IISER 2024 Syllabus: Biology, Physics, Chemistry & Mathematics

Sets and Logic

- Representation of sets - Various operations on sets - Venn diagram - Cartesian products - Equivalence relation - Types of functions - Composition and inverse of functions - Permutations and combinations - Binomial theorem

Basic counting techniques

- Fundamental principles of counting - Permutations and combinations - Applications

Complex numbers, linear and quadratic equations

- Representation of complex numbers - Polar representation and Argand plane - Algebra of complex numbers - Quadratic equations - Relation between roots and coefficients - Linear inequalities - Graphical representation

Trigonometric functions

- Measures of angles and their conversions - Trigonometric functions and identities - Inverse trigonometric functions - Graphs of trigonometric functions - Applications

Vectors

- Magnitude and direction of vectors - Dot and cross products - Projection of vectors - Types of vectors - Addition and multiplication of vectors

Matrices & determinants

- Concept, notation, and types of matrices - Properties of matrices - Invertible matrices - Determinants and their properties - Adjoint and inverse of matrices - Applications

Coordinate geometry

- Cartesian system of rectangular coordinates - Equations of lines and conic sections - Distance between points - Section formula - Angle between lines and planes - Equation of planes - Distance of a point from a plane

Three-dimensional geometry

- Coordinate axes and planes - Distance between points - Direction cosines and ratios - Equations of lines and planes - Angle between lines and planes - Distance between lines - Cartesian and vector equation of a plane

Sequences & series

- Arithmetic and Geometric progressions - Sums of finite and infinite series - Arithmetic mean and geometric mean - Relation between A.M and G.M

Limit & continuity

- Limits and continuity of functions - Algebraic properties of limits - Differentiation - Application of derivatives - Integration - Applications of integration

Differential equations

- Definition and solution of differential equations - Homogeneous differential equations - Separation of variables - Solution of first order and degree equations

Statistics, Probability & Linear Programming

- Measure of dispersion - Probability theory - Axiomatic probability - Conditional probability - Baye's theorem

Units and Measurements

- International system of units - Significant figures - Dimensions of physical quantities - Dimensional analysis - Kinematic equations - Projectile motion

Laws of Motion

- Law of inertia - Newton's laws - Conservation of momentum - Circular motion

Work, Energy and Power

- Work-energy theorem - Kinetic and potential energy - Power - Collisions

System of Particles and Rotational Motion

- Centre of mass - Linear and angular momentum - Torque - Equilibrium of rigid bodies - Moment of inertia

Gravitation

- Kepler's laws - Universal law of gravitation - Gravitational potential energy - Earth satellites

Mechanical Properties of Solids

- Stress and strain - Hooke's law - Elastic moduli

Mechanical Properties of Fluids

- Pressure - Bernoulli's principle - Viscosity - Surface tension

Thermal Properties of Matter

- Temperature and heat - Thermal expansion - Specific heat capacity - Change of state - Heat transfer

Thermodynamics

- Zeroth and first law of thermodynamics - Thermodynamic processes - Second law of thermodynamics - Carnot engine

Kinetic Theory

- Behaviour of gases - Kinetic theory of an ideal gas - Specific heat capacity

Oscillations

- Simple harmonic motion - Pendulum

Waves

- Transverse and longitudinal waves - Superposition of waves - Reflection and refraction - Diffraction

Electric Charges and Fields

- Coulomb's law - Electric field - Gauss's law - Electric potential - Capacitance

Current Electricity

- Ohm's law - Resistance - Cells and emf - Kirchhoff's rules

Moving Charges and Magnetism

- Magnetic force - Biot-Savart law - Ampere's law - Electromagnetic induction

Electromagnetic Waves

- Displacement current - Electromagnetic spectrum

Ray Optics and Optical Instruments

- Reflection and refraction - Total internal reflection - Optical instruments

Wave Optics

- Interference - Diffraction - Polarisation

Dual Nature of Radiation and Matter

- Photoelectric effect - Photon - De Broglie's hypothesis - Atomic spectra

Atoms

- Rutherford's model - Bohr model - Atomic spectra

Nuclei

- Nuclear forces - Radioactivity - Nuclear energy

Semiconductor Electronics

- p-n junction - Semiconductor diode - Rectification

Some Basic Concepts of Chemistry

- Matter and its nature - Dalton's atomic theory - Atom, molecule, element, and compound - Laws of chemical combination - Atomic and molecular masses - Mole concept - Percentage composition - Empirical and molecular formulae - Chemical equations - Stoichiometry

