Notes for JEE Main & Advanced

Recent Notes

Matrices of Rotation of Axes
Geometrical Transformations
Cayley-Hamilton Theorem
Consistency of a System of Linear Equation \[\mathbf{AX=B,}\] where \[\mathbf{A}\] is a square matrix
Homogeneous and Non-homogeneous Systems of Linear Equations
Echelon Form of a Matrix
Rank of Matrix
Inverse of a Matrix
Adjoint of a Square Matrix
Special Types of Matrices
Transpose of a Matrix
Positive Integral Powers of a Matrix
Multiplication of Matrices
Scalar Multiplication of Matrices
Addition and Subtraction of Matrices
Trace of a Matrix
Types of Matrices
Equality of Matrices
Order of a Matrix
Some Special Determinants
Application of Determinants in Solving a System of Linear Equations
Differentiation and Integration of Determinants
Product of Two Determinants
Minors and Cofactors
Properties of Determinants
Lagrange's Mean Value Theorem
Rolle's Theorem
Greatest and Least Values of a Function Defined on an Interval \[[a,\,\,b]\]
Properties of Maxima and Minima
Higher Order Derivative Test
Sufficient Criteria for Extreme Values (1st Derivative Test)
Necessary Condition for Extreme Values
Length of Perpendicular from Origin to the Tangent
Length of Intercept Made on Axes by The Tangent
Length of Tangent, Normal, Subtangent, Subnormal
Angle of Intersection of Two Curves
Equation of the Tangent and Normal
Slope of the Tangent and Normal
Velocity and Acceleration in Rectilinear Motion
Derivative as the Rate of Change
Deduction of Euler?s Theorem
Euler's Theorem on Homogeneous Functions
Higher Partial Derivatives
Leibnitz?s Theorem
Differentiation of Integral Function
\[{{n}^{th}}\] Derivative Using Partial Fractions
Successive Differentiation or Higher Order Derivatives
Differentiation of a Function with Respect to Another Function
Methods of Differentiation
Theorems for Differentiation
Some Standard Differentiation
Relation Between A.P., G.P. and H.P.
Properties of Arithmetic, Geometric, Harmonic Means Between Two Given Numbers
Special Series
Method of Difference
Method for Finding Sum
Sum of A.G.P.
\[{{n}^{th}}\]term of A.G.P.
Properties of H.P.
Harmonic Mean
General Term of an H.P.
Properties of G.P.
Geometric Mean
Sum of infinite terms of a G.P.
Sum of first 'n' terms of a G.P.
Selection of Terms in a G.P.
General term of a G.P.
Properties of A.P.
Arithmetic Mean
Sum of n terms of an A.P.
Selection of Terms in an A.P.
General Term of an A.P.
Some Important Results
Some Properties Related to Circle
Some Terminology Related to Height and Distance
Solutions of Triangles
Regular Polygon
Cyclic Quadrilateral
Ex-central Triangle
Pedal Triangle
Circle Connected With Triangle
Half Angle Formulae
Area of Triangle
Napier's Analogy (Law of Tangents)
Theorem of The Medians: (Apollonius Theorem)
Projection Formulae
The Law of Cosines or Cosine Rule
Relation Between Sides and Angles
Periodic Functions
Important Points to be Taken in Case of While Solving Trigonometrical Equations
Method for Finding Principal Value
General Solution of The Form \[\mathbf{acos}\,\mathbf{\theta +bsin}\,\mathbf{\theta =c}\]
Trigonometrical Equations With Their General Solution
Trigonometrical Equations and Inequations Definition
Differentiability of a Function at a Point
Discontinuous Function
Continuity From Left and Right
Continuity of a Function at a Point
Methods of Evaluation of Limits
Fundamental Theorems on Limits
Limit of a Function
Inverse Function
Composite Function
Periodic Function
Even and Odd Function
Conditional Trigonometrical Identities
Kinds of function
Algebra of Functions
Domain, Co-domain and Range of Function
Definition of Function
Maximum and Minimum Value of a \[\mathbf{cos}\,\,\mathbf{\theta }\,\,\mathbf{+}\,\mathbf{b}\,\,\mathbf{sin}\,\,\mathbf{\theta }\]
Some Important Definitions
Trigonometric Ratio of Sub-multiple of an Angle
Trigonometric Ratio of Multiple of an Angle
Formulae to Rransform The Product Into Sum or Difference
Trigonometrical Ratios In Terms of Each Other
Trigonometrical Ratios for Some Special Angles
Trigonometrical Ratios for Various Angles
Trigonometrical Ratios of Allied Angles
Trigonometrical Ratios or Functions
Domain and Range of a Trigonometrical Function
Angle of Intersection of Two Spheres
Intersection of Straight Line and a Sphere
Condition of Tangency of a Plane to a Sphere
Relation Between an arc and an Angle
Relation Between Three Systems of Measurement of an Angle
System of Measurement of Angles   
Section of a Sphere by a Plane
Equation in Sphere in Various Forms
General Equation of Sphere
Projection of a Line on a Plane
Angle Between Line and Plane
Intersection Point of a Line and Plane
Equation of Plane Through a Given Line
Coplanar Lines
Image of a Point in a Plane
Equation of Planes Bisecting Angle Between Two Given Planes
Angle Between Two Planes
Foot of Perpendicular from a Point \[\mathbf{A(\alpha ,}\,\,\mathbf{\beta ,}\,\,\mathbf{\gamma )}\]to a given plane \[\mathbf{ax+by+cz+d=0}\].
