How to Prepare for IIT JAM 2025 Exam in 2 Months?

Week of Study

Topic to Study

Sub-topic to Study

1

Mechanics and General Properties of Matter-I

Newton’s Laws of Motion and Applications

Kepler’s Law Planetary Motion

Polar and Cylindrical Coordinate Systems,

Conservative and Non-Conservative Forces

Centrifugal and Coriolis Forces

Motion Under a Central Force

Uniformly Rotating Frame

Gravitational Law and Field

Velocity and Acceleration in Cartesian

2

Mechanics and General Properties of Matter-II

System of Particles

Conservation of Linear and Angular Momentum

Conservation of Energy

Center of Mass

Equation of Motion of the Center of Mass

Elastic and Inelastic Collisions

Fixed Axis Rotations

Rigid Body Motion

Rotation and Translation

Parallel and Perpendicular Axes Theorem

Moments of Inertia and Products of Inertia

Principal Moments and Axes

Equation of Continuity

Kinematics of Moving Fluids

Euler’s Equation

Bernoulli’s Theorem

3

Mathematical Methods-I

Stokes’ Theorem

Green’s Theorem

Divergence Theorem

Multiple Integrals

Vector Calculus

Vector Algebra

Fourier Series

Taylor Expansion

Imperfect and Perfect Differentials

Jacobian Matrix

Partial Derivatives

Calculus of Single and Multiple Variables

4

Mathematical Methods-II

 First Order Equations

Linear Second Order Differential Equations with Constant Coefficients

Algebra of Complex Numbers

Matrices and Determinants

Week of Study

Topic to Study

Sub-topic to Study

5

Electricity and Magnetism-I

Coulomb’s Law

Gauss’s Law

Electric Field and Potential

Electrostatic Boundary Conditions

Solution of Laplace’s Equation for Simple Cases

Capacitors

Conductors

Dielectric Polarization

Electrostatic Energy

Volume and Surface Charges

6

Oscillations, Waves and Optics-I

Differential Equation for Simple Harmonic Oscillator and Its General Solution (Brush up on the Simple Harmonic Motion definition)

Superposition of Two or More Simple Harmonic Oscillator

Damped and Forced Oscillators

Resonance

7

Oscillations, Waves and Optics-II

Energy Density and Energy Transmission in Waves

Wave Equation

Group Velocity and Phase Velocity

Sound Waves in Media

Doppler Effect

Wave Equation

Fermat’s Principle

8

Oscillations, Waves and Optics-III

General Theory of Image Formation

Thick Lens, Thin Lens and Lens Combinations

Fraunhofer Diffraction

Rayleigh Criterion and Resolving Power

Diffraction Gratings

Polarization

Double Refraction and Optical Rotation

Week of Study

Topic to Study

Sub-topic to Study

1

General Biology

Heredity

Taxonomy

Conservation

Genetic Variation

Principles of Ecology

Techniques in Modern Biology

Evolution

2

Molecular Biology

DNA

RNA

Proteins, Lipids and Membranes

Replication

Operon Model

Gene Transfer

3

Basic Biotechnology

Tissue Culture

Application of Enzymes

Antigen-Antibody Interaction

Antibody Production

Diagnostic Aids

4

Biochemistry and Physiology

Carbohydrates

Proteins

Lipids

Nucleic

Acids

Enzymes

Vitamins

Hormones

Metabolism-Glycolysis

TCA Cycle

Oxidative Phosphorylation

Photosynthesis Nitrogen Fixation

Fertilisation and Osmoregulation

Vertebrates-Nervous System

Endocrine System

Vascular System

Immune System

Digestive System and Reproductive System

Week of Study

Topic to Study

Sub-topic to Study

5

Cell Biology

Cell Cycle

Cytoskeletal Elements

Mitochondria

Endoplasmic Reticulum

Chloroplast

Golgi Apparatus

Signaling

6

Chemical Thermodynamics (First and Second Law)

-

Chemical Kinetics (Zero, First, Second and Third Order Reactions)