Structure of the Atom

- Discovery of sub-atomic particles - Atomic models - Bohr’s model of atom - Quantum mechanical model of atom

Classification of Elements and Periodicity

- Genesis of periodic classification - Modern periodic law - Periodic table - Electronic configurations of elements - s-, p-, d-, f-blocks - Periodic trends in properties of elements

Chemical Bonding and Molecular Structure

- Kössel-Lewis approach - Ionic or electrovalent bond - Valence shell electron pair repulsion (VSEPR) theory - Valence bond theory - Hybridisation - Molecular orbital theory - Bonding in some homonuclear diatomic molecules - Hydrogen bonding

The d- & f-block elements

- Position in the periodic table - Electronic configurations - General properties - Some important compounds - Lanthanoids and actinoids - Applications

Coordination compounds

- Werner's theory - Definitions - Nomenclature - Isomerism - Bonding - Metal carbonyls - Importance and applications

Thermodynamics

- Terms - Measurement of ΔU and ΔH - Calorimetry - Enthalpy change - Reaction enthalpy - Spontaneity - Gibbs energy change and equilibrium

Equilibrium

- Physical and chemical equilibrium - Law of chemical equilibrium - Homogeneous and heterogeneous equilibria - Applications - Ionic equilibrium - Acids, bases, and salts - Ionization - Buffer solutions - Solubility equilibria

Redox Reactions

- Oxidation and reduction - Electron transfer reactions - Oxidation number - Electrode processes

Solutions

- Types - Concentration expressions - Solubility - Vapour pressure - Ideal and non-ideal solutions - Colligative properties - Determination of molar mass - Abnormal molar masses

Electrochemistry

- Electrochemical cells - Galvanic cells - Nernst equation - Conductance of electrolytic solutions - Electrolytic cells and electrolysis - Batteries - Fuel cells - Corrosion

Chemical Kinetics

- Rate of a chemical reaction - Factors influencing rate - Integrated rate equations - Temperature dependence - Collision theory

Organic Chemistry

- Basic principles and techniques - Tetravalence of carbon - Shapes of organic compounds - Classification - Nomenclature - Isomerism - Organic reaction mechanism - Purification methods - Qualitative and quantitative analysis

Hydrocarbons

- Classification - Alkanes, alkenes, alkynes - Aromatic hydrocarbons - Carcinogenicity and toxicity

Haloalkanes and haloarenes

- Classification - Nomenclature - Preparation - Physical and chemical properties

Alcohols, phenols, and ethers

- Classification - Nomenclature - Structures of functional groups - Preparation - Properties

Aldehydes, ketones, and carboxylic acids

- Nomenclature - Structure of carbonyl group - Preparation - Properties - Uses

Organic compounds containing nitrogen

- Structure of amines - Classification - Nomenclature - Preparation - Properties - Diazonium salts

Biomolecules

- Carbohydrates, proteins, enzymes, vitamins, nucleic acids, hormones

Diversity In the Living World

• Diversity in the living world 
• Taxonomic categories 
• Biological classification: Kingdoms (Monera, Protista, Fungi, Plantae, and Animalia) 
• Viruses, Viroids and Lichens

Structural Organisation In Plants And Animals

• Morphology of flowering plants: The Root, The Stem, The Leaf, The Inflorescence, The Flower, The Fruit, The Seed, Semi-technical Description of a Typical, Flowering Plant, Description of Some Important Families 
• Anatomy of flowering plants: The Tissue System, Anatomy of Dicotyledonous and Monocotyledonous Plants 
• Structural organisation in animals: Organ and Organ System, Amphibian-Frog