Transformation of Axes
Equation of Plane Passing Through the Given Point
Area of Some Geometrical Figures
Definition of Plane and Its Equations
Shortest Distance Between two Straight Lines
Foot of Perpendicular from a Point to The Line
Intersection of Two Lines
Changing Unsymmetrical form to Symmetrical Form
Some Points of a Triangle
Straight Line in Space
Angle Between Two Lines
Direction Cosines and Direction Ratios
Triangle and Tetrahedron
Section Formulae
Section Formula
Distance Formula
Properties of Some Geometrical Figures
Co-ordinates of a Point in Space
Distance Formula
Polar Co-ordinates
Cartesian Co-ordinates of a Point
Binomial Distribution
Total Probability and Baye's Rule
Conditional Probability
Addition Theorems on Probability
Odds in Favour and Odds Against an Event
Problems Based on Combination and Permutation
Classical Definition of Probability
Definitions of Various Terms
Distance Between The Pair of Parallel Straight Lines     
Removal of the term \[\mathbf{xy}\] from \[\mathbf{f(X,}\,\mathbf{Y)=a}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+2hxy+b}{{\mathbf{y}}^{\mathbf{2}}}\] Without Changing the Origin
Removal of First Degree Terms
Equation of the Lines Joining the Origin to the Points of Intersection of a Given Line and a Given Curve
Bisectors of the Angles Between the Lines
Angle Between the Pair of Lines
Point of Intersection of Lines Represented by \[\mathbf{a}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+ 2hxy+b}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+ 2gx+ 2fy+c= 0}\]
Equation of Pair of Straight Lines
Logic Gates
Switching Circuits
Boolean Functions
Algebra of Statements
Tautologies and Contradictions
Negation of Compound Statements
Logical Equivalence
Basic Logical Connectives or Logical Operators
Truth Tables
Types of Statements
Use of Venn Diagrams in Checking Truth and Falsity of Statements
Statements or Propositions
Advantages and Limitations of L.P.P.
To Find The Vertices of Simple Feasible Region Without Drawing a Graph
Graphical Solution of Two Variable Linear Programming Problem
Mathematical Formulation of a Linear Programming Problem
Terms of Linear Programming
Linear Inequations
Inverse Trigonometric Ratios of Multiple Angles
Formulae for Sum, Difference of Inverse Trigonometric Function
Properties of inverse trigonometric functions
Domain and Range of Inverse Trigonometric Functions
Graphs of Inverse Trigonometric Functions
Integration of Hyperbolic Functions
Integration of Trigonometric Functions
Integration of Rational Functions by Using Partial Fractions
Integrals of the form \[\int{\frac{a sinx+b cosx}{c sinx+d cosx} }\]and \[\int{\frac{a\,sinx+bcos\,x+q}{c\,sinx+d\,cosx+r}}\]
Integrals of the form \[\int_{{}}^{{}}{\frac{dx}{a+b\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}x},\,\int_{{}}^{{}}{\frac{dx}{a+b\,\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}x},}}\]\[\int_{{}}^{{}}{\frac{dx}{a\,\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}x+b\,\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}x}\mathbf{,}}\]\[\int_{{}}^{{}}{\frac{dx}{{{\mathbf{(}a\,\sin x+b\,\mathbf{cos}\,x\mathbf{)}}^{\mathbf{2}}}}\mathbf{,}}\int_{{}}^{{}}{\frac{dx}{a\,+b\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}x+c\,\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}x}}\]
Integrals of the Form \[\int{\frac{dx}{a+bcosx+csinx}}\,,\,\,\int{\frac{dx}{asinx+bcosx}}\]
Integrals of the Form \[\int{\frac{dx}{a+b\,cos\,x}}\] and \[\int{\frac{dx}{a+b\,sin\,x}}\]
Evaluation of the Various Forms of Integrals by Use of Standard Results
Position of Centre of Gravity in Some Special Cases
Integration by Parts
Centre of Gravity of a Compound Body and Remainder
Centre of Gravity
Limiting Equilibrium on an Inclined Plane
Coefficient of Friction
Equilibrium of Coplanar Forces
Triangle Theorem of Couples
Integration By Substitution
Parallel Forces
Lami's Theorem
Polygon Law of Forces
Triangle Law of Forces
Parallelogram Law of Forces
Fundamental Integration Formulae
Image of a Point in Different Cases
Reflection on The Surface
Concurrent Lines
Position of Two Points with Respect to a Line
Position of a Point with Respect to a Line
Length of Perpendicular
Equations of the Bisectors of The Angles Between two Straight Lines
Equation of Straight Line Through a Given Point Making a Given Angle With a Given Line
Angle Between two Non-parallel Lines
General Equation of Lines Through the Intersection of Two Given Lines
Point of Intersection of Two Lines
General Equation of a Straight Line and its Transformation in Standard Forms
Equation of Parallel and Perpendicular Lines to a Given Line
Equations of Straight Line in Different Forms
Slope (Gradient) of a Line
Miscellaneous Differential Equation
Application of Differential Equation
