forconcurrence of three lines, distanceof a pointfrom a line, equations ofinternal and external bisectors ofanglesbetween two lines, coordinatesof centroid, orthocentre andcircumcentreof a triangle, equation offamily of lines passing throughthe point ofintersection of twolines.

Circles, conic sections:Standard formofequation of a circle, general form of the equation ofa circle,itsradius and centre, equation of a circle when the endpoints ofadiameter are given, points of intersection of a line and acirclewiththe centre at the origin and condition for a line to betangent toacircle, equation of the tangent. Sections of cones,equations ofconicsections (parabola, ellipse and hyperbola) instandard forms,conditionfor y = mx + c to be a tangent and point (s)oftangency.

UNIT 12: Three DimensionalGeometry:Coordinatesof a point in space, distancebetween two points, sectionformula,direction ratios and directioncosines, angle between twointersectinglines. Skew lines, the shortestdistance between them andits equation.Equations of a line and a planein different forms,intersection of aline and a plane, coplanarlines.

UNIT 13:VectorAlgebra:Vectors and scalars, addition ofvectors,components of a vector in twodimensions and three dimensionalspace,scalar and vector products,scalar and vector tripleproduct.

UNIT 14: STATISTICSANDPROBABILITY:Measures of Dispersion: Calculation ofmean,median, mode of groupedand ungrouped data. Calculation ofstandarddeviation, variance andmean deviation for grouped andungroupeddata.

Probability:Probability of anevent,addition and multiplication theorems ofprobability, Baye'stheorem,probability distribution of a randomvariate, Bernoulli trialsandBinomial distribution.

UNIT 15:Trigonometry:Trigonometricalidentities and equations. Trigonometricalfunctions.Inversetrigonometrical functions and their properties.HeightsandDistances.

UNIT16: MATHEMATICALREASONING:Statements, logicaloperations and, or, implies,implied by, if andonly if. Understandingof tautology, contradiction,converseandcontrapositive.



AIEEE Physics Syllabus 2024:

The syllabus contains two Sections - Aand B. Section- A pertains to theTheory Part having 80% weightage,while Section - Bcontains PracticalComponent (Experimental Skills)having 20%weightage.
SECTION A

UNIT 1: PHYSICSANDMEASUREMENT:Physics, technology and society, S Iunits,Fundamental and derivedunits. Least count, accuracy and precisionofmeasuring instruments,Errors in measurement, Significantfigures.Dimensions of Physicalquantities, dimensional analysis anditsapplications.

UNIT 2:KINEMATICS: Frame of reference. Motion ina straightline: Position-time graph, speed andvelocity.

Uniformand non-uniform motion, averagespeed andinstantaneous velocityUniformly accelerated motion,velocity-time,position-time graphs,relations for uniformly acceleratedmotion.Scalars and Vectors, Vectoraddition and Subtraction, ZeroVector,Scalar and Vector products, UnitVector, Resolution of aVector.Relative Velocity, Motion in a plane,Projectile Motion,UniformCircular Motion.

UNIT3: LAWS OF MOTION:Force and Inertia,Newton's First Lawof motion; Momentum, Newton'sSecond Law of motion;Impulse; Newton'sThird Law of motion. Law ofconservation of linearmomentum and itsapplications, Equilibrium ofconcurrent forces. Staticand Kineticfriction, laws of friction,rolling friction. Dynamics ofuniformcircular motion: Centripetalforce and itsapplications.

UNIT 4: WORK, ENERGY ANDPOWER:Work done by aconstant force and a variableforce; kinetic andpotential energies,work-energy theorem, power.Potential energy of aspring, conservation ofmechanical energy,conservative andnon-conservative forces; Elastic andinelasticcollisions in one andtwodimensions.

UNIT 5: ROTATIONALMOTION:Centre of mass of atwo-particle system, Centreof mass of a rigidbody; Basic concepts ofrotational motion; moment ofa force, torque,angular momentum,conservation of angular momentum anditsapplications; moment of inertia,radius of gyration. Values ofmomentsof inertia for simple geometricalobjects, parallel andperpendicularaxes theorems and their applications.Rigid body rotation,equations ofrotational motion.

UNIT 6: GRAVITATION:The universal lawofgravitation. Acceleration due to gravity and itsvariation withaltitudeand depth. Kepler's laws of planetary motion.Gravitationalpotentialenergy; gravitational potential. Escapevelocity. Orbitalvelocity of asatellite. Geo-stationarysatellites.