-

Photochemistry

-

Electrochemistry

-

7

Microbiology

Isolation

Cultivation

Structural Features of Virus

Bacteria

Fungi

Protozoa

Pathogenic Microorganisms

8

Bohr’s Theory and Schrodinger Wave Equation

-

Periodicity in Properties

-

Chemical Bonding

-

Properties Of S, P, D and F Block Elements

-

Complex Formation

-

Coordination Compounds

-

Chemical Equilibria

-

Week of Study

Topic to Study

Sub-topic to Study

1

Periodic Table [Inorganic Chemistry]

Periodic Classification of Elements and Periodicity in Properties

General Methods of Isolation and Purification of Elements

2

Chemical Bonding and Shapes of Compounds [Inorganic Chemistry]

Types of Bonding

VSEPR Theory and Shapes of Molecules

Hybridisation

Dipole Moment

Ionic Solids

Structure of NaCl, CsCl, Diamond and Graphite

Lattice Energy

3

Transition Metals (D Block) [Inorganic Chemistry]

Characteristics of 3D Elements, Oxide, Hydroxide and Salts of First Row Metals

Coordination Complexes: Structure, Isomerism, Reaction Mechanism and Electronic Spectra

VB, Mo and Crystal Field Theoretical Approaches for Structure, Color and Magnetic Properties of Metal Complexes

Organometallic Compounds Having Ligands with Back Bonding Capabilities such as Metal Carbonyls, Carbenes, Nitrosyls and Metallocene, Homogeneous Catalysis

4

Main Group Elements (S and P Blocks)

[Inorganic Chemistry]

General Concepts on Group Relationships and Gradation in Properties

Structure of Electron Deficient

Compounds Involving Main Group Elements

Week of Study

Topic to Study

Sub-topic to Study

5

Solid State [Physical Chemistry]

Crystals and Crystal Systems

X-Rays

NaCl and KCl Structures

Atomic and Ionic Radii

Radius Ratio Rules

Lattice Energy

Born-Haber Cycle

Isomorphism

Heat Capacity of Solids

6

Chemical Thermodynamics [Physical Chemistry]

Reversible and Irreversible Processes

First Law and Its Application to Ideal and Non-Ideal Gases

Thermochemistry

Entropy and Free Energy

7

Theory of Gases [Physical Chemistry]

Equation of State for Ideal and Non-Ideal (Van Der Waals) Gases

Kinetic Theory of Gases

Maxwell- Boltzmann Distribution Law

Equipartition of Energy

8

Atomic and Molecular Structure [Physical Chemistry]

Fundamental Particles

Bohr’s Theory of Hydrogen-Like Atom

Wave-Particle Duality

Uncertainty Principle

Schrodinger’s Wave Equation

Quantum Numbers

Shapes of Orbitals

Hund’s Rule and Pauli’s Exclusion Principle

Electronic Configuration of Simple Homonuclear Diatomic Molecules

Week of Study

Topic to Study

Sub-topic to Study

1

Sequences and Series

Convergence of Sequences of Real Numbers

Comparison, Root and Ratio Tests for Convergence of Series of Real Numbers

2

Differential Calculus

Limits

Continuity and Differentiability of Functions of One and Two Variables

Rolle’s Theorem

Mean Value Theorems

Taylor’s Theorem

Indeterminate Forms

Maxima and Minima of Functions of One and Two Variables

3

Integral Calculus

Fundamental Theorems of Integral Calculus

Double and Triple Integrals

Applications of Definite Integrals

Arc Lengths, Areas and Volumes

4

Matrices

Rank

Inverse of a Matrix

Systems of Linear Equations

Linear Transformations

Eigenvalues and Eigenvectors

Cayley Hamilton Theorem

Symmetric, Skew-Symmetric and Orthogonal Matrices

Week of Study

Topic to Study

Sub-topic to Study

5

Random Variables

Probability Mass Function

Probability Density Function and Cumulative Distribution Functions

Distribution of a Function of a Random Variable

Mathematical Expectation

Moments and Moment Generating Function

Chebyshev’s Inequality

6

Standard Distributions

Binomial, Negative Binomial

Geometric, Poisson, Hypergeometric

Uniform, Exponential, Gamma, Beta and Normal Distributions

Poisson and Normal Approximations of a Binomial Distribution

7

Joint Distributions

Joint, Marginal and Conditional Distributions

Distribution of Functions of Random Variables

Joint Moment Generating Function

Product Moments, Correlation, Simple Linear Regression

Independence of Random Variables

8

Probability

Axiomatic Definition of Probability and Properties, Conditional Probability, Multiplication Rule

