Grade 12 IIT JEE
May 27, 2025 2025-07-21 18:34Grade 12 IIT JEE
Course Description
The Grade 12 JEE course for Physics, Chemistry, and Mathematics (PCM) is structured to deliver a comprehensive and rigorous preparation for one of the toughest engineering entrance exams. The curriculum systematically advances through the critical concepts in all three subjects, blending theoretical understanding with advanced problem-solving techniques. It is designed to strengthen conceptual clarity, sharpen analytical skills, and enhance application-oriented learning to meet the challenges of JEE Main and Advanced.
Learning Objective
The course aims to equip students with a thorough grasp of core principles across Physics, Chemistry, and Mathematics. Students will develop strong problem-solving strategies, improve speed and accuracy, and learn to handle complex multi-concept questions. Focus will be on building analytical thinking, logical reasoning, and the ability to apply fundamental concepts to novel situations, all essential for excelling in JEE and other competitive exams.
What Will I Learn?
Students will explore advanced topics in Physics such as electrostatics, current electricity, magnetism, optics, dual nature of matter, atoms, nuclei, and semiconductors. Chemistry will cover the structure of solids, chemical kinetics, electrochemistry, surface chemistry, p-block and d-block elements, coordination compounds, organic reactions, and biomolecules. In Mathematics, students will master calculus including limits, continuity, differentiability, and integrals, differential equations, matrices, determinants, probability, vectors, and three-dimensional geometry. The course is designed to build confidence through systematic practice, comprehensive concept coverage, and exposure to JEE-level problem-solving.
Additional Info

Practice
Regular exercises and interactive activities to reinforce key concepts in each subject.

Doubt-Solving
Dedicated sessions to address and clarify any questions or difficulties students encounter.

Reports
Detailed reports on experiments and projects to track progress and understanding.
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Physics
Chemistry
Mathematics
Electrostatics
Electric charge and its Properties
Charging of a body Coulomb's Law
Vector form of Coulomb's Law
Principle of Superposition
Electrostatic Equilibrium
Introduction to Electric field
Electric field intensity
Electric field due to a point charge
Electric field due to uniformly charged Arc
Electric field due to uniformly charged Ring on its axis
Electric field due to uniformly charged wire
Electric field due to uniformly charged infinite non-conducting sheet
Electric field due to disc
Electric field due to uniformly charged thin spherical shell
Electric field due to a Uniformly charged non–conducting sphere
Electrostatic Potential and its properties
Potential due to point charge
Electric potential due to system of charges
Potential due to ring
Potential due to uniformly charged disc
Potential Due To Uniformly Charged Spherical shell
Potential Due To Uniformly Charged Solid Sphere
Potential Difference
Potential difference due to infinitely long wire
Potential difference due to infinitely long thin sheet
Equipotential surfaces
Electrical potential energy
Electrostatic Potential Energy of a System of Charges
Relation between Electric Field Intensity and Electric Potential
Electric Dipole
Electric field due to a dipole at equatorial, axial position and at General point
Electric potential due to a dipole at equatorial, axial position and at General point
Dipole in uniform electric field
Force on dipole in Non-uniform electric field
Electric lines of Force
Solid Angle
Electric Flux
Gauss' Theorem and its application
Conductors and their properties
Electrostatic pressure on the surface of conductor
Electrostatic Shielding
Sharing of charge
Electric field due to conducting and non-conducting uniformly charged infinite sheets
Van de graff generator
Current Electricity
Introduction of Current Electricity and Electric Current
Conductors
Insulator