UNIT 7: PROPERTIES OF SOLIDS ANDLIQUIDS:Elasticbehaviour, Stress-strain relationship, Hooke'sLaw, Young'smodulus, bulkmodulus, modulus of rigidity. Pressure due toa fluidcolumn; Pascal'slaw and its applications. Viscosity, Stokes'law,terminal velocity,streamline and turbulent flow, Reynoldsnumber.Bernoulli's principle andits applications. Surface energy andsurfacetension, angle of contact,application of surface tension -drops,bubbles and capillary rise. Heat,temperature, thermalexpansion;specific heat capacity, calorimetry;change of state, latentheat. Heattransfer-conduction, convection andradiation, Newton's lawof cooling.

UNIT8:THERMODYNAMICS:Thermal equilibrium, zeroth lawofthermodynamics, concept oftemperature. Heat, work and internalenergy.First law ofthermodynamics. Second law of thermodynamics:reversibleandirreversible processes. Carnot engine and itsefficiency.

UNIT 9: KINETIC THEORY OFGASES:Equationof state of a perfect gas, work done oncompressing a gas.Kinetic theoryof gases - assumptions, concept ofpressure. Kineticenergy andtemperature: rms speed of gas molecules;Degrees of freedom,Law ofequipartition of energy, applications tospecific heatcapacities ofgases; Mean free path, Avogadro'snumber.

UNIT 10:OSCILLATIONS ANDWAVES:Periodic motion - period,frequency, displacement asa function oftime. Periodic functions.Simple harmonic motion (S.H.M.)and itsequation; phase; oscillations ofa spring - restoring force andforceconstant; energy in S.H.M. -kinetic and potential energies;Simplependulum - derivation ofexpression for its time period; Free,forcedand damped oscillations,resonance. Wave motion. Longitudinalandtransverse waves, speed of awave. Displacement relation foraprogressive wave. Principle ofsuperposition of waves, reflectionofwaves, Standing waves in stringsand organ pipes, fundamental modeandharmonics, Beats, Doppler effectin sound

UNIT11:ELECTROSTATICS:Electric charges: Conservation ofcharge,Coulomb's law-forces betweentwo point charges, forces betweenmultiplecharges; superpositionprinciple and continuous chargedistribution.Electric field: Electricfield due to a point charge,Electric fieldlines, Electric dipole,Electric field due to a dipole,Torque on adipole in a uniformelectric field. Electric flux, Gauss'slaw and itsapplications to findfield due to infinitely long uniformlychargedstraight wire, uniformlycharged infinite plane sheet anduniformlycharged thin sphericalshell. Electric potential and itscalculation fora point charge,electric dipole and system of charges;Equipotentialsurfaces,Electrical potential energy of a system of twopoint chargesin anelectrostatic field. Conductors and insulators,Dielectricsandelectric polarization, capacitor, combination ofcapacitors inseriesand in parallel, capacitance of a parallel platecapacitor withandwithout di electric medium between the plates, Energystored inacapacitor.


AIEEE Chemistry Syllabus 2024:Page 2

SECTION-A: PHYSICALCHEMISTRY

UNIT 1: Some Basic conceptS INCHEMISTRY:Matterand its nature, Dalton's atomic theory;Concept of atom,molecule,element and compound; Physical quantities andtheirmeasurements inChemistry, precision and accuracy, significantfigures,S.I. Units,dimensional analysis; Laws of chemical combination;Atomicand molecularmasses, mole concept, molar mass, percentagecomposition,empirical andmolecular formulae; Chemical equationsandstoichiometry.

UNIT2: States of Matter: Classification ofmatter intosolid, liquid and gaseous states.

GaseousState:Measurable properties of gases; Gas laws - Boyle's law, Charle'slaw,Graham's law of diffusion, Avogadro'slaw,

Dalton'slaw of partial pressure; Concept ofAbsolutescale of temperature;Ideal gas equation, Kinetic theory ofgases (onlypostulates); Conceptof average, root mean square and mostprobablevelocities; Real gases,deviation from Ideal behaviour,compressibilityfactor, van der Waalsequation, liquefaction of gases,criticalconstants. Liquid State:Properties of liquids - vapourpressure,viscosity and surface tensionand effect of temperature onthem(qualitative treatment only). Solid State: Classification ofsolids:molecular, ionic, covalent andmetallic solids, amorphousandcrystalline solids (elementary idea);Bragg's Law and itsapplications;Unit cell and lattices, packing insolids (fcc, bcc and hcplattices),voids, calculations involving unitcell parameters,imperfection insolids; Electrical, magnetic anddielectricproperties.

