AEEE 2025 Syllabus PDF: Physics, Chemistry, Maths Topics & Weightage

Particulars

Details

Exam Name

Amrita Entrance Examination - Engineering

Conducting Body

Amrita Vishwa Vidyapeetham University

Mode of Application

Online

Mode of Examination

Computer-Based Test (CBT)

Language

English

Exam Frequency

Twice a Year

Exam Duration

150 minutes

Maximum Marks

300 Marks

Number of Questions

100 Questions

Marking Scheme

(+3) marks for every correct response (-1) marks for every incorrect answer

Syllabus Subjects

Physics, Mathematics, Chemistry, and English

AEEE 2025 Phase 2 Registration

Start Date: 10th February 2025

End Date: 1st May 2025

Exam Date: 7th to 11th May 2025

Units

Chapters

Sub-Topics

1

Sets, Relations, and Functions

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

2

Complex Numbers

Complex numbers in the form a+ib and their representation on 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.

3

Permutations and Combinations

Fundamental principle of counting; Permutation as an arrangement and combination as selection, simple applications

4

Binomial Theorem:

Binomial theorem for positive integral indices. General and middle terms in binomial expansions, simple applications

5

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. Special series ∑n, ∑n2, ∑n3.Arithmetico-Geometric Series, Exponential and Logarithmic Series

6

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 a matrix. Solution of simultaneous linear equations using determinants

7

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.

8

Trigonometry

Trigonometrical identities and equations. Inverse trigonometric functions and their properties. Properties of triangles, including centroid, incentre, circumcentre, and orthocentre., Solution of triangles. Heights and distances

9

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

10

Probability

Probability of an event, addition and multiplication theorems of probability and their applications; Conditional probability; Bayes’ theorem; Probability distribution of a random variate; Binomial and Poisson distributions and their properties

11

Differential Calculus

Polynomials, rational, trigonometric, logarithmic and exponential 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 upto two, Applications of derivatives; Maxima and Minima of functions one variable, tangents and normals, Rolle’s and Langrage’s Mean Value Theorems

12

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; Integral as a limit of sum; Properties of definite integrals. Evaluation of definite integral; Determining areas of the regions bounded by simple curves

13

Differential Equations

Ordinary differential equations, their order and degree; Formation of differential equations; Solutions of differential equations by the method of separation of variables; Solution of Homogeneous and linear differential equations of first order.

14

Co-ordinate Geometry

Review of Cartesian system of rectangular co-ordinates in a plane, distance formula, area of triangle, condition for the collinearity of three points, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes

15

The Straight Line and Pair of Straight Lines

Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line. Equations of internal and external bisectors of angles between two lines, equation of family 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 intersections and angles between two lines.

16

Circles and Family of Circles

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, equation of a circle when the end points of a diameter are given, points of intersection of a line and circle with the centre at the origin and condition for a line to be tangent, equation of a family of circles through the intersection of two circles, condition for two intersecting circles to be orthogonal.

17

Conic Sections

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

18

Vector Algebra

Vector and scalars, addition of two 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.

19

Three-Dimensional Geometry

Distance between two points. Direction cosines of a line joining two points. Cartesian and vector equation of a line. Coplanar and skew lines. Shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, and (iii) a line and a plane. Distance of a point from a plane.

Units

Chapters

Sub-Topics

1

Units and dimensions

Units for measurement, system of units, SI, fundamental and derived units, dimensional analysis

2

Kinematics

Uniform and non-uniform motion, average speed and instantaneous velocity, uniformly accelerated motion, velocity-time, position-time graph, relations for uniformly accelerated motion, Scalars and Vectors, Vector. Addition and subtraction, zero vector, scalar and vector products, Unit Vector, Resolution of a Vector. Relative Velocity, Motion in a plane, Projectile Motion, Uniform Circular Motion.

3

Mechanics

Motion in one dimension, uniform and non-uniform motion, uniformly accelerated motion; Scalars and Vectors, resolution of Vectors, vector properties. Motion in a plane, Projectile motion, Uniform circular motion. Newton’s laws of motion, conservation of linear momentum, Friction; Work-Energy theorem, kinetic energy, potential energy, conservation of energy; elastic collision in one and two dimensions. Centre of mass of a system of particles, centre of mass of a rigid body, rotational motion and torque, angular momentum and its conservation, moments of inertia for various geometries, parallel and perpendicular axes theorem. Universal law of gravitation, acceleration due to gravity, planetary motion, Kepler’s laws, Satellites, gravitational potential and potential energy, and escape velocity.