Linear Differential Equation
Solution by Inspection
Exact Differential Equation
Homogeneous Differential Equation
Variable Separable Type Differential Equation
Formation of Differential Equation
Symmetrical Area
Application of Vectors in 3-dimensional Geometry
Rotation of a Vector About an Axis
Vector Product of Four Vectors
Area of Bounded Regions
Scalar Product of Four Vectors
Vector Triple Product
Integration of Piecewise Continuous Functions
Scalar Triple Product
Volumes and Surfaces of Solids of Revolution
Some Important Results of Definite Integral
Area Between Two Curves
Vector or Cross Product
Scalar or Dot Product
Linear Independence and Dependence of Vectors
Linear Combination of Vectors
Position Vector
Leibnitz's Rule
Properties of Vectors
Walli's Formula
Types of Vector
Reduction Formulae for Definite Integration
Gamma Function
Summation of Series by Integration
Representation of Vectors
Properties of Definite Integral
Evaluation of Definite Integral by Substitution
Rectangular or Equilateral Hyperbola
Asymptotes of a Hyperbola
Subtangent and Subnormal of the Hyperbola
Diameter of The Hyperbola
Pole and Polar
Equation of The Chord Joining Two Points on The Hyperbola
Equation of the Chord of the Hyperbola Whose mid point \[\mathbf{(}{{\mathbf{x}}_{\mathbf{1}}}\mathbf{,}\,\,{{\mathbf{y}}_{\mathbf{1}}}\mathbf{)}\] is given
Equation of Chord of Contact of Tangents Drawn from a Point to a Hyperbola
Equations of Normal in Different Forms
Equation of Pair of Tangents
Equations of Tangent in Different Forms
Intersection of a Line and a Hyperbola
Position of a Point With Respect to a Hyperbola
Parametric Equations of Hyperbola
Auxiliary Circle of Hyperbola
Special form of Hyperbola
Conjugate Hyperbola
Standard Equation of the Hyperbola
Subtangent and Subnormal
Diameter of The Ellipse
Pole and Polar
Equation of The Chord Joining Two Points on an Ellipse
Equation of Chord With Mid Point \[\mathbf{(}{{\mathbf{x}}_{\mathbf{1}}}\mathbf{,}{{\mathbf{y}}_{\mathbf{1}}}\mathbf{)}\]
Chord of Contact
Auxiliary Circle
Equations of Normal in Different Forms
Equation of Pair of Tangents \[\mathbf{S}{{\mathbf{S}}_{\mathbf{1}}}\mathbf{=}{{\mathbf{T}}^{\mathbf{2}}}\]
Equations of Tangent in Different Forms
Intersection of a Line and an Ellipse
Position of a Point with Respect to an Ellipse
Special Forms of an Ellipse
Parametric Form of The Ellipse
Standard Equation of the Ellipse
Pole and Polar
Length of Tangent, Subtangent, Normal and Subnormal to \[{{\mathbf{y}}^{\mathbf{2}}}\mathbf{= 4ax}\,\,\mathbf{at }\,\mathbf{(a}{{\mathbf{t}}^{\mathbf{2}}}\mathbf{,2at)}\]
Length of Tangent, Subtangent, Normal, Subnormal
Diameter of a Parabola
Equation of the Chord Joining any Two Points on the Parabola 
Equation of the Chord of the Parabola Which is Bisected at a Given Point  
Equation of The Chord of Contact of Tangents to a Parabola 
Co-normal Points
Relation Between \[\mathbf{'}{{\mathbf{t}}_{\mathbf{1}}}\mathbf{'}\] and \[\mathbf{'}{{\mathbf{t}}_{\mathbf{2}}}\mathbf{'}\] if Normal at \[\mathbf{'}{{\mathbf{t}}_{\mathbf{1}}}\mathbf{'}\] Meets the Parabola Again at \[\mathbf{'}{{\mathbf{t}}_{\mathbf{2}}}\mathbf{'}\]
Point of Intersection of Normals at Any Two Points on The Parabola
Equations of Normal in Different Forms
Equation of Pair of Tangents From a Point to a Parabola
Point of Intersection of Tangents at Any Two Points on The Parabola
Equations of Tangent in Different Forms
Position of a Point and a Line With Respect to a Parabola
Parametric Equations of a Parabola
Special form of Parabola \[{{\mathbf{(yk)}}^{\mathbf{2~}}}\mathbf{= 4a}\,\,\mathbf{(xh)= a}\]
Standard Equation of The Parabola
Recognisation of Conics
General Equation of a Conic Section When Its Focus, Directrix and Eccentricity are Given
Definitions of Various Important Terms
Image of The Circle by The Line Mirror
Limiting Points
Co-axial System of Circles
Radical Centre
Radical Axis
Family of Circles
Angle of Intersection of Two Circles
Common Tangents to Two Circles
Pole and Polar
Diameter of a Circle
Common Chord of Two Circles
Chord of Contact of Tangents
Normal to a Circle at a Given Point
Power of Point with Respect to a Circle
Director Circle
Pair of Tangents
Length of Tangent
Tangent to a Circle at a Given Point
Intersection of a Line and a Circle
Position of a Point With Respect to a Circle
Intercepts on the Axes
Equation of a Circle in Some Special Cases
Standard Forms of Equation of a Circle
Divisibility Problems
Second Principle of Mathematical Induction
First Principle of Mathematical Induction
Some Important Points
Three / Four Consecutive Terms or Coefficients
Binomial Theorem for any Index
Multinomial Theorem (for Positive Integral Index)
An Important Theorem
Use of Differentiation and Integration in Binomial Theorem