Theorem of Total Probability

Bayes’ Theorem and Independence of Events

Week of Study

Topic to Study

Sub-topic to Study

1

The Planet Earth

Origin of the Solar System and the Earth

Geosphere and the Composition of the Earth

Shape and Size of the Earth

Earth-Moon System

Formation of Continents and Oceans

Dating Rocks and Age of the Earth

Volcanism and Volcanic Landforms

Interior of Earth

Earthquakes, Earth’s Magnetism and Gravity

Isostasy, Elements of Plate Tectonics, Orogenic Cycles

2

Structural Geology

Concept of Stratum, Contour, Outcrop Patterns

Maps and Cross Sections

Dip and Strike

Classification and Origin of Folds, Faults, Joints, Unconformities, Foliations and Lineation

Shear Zones

Stereographic and Equal Area Projections of Planes and Lines

Computation of True Thickness of Beds from Outcrops and Bore-Holes

3

Paleontology

Major Steps in the Evolution of Life Forms

Fossils; their Mode of Preservation and Utility

Morphological Characters

Major Evolutionary Trends and Ages of Important Groups of Animals - Brachiopod, Mollusca, Trilobite, Graptolitoidea, Anthozoa, Echinodermata

Gondwana Plant Fossils

Elementary Idea of Vertebrate Fossils in India

4

Geomorphology

Weathering and Erosion

Transportation and Deposition Due to Wind, Ice, River, Sea, and Resulting Landforms

Structurally Controlled Landforms

Week of Study

Topic to Study

Sub-topic to Study

5

Petrology

Definition and Classification of Rocks

Igneous Rocks-Forms of Igneous Bodies

Crystallization from Magma

Classification, Association and Genesis of Igneous Rocks

Sedimentary Rocks-Classification, Texture and Structure, Size and Shape of Sedimentary Bodies

Metamorphic Rocks - Classification, Facies, Zones and Texture

Characteristic Mineral Assemblages of Perlites in the Burrovian Zones and Mafic Rocks in Common Facies

6

Mineralogy

Symmetry and Forms in Common Crystal Classes

Physical Properties of Minerals

Isomorphism and Polymorphism

Classification of Minerals, Structure of Silicates

Mineralogy of Common Rock-Forming Minerals

Mode of Occurrence of Minerals in Rocks

Transmitted Polarized Light Microscopy and Optical Properties of Uniaxial and Biaxial Minerals

7

Economic Geology

Properties of Common Economic Minerals

General Processes of Formation of Mineral Deposits

Physical Characters, Mode of Occurrence and Distribution in India Both of Metallic and Nonmetallic Mineral Deposits

Coal and Petroleum Occurrences in India

8

Stratigraphy

Principles of Stratigraphy, Litho-, Chrono- and Biostratigraphy

Classification, Distribution and Classification of the Stratigraphic Horizons of India from Archaean to Recent

Week of Study

Topic to Study

Sub-topic to Study

1

Differential Equations-I

Ordinary Differential Equations of the First Order of the Form Y’=F (X, Y)

Bernoulli’s Equation

Exact Differential Equations

Integrating Factor

2

Differential Equations-II

Orthogonal Trajectories

Homogeneous Differential Equations

Variable Separable Equations

3

Differential Equations-III

Linear Differential Equations of Second Order with Constant Coefficients

Method of Variation of Parameters

Cauchy-Euler Equation

4

Functions of One Real Variable

Limit

Continuity

Intermediate Value Property

Differentiation

Rolle’s Theorem

Mean Value Theorem

L’Hospital Rule

Taylor’s Theorem

Maxima and Minima

Week of Study

Topic to Study

Sub-topic to Study

5

Integral Calculus-I

Integration as The Inverse Process of Differentiation

Definite Integrals and Their Properties

Fundamental Theorem of Calculus

6

Integral Calculus-II

Double and Triple Integrals

Change of Order of Integration

7

Integral Calculus-III

Calculating Surface Areas and Volumes Using Double Integrals

Calculating Volumes Using Triple Integrals

8

Functions of Two or Three Real Variables

Limit

Continuity

Partial Derivatives

Differentiability

Maxima and Minima

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