4

Solids and Fluids

Solids: Elastic properties, Hooke’s law, Young’s modulus, bulk modulus, rigidity modulus. Liquids: Cohesion and adhesion; surface energy and surface tension; flow of fluids; Bernoulli’s theorem and applications; viscosity, Stokes’s law, terminal velocity

5

Oscillations and Waves

Oscillations: Oscillatory motion - periodic and non-periodic motion; simple harmonic motion (SHM), angular SHM, linear harmonic oscillator – both horizontal and vertical; combination of springs – series and parallel, simple pendulum; Expression of energy – potential energy, kinetic energy and total energy; Graphical representation of SHM; Types of oscillations – free, damped, maintained and forced oscillations and resonance. Wave Motion: Properties of waves; Transverse and Longitudinal waves; Superposition of waves, Progressive and Standing waves; Vibration of strings and air columns, beats, Doppler Effect.

6

Heat and Thermodynamics

Heat, work and temperature; Ideal gas laws; Specific heat capacity, Thermal expansion of solids, liquids and gases, Relationship between Cp and Cv for gases; Newton’s law of cooling, black body, Kirchoff’s law, Stafan’s law and Wein’s law, thermodynamic equilibrium, internal energy; Zeroth, first and second law of thermodynamics, thermodynamic processes, Carnot cycle, efficiency of heat engines, refrigerator

7

Electrostatics, Current Electricity, and Magnetostatics

Electric charges and Fields Electrostatic potential and Capacitance Current Electricity Heating effects of current Magnetic effects Magnetostatics

8

Electromagnetic Induction and Electromagnetic Waves

Electromagnetic Induction: Induced e.m.f: Magnetic flux, Faraday’s law, Lenz’s Law and Conservation of Energy, self and mutual inductance. Alternating Current: Impedance and reactance; power in AC circuits; AC voltage applied to resistor, inductor, capacitor, LCR circuits, and resonance, transformer, and AC generator. Electromagnetic Waves: Electromagnetic waves characteristics, electromagnetic spectrum from gamma to radio waves.

9

Kinetic Theory of Gases

Equation of state of a perfect gas, work done on compressing a gas, Kinetic theory of gases - assumptions, the concept of pressure. Kinetic energy and temperature: RMS speed of gas molecules: Degrees of freedom. Law of equipartition of energy, applications to specific heat capacities of gases; Mean free path. Avogadro's number.

10

Ray and Wave Optics

Ray Optics and optical instruments: Reflection and refraction of light by plain spherical mirrors - Total Internal Reflection; optical fibre; deviation and dispersion of light by a prism; lens formula; magnification and resolving power; microscope and telescope. Wave Optics: Huygens principle: Wave nature of light, interference of light waves and Young’s experiment, thin films, Newton’s rings, Diffraction – single slit, grating, Polarization and applications.

11

Modern Physics

Dual nature of radiation and matter: De Broglie relation, Electron emission, photoelectric effect, experimental study, Einstein’s photoelectric equation: Energy quantum of radiation; particle nature of light, the photon, wave nature of matter. Atoms: Alpha-particle scattering and Rutherford’s nuclear model of the atom, atomic spectra, Bohr model of the hydrogen atom; the line spectra of the hydrogen atom. Nuclei: Atomic masses and composition of nucleus; size of the nucleus; mass-energy and nuclear binding energy; nuclear force; radioactivity; nuclear energy Semiconductor materials, devices and simple circuits: Energy bands in solids; classification of metals, conductors and semiconductors; intrinsic semiconductor, extrinsic semiconductor, p-n junction, semiconductor diode, junction diode as a rectifier, junction transistor, transistor as an amplifier.

Units

Chapters

Sub-Topics

1

Basic Chemical Calculations

Density - mole concept - empirical and molecular formula- stoichiometry - volumetry, equivalent and molecular masses, percentage composition

2

Atomic structure & periodicity

Atomic models, sub-atomic particles, orbital shapes, Pauli’s exclusion, Hund’s rule, Aufbau principle, de-Broglie relation, Heisenberg’s uncertainty, electronic configuration, and periodic properties.

3

Chemical bonding

Ionic bonding, lattice energy-Born-Haber cycle, covalent bond - Fajan’s Rule - VSEPR theory - hybridisation, valence bond and molecular orbital theory, coordinate, metallic, and hydrogen bonding

4

S-block and hydrogen

Hydrogen, isotopes, liquid hydrogen as fuel, alkali metals, oxides and hydroxides, extraction and properties of lithium, sodium, and potassium. Group 2 elements and their properties.