Cell: Structure And Functions

• A Cell, The Cell Theory, An Overview of Cell, Prokaryotic Cells, Eukaryotic Cells 
• Biomolecules: Analysis of Chemical Composition of organisms, Primary and Secondary Metabolites, Biomacromolecules, Proteins, Polysaccharides, Nucleic Acids, Structure of Proteins, Enzymes 
• Cell cycle and cell division: Cell Cycle, Mitosis and Meiosis and its significance

Plant Physiology

• Photosynthesis in higher plants 
• Respiration in plants 
• Plant growth and development

Human Physiology

• Breathing and exchange of gases: Respiratory Organs, Mechanism of Breathing, Exchange of Gases, Transport of Gases, Regulation of Respiration, Disorders of Respiratory System 
• Body fluids and circulation: Tissue Fluids-Blood, Lymph, Circulatory Pathways, Double Circulation, Regulation of Cardiac Activity, Disorders of Circulatory System 
• Excretory products and their elimination: Human Excretory System, Urine Formation, Function of the Tubules, Mechanism of Concentration of the Filtrate, Regulation of Kidney Function, Micturition, Role of other Organs in Excretion, Disorders of the Excretory System 
• Locomotion and movement: Types of Movement, Muscle, Skeletal System, Joints, Disorders of Muscular and Skeletal System 
• Neural control and coordination: Neural System, Human Neural System, Neuron as Structural and Functional Unit of Neural System, Central Neural System 
• Chemical coordination and integration: Endocrine Glands and Hormones, Human Endocrine System, Hormones of Heart, Kidney and Gastrointestinal Tract, Mechanism of Hormone Action

Reproduction

• Sexual reproduction in flowering plants: Flower structure, Angiosperms, Prefertilisation: Structures and Events, Double Fertilisation, Post-fertilisation: Structures and Events, Apomixis and Polyembryony 
• Human reproduction: The Male Reproductive System, The Female Reproductive System, Gametogenesis, Menstrual Cycle, Fertilisation and Implantation, Pregnancy and Embryonic Development, Parturition and Lactation 
• Reproductive health: Reproductive Health – Problems and Strategies, Population Explosion and Birth Control, Medical Termination of Pregnancy, Sexually Transmitted Diseases, Infertility

Genetics And Evolution

• Principles of inheritance and variation: Mendel’s Laws of Inheritance, Inheritance of One Gene, Inheritance of Two Genes, Sex Determination, Mutation, Genetic Disorders 
• Molecular basis of inheritance: The DNA, The Search for Genetic Material, RNA World, Replication, Transcription, Genetic Code, Translation, Regulation of Gene Expression, Human Genome Project, DNA Fingerprinting 
• Evolution: Origin of Life, Evolution of Life Forms – A Theory, Evidence for Evolution, Adaptive Radiation, Biological Evolution, Mechanism of Evolution, Hardy – Weinberg Principle, Evolution, Origin and Evolution of Man

Biology In Human Welfare

• Human health and disease: Common Diseases in Humans, Immunity, AIDS, Cancer, Drugs and Alcohol Abuse 
• Microbes in human welfare: Microbes in Household Products, Microbes in Industrial Products, Microbes in Sewage Treatment, Microbes in Production of Biogas, Microbes as Biocontrol Agents, Microbes as Biofertilisers

Biotechnology

• Biotechnology: principles and processes: Principles of Biotechnology, Tools of Recombinant DNA Technology, Processes of Recombinant DNA Technology 
• Biotechnology and its application: Biotechnological Applications in Agriculture and Medicine, Transgenic Animals, Ethical Issues

Ecology

• Organisms and populations: Populations, Logistic growth, Population interactions 
• Ecosystem: Ecosystem–Structure and Function, Productivity, Decomposition, Energy Flow, Ecological Pyramids 
• Biodiversity and conservation: Biodiversity and Biodiversity conservation