Semiconductors
Current Density
Drift Velocity
Relation between I and V
Ohm's Law
Resistance and factors affecting it
Resistivity and factors affecting it
Conductivity
Temperature dependence of Resistivity and Resistance
Combination of Resistors
Electric Power
Cell
Electromotive Force (EMF)
Relative Potential
Kirchhoff's Laws
Wheatstone Bridge (4 Terminal network)
Unbalanced Wheatstone bridge (Star Delta Conversions)
Series combination of cells
Parallel combinations of cells
Mixed combinations of cells
Galvanometer
Ammeter
Voltmeter
Current Sensitivity
Potentiometer
Metre Bridge
Colour coding of Resistance
Capacitor
Introduction of Capacitor
Capacitance of an isolated conductor
Potential energy of an Isolated Conductor
Capacitance of an isolated spherical conductor
Sharing of Charges on joining two conductors
Capacitor
Parallel Plate Capacitor
Capacitors with Dielectric
Circuit solution for R-C Circuit
Distribution of charges on connecting two charged capacitors
Combination of Capacitors (Series, Parallel and Mixed combination)
Charging of a Capacitor
Discharging of a Capacitor
Combination of Parallel Plates (Concept of Multi Capacitor)
Spherical Capacitors
Cylindrical Capacitor
Magnetic Effects of Current and Moving Charge
Oersted’s experiment and observation
Frame dependence of B
Biot-Savart's law and its vector form
B due to a point charge
Magnetic field due to straight wire
Magnetic field due to circular loop
Magnetic field on the axis of circular loop
Solenoid
Application of Ampere's Law (Hollow current carrying long cylinder)
Application of Ampere's Law (Solid current carrying long cylinder)
Application of Ampere's Law (Toroid)
Magnetic Moment of Current Carrying Coil (Loop)
Current and Magnetic field due to Circular motion of a Charge
Magnetic Force on moving charges
Motion of Charged particles under the effect of magnetic force
Helical Path
Motion of a charged particle in combined electric and magnetic field
Magnetic Force on a current carrying wire
Right Hand Palm Rule and Fleming Left hand Rule
Point of Application of magnetic force
Magnetic force between two parallel infinite wires
Torque on a Current loop
Moving coil galvanometer
Current sensitivity
Voltage sensitivity
Magnetism & Magnetic Material
Magnet and Magnetism
Pole strength
Magnetic dipole and Magnetic dipole moment
Magnetic field and strength of magnetic field
B due to single pole
B due to Bar magnet
Magnetic lines of force of a Bar Magnet
Magnet in an external uniform and non-uniform magnetic field
Earth's Magnetism (Terrestrial Magnetism)
Elements of the Earth's Magnetism
Tangent Galvanometer
Deflection Magnetometer
Magnetic Substances and their properties
Classification of Magnetic Materials
Important terms used in magnetism
Curie temperature
Explanation of Dia, Para and Ferromagnetism on the basis of atomic model of Magnetism
Hysteresis (Retentivity & Coercivity)
Electromagnets
Electromagnetic Induction
Magnetic Flux
Introduction Of Electromagnetic Induction
Faraday's Experiments
Faraday's Law Of Electromagnetic Induction
Lenz's Law Of Electromagnetic Induction
Induced EMF
Current and Change in a Circuit
Fleming's Right Hand Rule
Direction of Induced EMF and Current
Motional EMF
Motional EMF on the basis of Lorentz Force
Induced EMF Due To Rotation of Rod
Rotation of a coil and due to Rotating Disc
Rectangular coil in a Uniform Magnetic Field
Fixed loop in a time varying Magnetic field
Self Induction
Self Inductance of Solenoid
Inductor
Energy Stored In an Inductor
Energy Density
Growth and Decay of Current in Series R-L Circuit
Grouping Of Inductors
Mutual Inductance
Eddy current and its Uses
Generator or Dynamo
Electric Motor
L-C Oscillations
Alternating Current and E.M. Waves
Alternating and Direct Current
Mean Or Average Value Of AC
Peak And RMS Value Of Alternating Current
AC Sinusoidal Source
Power Consumed in an AC
Power Factor
Impedance
Reactance
Phase And Phasor Diagrams
AC Circuit Containing Pure Resistor
AC Circuit Containing Pure Capacitor
AC Circuit Containing Pure Inductor
Series R-C Circuit
Series R-L Circuit
Choke Coil