Properties of Binomial Coefficients
Greatest Term and Greatest Coefficient
To Determine a Particular Term in the Expansion
Middle Term
Number of Terms In The Expansion of \[{{(a+b+c)}^{n}}\] and \[{{(a+b+c+d)}^{n}}\]
Independent Term or Constant Term
General Term
Some Important Expansions
Binomial Theorem for Positive Integral Index
Binomial Expression
Number of Divisors
Multinomial Theorem
Some Important Results For Geometrical Problems
Division Into Groups
Conditional Combinations
Number of Combinations With Repetition and All Possible Selections
Number of Combinations Without Repetition
Circular Permutations
Conditional Permutations
Number of permutations with repetition
Number of Permutations Without Repetition
Definition of Permutation
Some Important Result
Equations Which Can Be Reduced to Linear, Quadratic and Biquadratic Equations
Rational Algebraic Inequations
Descarte's Rule of Signs
Position of Roots
Wavy Curve Method
The Quadratic Expression
Properties of Quadratic Equation
Condition for Common Roots
Higher Degree Equations
Relations Between Roots and Coefficients
Nature of Roots
Solution of Quadratic Equation
Types of Quadratic Equation
Composition of Relations
Equivalence Classes of An Equivalence Relation
Types of Relations
Inverse Relation
Cartesian Product of Sets
Laws of Algebra of Sets
Some important results on number of elements in sets
Operations on sets
Venn-Euler Diagrams
Types of Sets
Nomenclature Of Simple Aromatic Compounds 
Nomenclature Of Spiro Compounds
Nomenclature Of Special Compounds
Nomenclature Of Bicyclic Compounds
Bond-Line Notation Of Organic Compounds
IUPAC System Of Nomenclature Of Complex Compounds      
General Rules For Naming Organic Compounds
Alkyl groups
Classification Of Carbon Atoms In Organic Compounds
Nomenclature Of Organic Compounds
New High Performance Materials
Plant Growth Hormones
Pheromones, Sex Attractants
Chemicals in food
 Chemical in cosmetics
Rocket Propellant
Drugs and Chemotherapy
Classification Of Organic Compounds   
Organometallic Compounds
Some More Important Halogen Derivatives
Allyl iodide or 3-iodopropene-1, \[IC{{H}_{\mathbf{2}}}CH\text{ }=\text{ }C{{H}_{\mathbf{2}}}\]
Purification And Characterisation Of Organic Compounds
Unsaturated Halides (Halo-alkene)
Tetra-Halides (Carbon tetrachloride, \[CC{{l}_{4}}\])
Tri-halides (Chloroform and iodoform)
Preparations And Properties Of Dihalides
Properties Of Alkyl Halides
General methods of preparation of Alkyl Halides
Chemical Reactions Involved In The Tests Of Basic Radicals
Volumetric Analysis
Systematic Procedure For Qualitative Analysis Of Inorganic Salts
Test For Different Gases
Refractory Materials
Main Types Of Metallurgical Processes
Extraction of Metals: Metallurgy
Metals in Biology
Occurrence of Metals
Liquefaction Of Gases 
Specific And Molar Heat Capacity Of Gases
Degrees Of Freedom Of A Gaseous Molecule 
The Critical State
Vander Waal's Equation
Real and Ideal gases
Molecular Speeds Or Velocities
Molecular Collisions
Kinetic Theory Of Gases
Graham's Law Of Diffusion And Effusion
Dalton's Law Of Partial Pressures
Ideal Gas Equation
Avogadros Law
Gay-Lussacs Law (Amonton's law)
Charles Law
Boyle's law
Measurable Properties Of Gases
Characteristics Of Gases
Digestion of food
Energy cycle or metabolism
Nucleic acids
Amino acids
Polysaccharide (Starch and cellulose)
Advance Level Information
Molecular Masses of Polymers
Biodegradable Polymers
Some Important Polymer and Their Uses
General Methods and Mechanism of Polymerisation
Classification of Polymers
Diazonium salts  
Some important conversions
Cyanides and Isocyanides
Aromatic Nitro Compounds
Alkyl nitrites and nitro alkanes
Fructose, fruit sugar \[({{C}_{6}}{{H}_{12}}{{O}_{6}})\] or ketohexose
Acid derivatives
Glucose; \[({{C}_{6}}{{H}_{12}}{{O}_{6}})\] or Aldo-hexose 
Aromatic Carboxylic Acids
Substituted Carboxylic Acids
Higher Fatty Acids
Unsaturated Dicarboxylic Acids
Dicarboxylic Acids
Individual Members Of Monocarboxylic Acids
Chemical Properties Of Monocarboxylic Acids
Acidic Nature Of Monocarboxylic Acids
Methods Of Preparation Of Monocarboxylic Acid
Benzophenone, \[{{\mathbf{C}}_{\mathbf{6}}}{{\mathbf{H}}_{\mathbf{5}}}\mathbf{CO}{{\mathbf{C}}_{\mathbf{6}}}{{\mathbf{H}}_{\mathbf{5}}}\]
Acetophenone, \[{{\mathbf{C}}_{\mathbf{6}}}{{\mathbf{H}}_{\mathbf{5}}}\mathbf{COC}{{\mathbf{H}}_{\mathbf{3}}}\mathbf{,}\] Acetyl Benzene
Aromatic Carbonyl Compounds
Some Commercially Important Aliphatic Carbonyl Compounds
Test Of Aldehydes And Ketones (Distinction)
Chemical Properties Of Carbonyl Compounds
Physical Properties Of Carbonyl Compounds
Preparation Of Carbonyl Compounds
Derivatives Of Phenol
Phenol (Carbolic acid), \[{{C}_{6}}{{H}_{5}}OH\] or Hydroxy benzene
Unsaturated Alcohols (Allyl alcohol)
Trihydric Alcohols.