5

P-block elements

Boron - borax, boranes, diboranes. Carbon - allotropes, oxides, carbides, halides, and sulphides of carbon group- silicon and silicates - silicones, Nitrogen - Fixation - compounds of nitrogen, Phosphorus - allotropes and compounds. Oxygen - oxides and peroxide. Sulphur - its compounds - inter-halogen compounds.

6

d and f block elements

d-block elements configuration and properties - transition elements, chromium, copper, zinc, silver, interstitial compounds and alloys, f-block elements and extraction, lanthanides and actinides

7

Solid state

Solids - amorphous and crystalline, classification of crystalline - unit cell, Miller indices - packing efficiency, unit cell dimensions, crystal structure, ionic crystals, imperfections in solids, electric and magnetic properties.

8

Coordination compounds

Terminology in coordination- isomerism, Werner, VBT, CFT theories - Bio- coordination compounds.

9

Gaseous State & Surface Chemistry

Gaseous state and gas laws, deviation- van der Waal’s constants - Joule-Thomson effect - liquefaction of gases, theory of catalysis, colloids and emulsions.

10

Colligative properties

Lowering of vapour pressure, Depression of freezing point, Elevation in boiling point, Osmotic pressure, abnormality - dissociation and association

11

Electrochemistry

Faraday’s laws - specific, equivalent and molar conductances, Kohlrausch’s law and applications- electrode potentials - EMF, electrochemical and galvanic cells, Nernst equation, batteries, fuel cells, corrosion and its prevention.

12

Thermodynamics

First and second law- internal energy, enthalpy, entropy, free energy changes - specific heats at constant pressure and constant volume - enthalpy of combustion, formation, and neutralisation, Kirchhoff law- Hess’s law - bond energy

13

Chemical and Ionic Equilibria

Law of chemical equilibrium, homogeneous and heterogeneous equilibrium, Le Chatelier’s principle, equilibrium constants, factors affecting- Ionic equilibrium, ionisation of acids and bases, buffer solutions, pH -solubility of sparingly soluble salts

14

Chemical kinetics

Order, molecularity, rate, and rate constant- first and second order reactions - temperature dependence, factors influencing rate of reaction, integrated rate equation, collision theory of chemical reaction

15

Basic Organic Chemistry

Classification, functional groups, nomenclature, and isomerism, types of organic reactions, mechanism, purification, qualitative and quantitative analysis, carbocation, carbanion, and free radical, electron displacement in covalent bond

16

Hydrocarbons & Polymers

IUPAC nomenclature, alkanes -alkynes - aromatic hydrocarbons, nomenclature, preparation, physical and chemical properties, uses. Polymerization - types, molecular mass, biodegradability, and commercial polymers.

17

Organic halogen compounds

Nature of C-X bond- preparation - properties and reactions of alkyl and aryl halides- polyhalogen compounds - substitution and elimination - mechanism- Grignard reagents.

18

Stereochemistry and Organic Nitrogen Compounds

Preparation - properties and uses of Aliphatic and aromatic nitro compounds-aliphatic and aromatic amines, nitriles, Diazonium salts- 1°, 2°, and 3° amines - distinction - Optical activity.

19

Organic functional groups- hydroxyl, carbonyl compounds, and ethers

Nomenclature, preparation, properties, and uses of alcohols, ethers, aldehydes, ketones, aliphatic carboxylic acids, benzoic acid - salicylic acid.

20

Biomolecules and Environmental Chemistry

Carbohydrates, proteins, amino acids - enzymes, vitamins, and nucleic acids - lipids. Pollution. - air, water, and soil - industrial waste, acid rain, greenhouse effect, global warming, Strategies to control pollution.

Unit

Topics

1

Articles

2

Synonyms

3

Antonyms

4

Prepositions

5

Verbs

Subject

No. Of Questions

Marks

Maths

40

120

Physics

30

90

Chemistry

25

75

English

5

15

Total

100 Questions

300 Marks

Subject

Books to Follow

Physics

• Objective Physics (Arihant)
• Concepts of Physics Vol 1 & 2 (HC Verma)
• Fundamentals of Physics (Halliday, Resnick, Walker)

Chemistry

• Organic Chemistry (O.P. Tandon)
• Inorganic Chemistry (O.P. Tandon)
• Numerical Chemistry (P. Bahadur)
• NCERT Chemistry (Class 11 & 12)

Mathematics

• Mathematics for Class 11 & 12 (R.D. Sharma)
• Higher Algebra (Hall Knight)
• NCERT Mathematics (Class 11 & 12)