Series L-C Circuit
Series LCR - Circuit
Resonance
Admittance
Susceptance and Conductance
Half-Power points
Frequencies
Band Width and Quality Factor
Sharpness of Resonance
Form factor
Transformer and its Uses
Power In AC Circuit
Introduction to Electromagnetic waves
Displacement Current
Maxwell Equations
Sources of EM Waves
Nature of EM Waves
Refractive Index
Energy and Momentum
Radiation Pressure
Electromagnetic Spectrum
Ray Optics and Optical Instruments
Introduction to Optics and Reflection of Light
Reflection By Plane Mirrors (Image Formation)
Reflection By Plane Mirrors
Field of view
Relation between Velocity of object and Image
Image formed by two Plane Mirrors
Spherical Mirrors and Associated Terms
Rules For Image Formation By Spherical Mirror
Image Formation By Spherical Mirrors
Use of Spherical Mirror
New Cartesian Sign Convention
Relation Between Radius of Curvature and Focal Length
Mirror Formula
Linear Magnification
Velocity of Image of Moving Object (Spherical Mirror)
Combination of Mirrors Problem
Cutting of mirror Problem
Introduction of Refraction
Refractive Index and Laws of Refraction
Deviation of Ray due to Refraction
Principle of Reversibility of Light
Refraction From Rectangular Glass Slab (Lateral Shift)
Refraction Through Multiple Parallel Slabs
Real and Apparent Depth
Normal Shift
Total Internal Reflection (TIR) in Prism
Application of TIR
Refraction Through Prism
Dispersion of Light
Refraction at Spherical Surfaces
Velocity of Spherical Refraction
Thin Lens
Terms related to lens
Rules for image formation by the lens
Images formed by convex and Concave lenses
Lens Makers Formula
Sign Convention For Lens
Transverse or Lateral Magnification
Velocity of Image in Lens
Displacement Method
Power of Lens
Combination of lenses
Combination of lens and Mirror
Silvering of Lens
Cutting of lens
Natural phenomena of Refraction
Human Eye
Simple Microscope
Compound Microscope
Astronomical Telescope
Terrestrial Telescope
Cassegrain Telescope
Wave Optics
Nature of Light
Huygens' Construction
Wavefronts
Principle Of Superposition
Coherence
Young’s Double Slit Experiment (YDSE)
Shape of Interference
Fringes In YDSE
YDSE With White Light
Geometrical Path and Optical Path
YDSE With Oblique Incidence
Thin-Film Interference
Intensity Distribution Curve For Interference
Comparison of Intensities At Maxima And Minima
Displacement of Interference Fringes
Fresnel Biprism Experiment
Introduction to Diffraction of Light
Fresnel and Fraunhofer Diffraction
Diffraction at a Single Slit
Width of Central and Secondary Maxima
Double Slit Diffraction
Fresnel Distance
Diffraction through Circular Slit
Rayleigh Criterion of Resolution
Resolving Power of Human Eye
Microscopes and Telescopes
Introduction of Polarization
Unpolarized and Polarized Light
Law of Malus
Brewster Law
Dual Nature of Radiation and Matter
Dual Nature of Light
Electron Emission
Different Experiments
Work Function
Einstein’s Theory of Light
Radiation Force and Pressure
Photoelectric Effect
Experimental Setup of Photoelectric Effect by Lenard
Observations of Lenard’s Experiment of Photoelectric Effect
Einstein’s Equation for Photoelectric Effect
Quantum Efficiency
Photocell
De-Broglie Hypothesis
De-Broglie Wavelength of charged Particle
De-Broglie Wavelength of Uncharged Particle
Davisson-Germer Experiment
Atoms
Dalton's Atomic Theory
Thomson's Model Of An Atom
Rutherford Atom Model
Distance Of Closest Approach
Impact Parameter
Bohr's Atomic Model
Bohr's Theory Of Hydrogen Atom (Radius of Permitted Orbit)
Bohr's Theory Of Hydrogen Atom (Velocity of Electron)
Bohr's Theory Of Hydrogen Atom (Energy Of The Electron)
Bohr's Theory Of Hydrogen Atom (Time Period Of Revolution Of Electron)
Bohr's Theory Of Hydrogen Atom (Frequency Of Revolution Of Electron)
Wavelength Of Photon
Spectral Series Of Hydrogen Atom
Energy Level Diagram For Hydrogen
Nuclei
Atomic Nucleus
Composition Of Nucleus
Atomic Masses
Nuclear Size
Nuclear Density
Nuclear Force
Mass-Energy Relation
Mass Defect
Binding Energy
Binding Energy Per Nucleon
Binding Energy Curve
Nuclear Energy Levels
Radioactivity