UNIT 3: AtomicStructure:Discovery of sub-atomicparticles (electron,proton and neutron);Thomson and Rutherford atomicmodels and theirlimitations; Nature ofelectromagnetic radiation,photoelectric effect;Spectrum of hydrogenatom, Bohr model of hydrogenatom - its postulates,derivation of therelations for energy of theelectron and radii of thedifferent orbits,limitations of Bohr's model;Dual nature of matter,de-Broglie'srelationship, Heisenberg uncertaintyprinciple. Elementaryideas ofquantum mechanics, quantum mechanicalmodel of atom, itsimportantfeatures, * and *2, concept of atomicorbitals as one electronwavefunctions; Variation of * and * 2 with rfor 1s and 2sorbitals;various quantum numbers (principal, angularmomentum andmagneticquantum numbers) and their significance; shapes ofs, p and d-orbitals, electron spin and spin quantum number; Rulesforfillingelectrons in orbitals � aufbau principle, Pauli' sexclusionprincipleand Hund's rule, electronic configuration ofelements, extrastabilityof half-filled and completely filledorbitals.

UNIT 4: Chemical Bonding and MolecularStructure:Kossel - Lewis approach to chemical bondformation, concept of ionic andcovalent bonds.

Ionic Bonding:Formation of ionicbonds, factors affecting the formation of ionicbonds; calculation oflattice enthalpy.

CovalentBonding:Concept ofelectronegativity, Fajan's rule,dipole moment; ValenceShell ElectronPair Repulsion (VSEPR) theory andshapes of simplemolecules. Quantummechanical approach to covalentbonding: Valencebond theory - Itsimportant features, concept ofhybridizationinvolving s, p and dorbitals; Resonance. MolecularOrbital Theory -Its important features,LCAOs, types of molecularorbitals (bonding,antibonding), sigma andpi-bonds, molecular orbitalelectronicconfigurations of homonucleardiatomic molecules, concept ofbondorder, bond length and bond energy.Elementary idea ofmetallicbonding. Hydrogen bonding and itsapplications.

UNIT 5: CHEMICALTHERMODYNAMICS:Fundamentals ofthermodynamics: Systemand surroundings, extensive andintensiveproperties, state functions,types of processes. First lawofthermodynamics - Concept of work, heatinternal energy andenthalpy,heat capacity, molar heat capacity; Hess'slaw of constantheatsummation; Enthalpies of bond dissociation,combustion,formation,atomization, sublimation, phase transition,hydration,ionization andsolution. Second law of thermodynamics-Spontaneity ofprocesses; DS ofthe universe and DG of the system ascriteria forspontaneity, DGo(Standard Gibbs energy change) andequilibriumconstant.

UNIT 6: SOLUTIONS:Different methodsforexpressing concentration of solution - molality,molarity,molefraction, percentage (by volume and mass both), vapourpressureofsolutions and Raoult's Law - Ideal and non-idealsolutions,vapourpressure - composition, plots for ideal andnon-idealsolutions;Colligative properties of dilute solutions -relativelowering ofvapour pressure, depression of freezing point,elevation ofboilingpoint and osmotic pressure; Determination ofmolecular massusingcolligative properties; Abnormal value of molarmass, van't Hofffactorand its significance.

UNIT 7:EQUILIBRIUM:Meaningof equilibrium, concept of dynamicequilibrium. Equilibriainvolvingphysical processes: Solid -liquid,liquid - gas and solid -gasequilibria, Henry's law, generalcharacterics of equilibriuminvolvingphysical processes. Equilibriainvolving chemical processes:Law ofchemical equilibrium, equilibriumconstants (Kp and Kc) andtheirsignificance, significance of DG and DGoin chemical equilibria,factorsaffecting equilibrium concentration,pressure, temperature,effect ofcatalyst; Le Chatelier's principle.Ionic equilibrium: Weakand strongelectrolytes, ionization ofelectrolytes, various conceptsof acids andbases (Arrhenius, Br?nsted -Lowry and Lewis) and theirionization, acid- base equilibria (includingmultistage ionization)and ionizationconstants, ionization of water, pHscale, common ioneffect, hydrolysisof salts and pH of their solutions,solubility ofsparingly soluble saltsand solubility products, buffersolutions.