Dihydric Alcohols
Monohydric Alcohols
Bi-phenyl \[{{C}_{6}}{{H}_{5}}\text{ }{{C}_{6}}{{H}_{5}}\]
Styrene \[({{C}_{6}}{{H}_{5}}CH=C{{H}_{2}})\text{ }\]
Xylenes (Dimethyl benzene) \[{{C}_{6}}{{H}_{4}}{{(C{{H}_{3}})}_{2}}\]
Toluene, methyl benzene or phenyl methane
Directive Effect In Substituted Benzene Derivatives
Benzene \[\left( {{\mathbf{C}}_{\mathbf{6}}}{{\mathbf{H}}_{\mathbf{6}}} \right)\]
General Characteristics Of Arenes
Aromatic Hydrocarbon
Distinction Between Alkanes, Alkenes And Alkynes
Separation of alkane, alkene and alkyne  
Individual members of alkanes
Alkanes [Paraffines]                         
Characteristics Of Hydrocarbons
Aliphatic Hydrocarbon
Conformational Isomerism  
Optical Isomerism
Geometrical Or Cis-Trans Isomerism
Constitutional or structural isomerism
Rearrangement Reactions
Elimination Reactions
Addition reactions
Types Of Organic Reactions
Attacking Reagents
Reaction Intermediates
Cleavage (Fission Or Breaking) Of Covalent Bonds
Electromeric Effect
Inductomeric Effect
Hyperconjugative Effect
Resonance Effect Or Mesomeric Effect
Inductive Effect Or Transmission Effect
Electronic Displacement In Covalent Bonds
Steric effect
Hybridisation In Organic Compounds
Bonding in co-ordination compounds (Werner's Coordination theory)
Isomerism In Co-ordination Compounds
Iupac Nomenclature Of Complex Compounds
Terminology Of Co-ordination Compounds
Double Salts And Co-ordination Compounds
Lanthanides And Actinides
Mercury And Its Compounds
Zinc And Its Compounds
Gold and its Compounds
Copper and its Compounds
Iron And Its Compounds
Manganese Containing Compound
Lanthanides And Actinides
Mercury And Its Compounds
Zinc And Its Compounds
Gold and its Compounds
Copper and its Compounds
Iron And Its Compounds
Chromium containing compounds
Physico-Chemical Properties Of d-Block Elements
d-Block Elements   
Oxygen Family
Noble Gases
Halogen Family
Nitrogen Family
Carbon Family
Boron Family
Alkaline Earth Metals and Their Compounds 
Alkali Metals And Their Compounds
Hydrogen Peroxide
Hydrogen Peroxide
Isotopes of Hydrogen
Refractory Materials
Main Types Of Metallurgical Processes
Extraction of Metals: Metallurgy
Metals in Biology
Occurrence of Metals
Diagonal relationship
Some other periodic properties
Electron affinity
Ionisation potential or ionisation energy
Covalent, Ionic And Vander Waal's Radii
Effective nuclear charge
The screening effect or shielding effect
Periodicity in properties
Extended or long form of periodic table
Classification Of Element On The Basis Of Electronic Configuration
Earlier Attempt To Classify Elements
Theories Of Catalysis
Application Of Colloids
Motional EMI Due to Rotational Motion
Triode as an Amplifiers
Constants of Triode Valve
Characteristic Curves of a Diode
Diode Valve
Vacuum Tubes and Thermionic Valves
Thermionic Emission
Electron Emission from Metal
Valve Electronics
Logic Gates Using 'NAND' Gate
Combination of Logic Gates
The 'NOT' Gate
The 'AND' Gate
The 'OR' Gate
Logic Gates and Truth Table
Boolean Algebra
Voltage Signal
Decimal and Binary Number System
Digital Electronics
Transistor as an Oscillator
Different Gains in CE/CB Amplifiers
Transistor as an Amplifier
Field-Effect Transistor
Transistor Configurations
Working of Transistor
P-N Junction Diode as a Rectifier
Special Purpose Diodes
Reverse Breakdown
P-N Junction Diode
Conductivity of Semiconductor
Density of Charge Carriers
P-Type Semiconductor
N-Type Semiconductor
Extrinsic Semiconductor
Intrinsic Semiconductors
Holes in Semiconductors
Energy Bands
Single, Poly and Liquid Crystals
Bonding Forces in Crystals
Earth's Atmosphere
EM Spectrum
Properties of EM Waves
Source, Production and Nature of EM Waves
Experimental Setup for Producing EM Waves
History of EM Waves
Maxwell's Contribution
Electromagnetic Waves
Methods of Producing Polarised Light
Polarisation of Light
Zone Plate
Diffraction Due to a Circular Aperture
Diffraction Due to a Circular Disc
Fresnel's Half Period Zone (HPZ)
Diffraction Gratings
Diffraction at Single Slit (Fraunhoffer Diffraction)