Properties Of Alpha, Beta and Gamma Rays
Radioactive Decay Law
Half Life
Mean Life
Alpha, Beta and Gamma Decay
Nuclear Reaction
Nuclear Fission
Nuclear Chain Reaction
Nuclear Reactor
Nuclear Fusion
Semiconductors and Logic Gates
Semiconductors
Semiconductor Diode
I-V Characteristics in forward and reverse bias
Diode as a rectifier
I-V Characteristics of LED
Photodiode
Solar Cell
Zener Diode
Zener Diode as a voltage regulator
Junction Transistor
Transistor Action
Characteristics of a Transistor
Transistor as an Amplifier (common emitter configuration) and Oscillator
Logic Gates (OR, AND, NOT, NAND and NOR)
Transistor as a Switch
Solid state
Classification of solids based on different binding forces, Amorphous and crystalline solids
Unit cell in two dimensional lattices, Unit cell in three dimensional lattices, different classes of crystals
SC, BCC and FCC, Calculation of density of unit cell
Packing in solids
Packing efficiency, Voids, Radius Ratio & Ionic Structure
Number of atoms per unit cell in a cubic unit cell
Crystal defects: Point defects, Frenkel and Schottky Defects
Electrical and magnetic properties
Conductors, Semi-conductors and Insulators
Dielectric Properties
Solutions and colligative properties
Introduction, Types of Solutions
Concentration terms: Mass %, Mass by Volume %, Volume % and Molarity
Molality, Normality, Mole Fraction and PPM
Vapour pressure of a pure liquid and solution, Solubility of gases in liquids: Henry's Law
Raoult’s Law: Ideal and Non-Ideal Solutions
Positive and Negative deviation solutions, Azeotropic Solutions
Colligative properties of dilute solutions
Relative lowering of vapour pressure, Elevation of boiling point
Depression of freezing point
Osmosis and Osmotic pressure
Determination of molecular mass using colligative properties, Abnormal value of molar mass
Van't Hoff factor
Electrochemistry
Introduction, Conductors and Non-Conductors
Electrolytes
Electrochemical cells
Salt Bridge, Electrode potential
Reference electrode, Calculation of electrode potential
Electrochemical Series
Nernst Equation
Solubility product and EMF
Electrolysis
Faraday's Law and Current efficiency
Electrolytic conductance, Factor affecting Conductance and Resistance
Molar conductivity, Equivalent conductance
Application of Kohlrausch's law
Battery: Primary and Secondary Batteries
Corrosion
Chemical Kinetics
Introduction
Rate of reaction, Factors affecting rate of chemical reaction
Rate Law, and Order of reaction
Characteristics of First and Second Order reactions
Graphical comparison of different order of reaction
Integrated rate law method and Initial rate method
Method of Half Life and Ostwald's Isolation method
Methods to monitor the progress of the reaction
Factors affecting Rate Constant
Arrhenius Theory of reaction rate
Catalyst and Catalysis
Comparison between Molecularity and Order of reaction, Mechanism of a reaction
Radioactivity, Application of radioactivity
Surface Chemistry
Introduction, Adsorption and Absorption
Physical and Chemical Adsorption, Adsorption of gases on solids
Freundlich and Langmuir Adsorption Isotherm
Application of Adsorption, Catalyst and Catalysis
Classification, Preparation and Purification of Colloids
Multimolecular, Macromolecular and Associated colloids
Mechanism of micelle formation and cleansing action of soaps
Preparation of Colloidal Sols, Purification of Colloidal Sols
Important properties of colloidal sols, Electrical properties (Electrophoresis)
Coagulation and protection of colloids: Gold Number, Emulsion, Micelle and Gel
Metallurgy
Introduction, Types of Metallurgy
Steps involved in Metallurgy
Physical and Chemical methods
Thermodynamics of Extraction: Ellingham Diagram
Metallurgy of some important metals-I
Metallurgy of some important metals-II
Purification or Refining of Metals
Electrolytic refining, Vapour Phase Refining, Van Arkel-De Boer process and uses of metals
P-Block Elements
Nitrogen and Oxygen Family: Introduction
Atomic and Physical properties, General trends and chemical properties
Compounds of Nitrogen and Phosphorus: Ammonia and Phosphine