UNIT 8:REDOX REACTIONS ANDELECTROCHEMISTRY:Electronic conceptsof oxidation andreduction, redox reactions,oxidation number, rules forassigningoxidation number, balancing ofredox reactions. Eectrolyticand metallicconduction, conductance inelectrolytic solutions, specificand molarconductivities and theirvariation with concentration:Kohlrausch's lawand its applications.Electrochemical cells -Electrolytic and Galvaniccells, differenttypes of electrodes,electrode potentials includingstandard electrodepotential, half - celland cell reactions, emf of aGalvanic cell andits measurement; Nernstequation and its applications;Relationshipbetween cell potential andGibbs' energy change; Dry celland leadaccumulator; Fuel cells;Corrosion and itsprevention.

UNIT 9: CHEMICALKINETICS: Rate of achemical reaction, factors affecting therate ofreactions:concentration, temperature, pressure and catalyst;elementaryandcomplex reactions, order and molecularity of reactions,rate law,rateconstant and its units, differential and integral forms ofzeroandfirst order reactions, their characteristics and half -lives,effectof temperature on rate of reactions - Arrheniustheory,activationenergy and its calculation, collision theory ofbimoleculargaseousreactions (no derivation).

UNIT 10: SURFACECHEMISTRY: Adsorption-Physisorption and chemisorption andtheir characteristics,factorsaffecting adsorption of gases on solids -Freundlich andLangmuiradsorption isotherms, adsorption from solutions.Catalysis -Homogeneousand heterogeneous, activity and selectivity ofsolidcatalysts, enzymecatalysis and its mechanism. Colloidal state-distinction among truesolutions, colloids andsuspensions,classification of colloids -lyophilic, lyophobic; multimolecular,macromolecular and associatedcolloids (micelles), preparationandproperties of colloids - Tyndalleffect, Brownianmovement,electrophoresis, dialysis, coagulation andflocculation;Emulsions andtheir characteristics.
SECTION-B: INORGANICCHEMISTRY

UNIT 11: CLASSIFICATON OF ELEMENTSAND PERIODICITY INPROPERTIES:Modem periodic law andpresent form of theperiodic table, s, p, d andf block elements,periodic trends inproperties of elements�atomic andionic radii,ionization enthalpy,electron gain enthalpy, valence,oxidation statesand chemicalreactivity.

UNIT 12: GENERAL PRINCIPLES AND PROCESSES OF ISOLATIONOFMETALS:Modes of occurrence of elements innature,minerals, ores; stepsinvolved in the extraction of metals-concentration, reduction(chemical. and electrolytic methods)andrefining with specialreference to the extraction of Al, Cu, Zn andFe;Thermodynamic andelectrochemical principles involved in theextractionof metals.

UNIT 13:HYDROGEN:Position of hydrogen inperiodic table,isotopes, preparation,properties and uses of hydrogen;Physical andchemical properties ofwater and heavy water; Structure,preparation,reactions and uses ofhydrogen peroxide; Classification ofhydrides -ionic, covalent andinterstitial; Hydrogen as afuel.

UNIT14: S - BLOCK ELEMENTS (ALKALIAND ALKALINE EARTHMETALS):Group - 1 and 2 ElementsGeneral introduction,electronic configurationand general trends inphysical and chemicalproperties of elements,anomalous properties ofthe first element of eachgroup, diagonalrelationships. Preparation andproperties of someimportant compounds -sodium carbonate, sodiumchloride, sodium hydroxideand sodium hydrogencarbonate; Industrialuses of lime, limestone,Plaster of Paris andcement; Biologicalsignificance of Na, K, Mg andCa.
AIEEE Aptitude Test Syllabus2024

PartI:

Awarenessofpersons,places, Buildings, Materials.) Objects, Texture relatedtoArchitectureand build~ environment. Visualising threedimensionalobjects from twodimensional drawings. Visualising.different sides ofthree dimensionalobjects. Analytical ReasoningMental Ability (Visual,Numerical andVerbal).

PartII:

Threedimensional - perception: Understandingandappreciation of scale andproportion of objects, building formsandelements, colour texture,harmony and contrast.Design and drawing ofgeometrical or abstractshapes and patternsinpencil.


Transformationof forms both 2 Dand 3 D union,substraction, rotation, development ofsurfaces andvolumes, Generationof Plan, elevations and 3 D views ofobjects.Creating two dimensionaland three dimensional compositionsusing givenshapes andforms.

Sketching ofscenes andactivitiesfrom memory of urbanscape (public space, market,festivals,streetscenes, monuments, recreational spaces etc.),landscape (riverfronts,jungles. gardens, trees, plants etc.) andrurallife.

Note: Candidatesare advised to bring pencils,own geometry box set, erasers and colourpencils and crayons for theAptitude Test.