Types of Diffraction
Hexagonal Close Packed (HCP) Structure
Diffraction of Light
Doppler's Effect of Light
Different Types of Symmetry in Cubic Lattices
Newton's Rings
Terms Related with Crystal Structure
Fresnel's Biprims
Semiconductor electronics
Lloyd's Mirror
Interference in Thin Films
dc Generator                
Missing Wavelength in Front of One Slit in YDSE
ac Generator/Alternator/Dynamo
dc Motor
Eddy Current
LC- Oscillation
Fringe Visibility (V)
Growth and Decay of Current In LR- Circuit
Shifting of Fringe Pattern in YDSE
Combination of Inductance
Mutual Induction
Condition for Observing Interference
Useful Results
Young's Double Slit Experiment (YDSE)
Interference of Light
Resultant Amplitude and Intensity
Important Terms
Super Position of Waves
Reflection and Refraction of Wavefront
Huygen's Wave Theory
Newton's Corpuscular Theory
Resolving Limit and Resolving Power
Reflecting Telescope
Galilean Telescope
Terrestrial Telescope
Astronomical Telescope (Refracting Type)
Lens Camera
Defects in Eye
Human Eye
Colours of Objects
Scattering of Light
Dispersion Through a Prism
Defects in Lens
Silvering of Lens
Combination of Lens
Self Induction
Cutting of Lens
Displacement Method
Lens Immersed in a Liquid
Newton's Formula
Periodic EMI
Motional Emi in Loop by Generated Area
Lens Maker's Formula and Lens Formula
Dynamic (Motional) EMI Due to Translatory Motion
Induced Electric Field
Rules of Image Formation by Lens
Lenz's Law
Focal Length, Power and Aperture of Lens
Faraday's Laws of Electromagnetic Induction
Magnetic Flux
Refraction From Spherical Surface
Common Examples of TIR
Total Internal Reflection (TIR)
Refraction Through a Glass Slab
Real and Apparent Depth
Refractive Index
Refraction of Light
Mirror Formula and Magnification
Image Formation by Curved Mirrors
Curved Mirror
Reflection From a Plane Surface (Plane Mirror)
Reflection of Light
Real and Virtual Images
Helium-Neon Laser
Principle of Laser
Concepts Related to Production of LASER  
Advantages of Optical Fibres Over Wires
Optical Fibre
Optical Communication
Telephone Links
Impedance of Line
Two Wire Transmission Line
Line Communication
Remote Sensing
Satellite Communication
Space Wave Propagation
Space Communication
Modem and Fax
Data Transmission and Retrieval
Pulse Code Modulation
Pulse Modulation
Frequency Modulation (FM)
Amplitude Modulation (AM)
Analog and Digital Signals
Types of Communication System
Basic Communication System
Uses of Radioactive Isotopes
Successive Disintegration and Radioactive Equilibrium
Radioactive Series
Radioactive Disintegration
Nuclear Radiations
Nuclear Fusion
Nuclear Reactor
Difficulties in Chain Reaction          
Chain Reaction
Nuclear Fission
Nuclear Reactions
Binding Energy Curve
Mass Defect and Binding Energy
Nuclear Stability
Pair Production and Pair-Annihilation
Atomic Mass Unit (amu)
Nuclear Force
Size of Nucleus
Types of Nuclei
Thermal Neutrons
Electronic Configurations of Atoms
Quantum Numbers
Hydrogen Spectrum and Spectral Series
Transition of Electron
Bohr's Orbits (for Hydrogen and \[{{H}_{2}}\]-like Atoms)
Draw Backs of Bohr's Atomic Model
Bohr's Atomic Model
Failure of Rutherford's Model
Rutherford's Atomic Model
a-Scattering Experiment
Thomson's Atomic Model
Uses of X-Rays
Mosley's Law
Characteristic X-Rays
Continuous X-Rays
Classification of X-Rays
Absorption of X-Rays
Properties of X-Rays
Coolidge X-Ray Tube
Compton Effect
Important Formulae for Photoelectric Effect
Effect of Intensity and Frequency of Light
Experimental Setup for Photoelectric Effect
Photo-Electric Effect
Heisenberg Uncertainty Principle
Davision and Germer Experiment
Characteristics of Matter Waves
Matter Waves (de-Broglie Waves)
Bainbridge Mass Spectrograph
Thomson's Mass Spectrograph
Positive Rays
Millikans Oil Drop Experiment
J.J. Thomson's Experiment
Cathode Rays
Electric Discharge Through Gases
Choke Coil
Wattless Current
Parallel RLC Circuits
Series RLC-Circuit
Inductive, Capacitive Circuit (LC-Circuit)
Resistive, Capacitive Circuit (RC-Circuit)