Oxides of Phosphorus, Halides and Oxyhalides of Phosphorus
Oxygen Family: Atomic and Physical properties, Allotropy
General trends and chemical properties
Compounds of Oxygen and Sulphur: Hydrides and Oxides
Compounds of Oxygen and Sulphur: Oxyacids
Miscellaneous Compounds: Hydrogen peroxide
Halogen Family: Physical and Chemical properties
Anomalous behaviour of Fluorine, Oxidising and Bleaching properties of Chlorine
The Zero group family: Atomic and Physical properties, Compounds of Nobel gases
d & f - Block Elements
General Introduction and Electronic Configuration
d-orbital and Lanthanide contraction, Oxidation state and Color
E⁰ M²⁺/M, Comparative graph of E⁰ M²⁺/M and E⁰ M³⁺/M²⁺
Melting and Boiling Point, Magnetic Character, Ferromagnetism
Catalytic properties, Formation of Interstitial compounds
Formation of Alloys and some important Alloys and its composition
Important d-block compounds - Silver Nitrate: Preparation, Physical and Chemical Properties
Potassium Permanganate: Preparation, Physical and Chemical Properties
Potassium Dichromate: Preparation, Physical and Chemical Properties
f-block elements: General properties, Electronic configuration, Atomic and Ionic Sizes and Oxidation States
General properties of the Actinides, Electronic Configuration, Oxidation states
General characteristics and comparison with Lanthanides, Application of d and f-block elements
Coordination Compounds
Introduction, Addition compounds, Double Salts and Coordination compounds
Coordination Sphere, Central Atom/Ion and Ligands
Coordination Number, Oxidation number of CMA, Homoleptic and Heteroleptic complexes
Nomenclature of Coordination Compounds-I
Nomenclature of Coordination Compounds-II
EAN Rule and Werner's Theory
VBT and Magnetic properties of Coordination compounds
Crystal Field Theory: Crystal field splitting in Octahedral, Crystal field splitting in Tetrahedral complexes
Colors and stability of Coordination compounds
Limitations of CFT, Isomerism in coordination compounds
Ionisation, Hydration, Linkage, Coordination
Stereoisomerism and Optical Isomerism
Organometallic compounds, application of coordination and organometallic compounds
Haloalkanes and Haloarenes
Introduction, Leaving group tendency, Nucleophilicity, Solvents, Nucleophilicity vs Basicity
Substitution Reactions, SN2, Kinetics
Mechanism, Stereochemistry, Substrate effect
General mechanism of SN-NGP, SN1, Kinetics
Mechanism, Stereochemistry, Substrate effect
G.M.P. Alkyl Halide, Hunsdiecker reaction, Simonini Reaction
Reaction of R-OH with HCl, Reaction of R-OH with HCl + ZnCl₂, Reaction of R-OH with NaCl + H₂SO₄
Reactions of PCl₅ with ether, Reactions of PCl₅ with aldehyde, Reactions of PCl₅ with ketone
Reactions of PCl₅ with acid, Reactions of PCl₅ with ester, Reactions Of PCl₅ with acid anhydride
Reactions Of PCl₅ with amide, Finkelstein and Swarts Reaction, Williamson synthesis
Open chain ether cleavage By HX, Open chain ether cleavage By H₃O⁺, cyclic ether cleavage in neutral
Cyclic ether cleavage in acidic, cyclic ether cleavage in basic, Elimination vs Substitution
Haloform reaction, Reactions of Polyhalogen compounds (CHCl₃), Reactions of Polyhalogen compounds (CCl₄)
Nucleophilic addition, Addition elimination, Nucleophilic substitution
Alcohol, Phenol and Ether
Introduction, Classification of alcohol, Nomenclature
Alcohol: Methods of Preparation
Alcohol: Organometallic Reagents
Alcohol: Grignard Reagents
Alcohol: Chemical Properties, Alcohol: Chemical Reactions
Introduction to Ethers, Structure
Nomenclature
Methods of Preparation
Ether: Physical Properties, Ether: Chemical Properties
Ether: Reactions, Introduction to Phenol, Nomenclature
Phenol: Methods of Preparation
Physical Properties of Phenol, Phenol: Chemical Properties
Phenol: Reactions
Aldehydes, Ketones, Carboxylic Acids, and Derivatives
Introduction
Basic Concept About Aldehyde & Ketone
Physical Properties
Methods of Preparation of Aldehyde & Ketone
Chemical Reactions (Oxidation & Reduction)
Addition Reaction of Nucleophiles To Carbonyl Group
Halogenation
Aldol Reactions
Cannizzaro's Reactions
Reformatsky Reactions
Oxidation & Reduction of Aldehyde & Ketone
Polymerisation Reactions
Some Other Important Chemical Reaction of Carbonyl Groups
Reaction Shown By Aldehyde & Ketone
Aromatic Carbonyl Compounds
Introduction, G.M.P. of Carboxylic Acids
Reactions of Carboxylic acid with Na, Reactions of Carboxylic acid with NaOH
Reactions of Carboxylic acid with SOCl₂, Reactions of Carboxylic acid with PCl₃
Reactions of Carboxylic acid with PCl₅, Reactions of Carboxylic acid with NH₃
Reactions of Carboxylic acid with ROH, Degradation reactions
Hoffmann bromamide degradation, Schmidt reaction, Curtius Reaction
G.M.P. of acid derivatives
Reactions of acid derivatives
Acyloin condensation, Acylation
Benzoylation, Hydrolysis of Ester AAc₂, Hydrolysis of Ester BAc₂
Hydrolysis of Ester BAl₂, Hydrolysis of Ester BAl₁, Hydrolysis of Ester AAl₁
Amines
Introduction
G.M.P. for Amines
Gabriel phthalimide reaction
G.R. of Amines, Carbylamine test
Hinsberg's test
Mustard oil reactions
Preparation and Reactions of cyanide
Preparation and Reactions of Isocyanide
Nitro Compounds, Urea
Biomolecules
Introduction
Classification of Carbohydrates
Study of Proteins
Study of Vitamins
Nucleic Acids
Enzyme
Polymers
Introduction to Polymers
Classification of Polymers
Types of Polymerization Reaction
Preparation of Polymers - I
Preparation of Polymers - II, Importance of Polymers
Chemistry in Everyday Life
Chemicals in medicines, Analgesics, Tranquillisers, Antiseptics
Disinfectants, Antimicrobials, Antifertility drugs
Antibiotics, Antacids, Antihistamines - their meaning and common examples
Chemicals in food: Preservatives
Chemicals in food: Artificial sweetening agents - common examples
Cleansing agents: Soaps and detergents, cleansing action
Qualitative Analysis
Introduction, Dry Test, Flame and Borax Bead Test, Charcoal Cavity Test, Cobalt Nitrate Test
Analysis of Anions: Dilute Sulphuric acid group
Analysis of Anions: Conc. Sulphuric acid group
Analysis of Cations: Zero Group, I, II, and III group
Analysis of Cations: IV, V, and VI group
Functions
Functions - Introduction
Different Functions (Polynomial, Modulus, Exponential, Logarithmic, GIF, Fractional Part, Sgn)
Methods to find Domain of Function
Methods to find Range of Function - I
Methods to find Range of Function - II
One-One & Many-One and Onto & Into Functions
Composite Functions
Equal or Identical Functions, Even and Odd Functions
Inverse Function
Periodic Function
Functional Equations
Graphical transformations
Inverse Trigonometric Functions
Introduction, Domain and Range of ITF, Graph of Inverse Trigonometric functions
Problems on ITF
Properties of inverse trigonometric function I
Properties of inverse trigonometric function II
Interconversion of ITF
Identities involving inverse trigonometric functions - I
Identities involving inverse trigonometric functions - II
Simplified ITF and their graphs, Series involving ITF
Limits
Introduction, LHL & RHL & Existence of Limit
Indeterminate forms, Fundamental theorems on limits
Solving limit (0/0) using Rationalization, Factorization
Solving limit using Standard Limits
Solving (0/0), (∞/∞) form using substitution
Solving (∞−∞) form, Important series expansions, L-Hôpital’s Rule
Solving 1∞, 0∞ and ∞0 form, Sandwich Theorem
Continuity
Introduction, continuity at a point
Reason and types of Discontinuity
Properties of Continuous Function
Continuity of Composite Function
Continuity in an interval
Intermediate Value Theorem
Differentiability
Introduction to Differentiability
Reasons for non-derivability, Relation between continuity and differentiability
Derivative using first principle, Differentiability in an Interval
Theorems on derivability
Standard derivatives, Algebra on differentiation
Derivative of composite function
Differentiation of Inverse Trigonometric Functions
Differentiation using substitutions, Graphical Approach for ITF
Logarithmic Differentiation, Differentiation of Implicit Functions
Differentiation of a Function in Parametric Form, Derivative of one function w.r.t. Another
Derivatives of higher order, Derivative of infinite series