Resistive, Inductive Circuit (RL-Circuit)
Capacitive Circuit (C-Circuit)
Inductive Circuit (L-Circuit)
Resistive Circuit (R-Circuit)
Power Factor
Power in ac Circuits
Impedance, Reactance, Admittance and Susceptance
Measurement of Alternating Quantities
Important Values of Alternating Quantities
Alternating Quantities (i or V)
Magnetic Maps and Neutral Points
Hysteresis Curve
Magnetic Materials
Vibration Magnetometer
Deflection Magnetometer
Tangent Galvanometer
Tangent Law
Magnetic Maps and Neutral Points
Elements of Earth's Magnetic Field
Earth's Magnetic Field (Terrestrial Magnetism)
Force and Field
Various Terms Related to Magnetism
Bar Magnet
Force On a Current Carrying Conductor In Magnetic Field
Hall Effect
Lorentz Force
Trajectory of a Charged Particle in a Magnetic Field
Moving Coil Galvanometer
Behaviour of Current Loop in a Magnetic Field
Current Loop as a Magnetic Dipole
Standard Cases For Force on Current Carrying Conductors
Force Between Two Moving Charges
Force Between Two Parallel Current Carrying Conductors
Force On a Charged Particle in Magnetic Field
Magnetic Field Due to an Infinite Sheet Carrying Current
Magnetic Field Due to a Cylindrical Wire
Magnetic Field Due to a Straight Wire
Magnetic Field at Centre O in Different Conditions of Circular Current
Magnetic Field Due to Circular Current
Ampere's Law
Meaning of Cross and dot
Direction of Magnetic Field
Biot-Savart's Law
Application of Thermo Electric Effect
Thomson's Effect
Peltier Effect
Seeback Effect
Electro Chemical Cell
Faraday's Law of Electrolysis
Chemical Effect of Current
Combination of Bulbs
Electricity Consumption
Electric Power
Joules Heating
Application of Potentiometer
Different Measuring Instruments
Kirchoff's Laws
Grouping of Cells
Cell in Various Positions
Grouping of Resistance
Colour Coding of Resistance
Electrical Conducting Materials For Specific Use
Stretching of Wire
Resistivity (p), Conductivity and Conductance (C)
Ohm's Law
Drift Velocity
Current Density (J )
Electric Current
Kirchhoff?s Law for Capacitor Circuits
Charging and Discharging of Capacitor in Series RC Circuit
Grouping of Capacitor
Capacity of Various Capacitor
Capacitor or Condenser
Redistribution of Charges and Loss of Energy
Combination of Charged Drops
Gauss's Law and it's Application
Electric Flux
Electric Dipole
Equilibrium of Charged Soap Bubble
Force on a Charged Conductor
Electrostatic Potential Energy
Neutral Point and Zero Potential
Time Period of Oscillation of a Charged Body
Equilibrium of Charges
Electric Lines of Force
Motion of Charge Particle in Electric Field
Equipotential Surface
Relation Between Electric Field and Potential
Potential Due to Concentric Spheres 
Electric Field and Potential Due to Various Charge Distribution
Electric Potential
Electric Field
Coulomb's Law
Methods of Charging
Electric Charge
Accoustics of Buildings
Musical Sound
Conditions for No Doppler's Effect
Some Typical Cases of Doppler's Effect
Common Cases in Doppler's Effect
Doppler's Effect
Determination of Unknown Frequency
Kundt's Tube
Resonance Tube
End Correction
Tuning Fork
Standing Wave in a Organ Pipe
Vibration of Composite Strings
Melde's Experiment
Standing Waves on a String
Terms Related to the Application of Stationary Wave
Characteristics of Standing Waves
Standing Waves or Stationary Waves
Quink's Tube
Interference of Sound Waves
Principle of Superposition
Reflection and Refraction of Waves
Pressure Waves
Equation of a Plane Progressive Waves
Factors Affecting Velocity of Sound in Gaseous Medium
Velocity of Longitudinal Wave (Sound Wave)
Velocity of Transverse Wave
Important Terms Regarding Wave Motion
Types of Waves
Characteristics of Wave Motion
Super Position of S.H.M's (Lissajous Figures)
Free, Damped, Forced and Maintained Oscillations
Various Formulae of S.H.M.
Oscillation of Spring Combination
Spring Pendulum
Spring System
Some Other Types of Pendulum
Oscillation of Pendulum in Different Situations
Factor Affecting Time Period of Simple Pendulum
Simple Pendulum
How to Find Frequency and Time Period of S.H.M.