Differentiation of a Determinant, Derivation of inverse function
Functional equations
Graphical approach to find differentiability
Indefinite Integration
Introduction, Standard Integrals - I
Problems on Standard Integral - I
Integration by substitution
Standard Integrals II
Integration By Part - I
Integration By Part - II, Standard Integrals - III
Integration of Trigonometric functions
Integration of Rational function by partial fraction
Integration of Irrational function
Some Special types of Integrals
Reduction Formulae
Definite Integration and Area under the Curve
Geometrical interpretation of Definite Integral
Elementary definite integral
Properties of Definite Integrals
Properties of Definite Integrals
Properties of Definite Integrals
Definite Integral as the limit of a Sum
Leibnitz Rule
Estimation and Inequalities
Estimation and Inequalities
Walli's Formula and Reduction Formula
Area enclosed between two curves
Area enclosed between two curves
Standard areas
Area under various cases
Application of Derivatives
Tangent and Normal
Problems on tangent and normal
Angle of Intersection
Length of tangent, normal, subtangent and subnormal
Monotonicity
Local Maxima and minima, First order derivative test
Second order derivative test, Global Maxima and minima
Proving inequalities using curvature
Rolle’s theorem
LMVT theorem
Geometry based problems
Derivative as a Rate Measure
Error and Approximation
Differential Equation
Introduction, Order & Degree of a differential equation
Formation of differential equation
Solution of differential equation, Variable Separable Method
Problems on Variable Separable Method
Equations Reducible to the Variables Separable form
Homogeneous Differential Equation
Equation reducible to homogeneous form
Linear Differential Equation
Bernoulli’s Differential Equation
Exact Differential Equation
Orthogonal trajectory, Application of Differential Equation
Matrices
Introduction to Matrices, Order of Matrix
Types of Matrix, Equality of Matrices
Addition and Subtraction of matrices
Multiplication of Matrices
Properties of Matrix Multiplication, Transpose of matrix
Properties of Transpose Matrix, Symmetric and skew Symmetric Matrices
Properties of symmetric and skew matrix and some special type of Matrices
Minor, Cofactor and Adjoint of a Matrix
Invertible Matrix and Inverse Matrix
Elementary Operation (Transformation of Matrix)
Inverse of Matrix by Elementary Operations
Determinants
Introduction to Determinant, Expansion of Determinant
Minor and Cofactor, Determinant of order 3
Properties of Determinant
Row Column Operation in Determinants
Special Determinants, Product of two determinants and Differentiation of Determinants
Nature of Solution of System of Linear Equations using Cramer's Rule
Probability
Basic Terms, Types of Events, Algebra of Events
Probability of Equally Likely Outcomes, Axiomatic Approach to Probability
Probability of the Event A or B, Probability of Event not A
Conditional Probability, Multiplication Theorem on Probability
Independent Events, Baye's Theorem, Random Variable and Probability Distributions
Mean of a Random Variable, Variance of a Random Variable
Bernoulli Trial and Binomial Distribution, Poisson's Probability distribution
Vectors
Vector Quantity, Position Vector, Types of Vector
Addition of Vectors, Multiplication of a Vector by a Scaler
Component of Vector, Vector Joining two Points
Section Formulae, Scalar (Dot) Product
Projection of a Vector, Vector (Cross) Product
Properties of Scalar and Vector Product
Direction Cosine, Direction Ratios
3D
Equation of a Line, Angle between Two Lines
Shortest Distance between Two Lines
Equation of a Plane in Normal Form
Equation of a Plane Perpendicular to a Given Vector and Passing Through a Given Point
Equation of a Plane Passing Through Three Non-Collinear Points
Intercept Form
Plane Passing Through the Intersection of Two Given Planes
Coplanarity of Two Lines
Angle between Two Planes, Distance of a Point from a Plane
Angle between a Line and a Plane
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