Differential Equation of S.H.M.
Average Value of P.E. and K.E.
Energy in S.H.M.
Comparative Study of Displacement Velocity and Acceleration
Acceleration in S.H.M.
Velocity in S.H.M.
Displacement in S.H.M.
Some Important Definitions
Simple Harmonic Motion
Periodic and Oscillatory (Vibratory) Motion
Temperature of the Sun and Solar Constant
Law of Distribution of Energy (Plank's Hypothesis)
Wien's Displacement Law
Distribution of Energy in the Spectrum of Black Body
Determination of Specific Heat of Liquid
Cooling Curves
Newton's Law of Cooling
Rate of Loss of Heat <img
Stefan's Law
Applications of Kirchoff's Law
Kirchoff's Law
Prevost Theory of Heat Exchange
Perfectly Black Body
Emissive Power, Absorptive Power and Emissivity
Interaction of Radiation with Matter
Colour of Heated Object
Growth of Ice on Lake
Searle's Experiment
Ingen-Hauz Experiment
Combination of Metallic Rods
Applications of Conductivity in Daily Life
Conduction in Metallic Rod
Transmission of Heat
Carnot Engine
Second Law of Thermodynamics
Refrigerator or Heat Pump
Heat Engine
Mixed Graphical Representation
Reversible and Irreversible Process
Quasi Static Process
Cyclic and Non-cyclic Process
Adiabatic Process
Isothermal Process
Isochoric or Isometric Process
Isobaric Process
First Law of Thermodynamics (FLOT)
Heat, Internal Energy and Work in Thermodynamics
Zeroth Law of Thermodynamics
Some Definitions
Gaseous Mixture
Specific Heat in Terms of Degree of Freedom
Mayer's Formula          
Specific Heat (\[{{C}_{P}}\] and \[{{C}_{V}}\]) of a Gas
Law of Equipartition of Energy
Kinetic Energy of Ideal Gas
Degree of Freedom
Mean Free Path
Maxwellís Law (or the Distribution of Molecular Speeds
Various Speeds of Gas Molecules
Pressure of an Ideal Gas
Real Gases
Equation of State or Ideal Gas Equation
Gas Laws
Assumption of Ideal Gases (or Kinetic Theory of Gases)
Heating Curve
Principle of Calorimetry
Joule's Law (Heat and Mechanical Work)
Some Important Terms
Thermal Capacity and Water Equivalent
Phase Change and Latent Heat
Specific Heat of Gases
Specific Heat of Liquid (Water)
Specific Heat of Solids
Specific Heat
Expansion of Gases
Variation of Density with Temperature
Thermal Expansion in Liquids
Application of Thermal Expansion in Solids
Scales of Temperature
Thermal Expansion
Poiseuille's Formula
Stoke's Law and Terminal Velocity
Viscosity and Newton's law of Viscous Force
Velocity of Efflux
Applications of Bernoulli's Theorem
Bernoulli's Theorem
Energy of a Flowing Fluid
 Equation of Continuity
Critical Velocity and Reynold's Number
Streamline, Laminar and Turbulent Flow
Archimedes Principle
Pascal's Law
Useful Facts and Formulae
Shape of Drops
Ascent Formula
Angle of Contact
Shape of Liquid Meniscus
Excess Pressure
Formation of Bigger Drop
Splitting of Bigger Drop
Work Done in Blowing a Liquid Drop or Soap Bubble
Surface Energy
Molecular Theory of Surface Tension
Applications of Surface Tension
Factors Affecting Surface Tension
Examples of Surface Tension
Force Due to Surface Tension
Surface Tension
Intermolecular Force
Practical Applications of Elasticity
Important Facts About Elasticity
Factors Affecting Elasticity
Elastic Hysteresis
Interatomic Force Constant
Torsion of Cylinder
Relation between \[\mathbf{Y,}\,\mathbf{k,}\,\mathbf{\eta ,}\,\] and \[\mathbf{\sigma }\]
Relation Between Volumetric Strain, Lateral Strain and Poisson's Ratio
Poisson's Ratio
Modulus of Rigidity
Fractional Change in the Radius of Sphere
Density of Compressed Liquid
Bulk Modulus
Breaking of Wire
Work Done in Stretching a Wire
Young's Modulus (Y)
Hooke's law and Modulus of Elasticity
Stress-strain Curve
Elastic Property of Matter
Types of Solids
States of Matter
Comparison Between Interatomic and Intermolecular Forces
Intermolecular Forces
Interatomic Forces
Weightlessness in a Satellite
Change in the Orbit of Satellite
Energy of Satellite
Angular Momentum of Satellite
Geostationary Satellite
Height of Satellite
Time Period of Satellite
Orbital Velocity of Satellite
Some Properties of the Planet
Velocity of a Planet in Terms of Eccentricity
Kepler's Laws of Planetary Motion
Escape Velocity
Work Done Against Gravity
Gravitational Potential Energy
Gravitational Potential for Different Bodies
Gravitational Potential
Gravitational Field Intensity for Different Bodies
Gravitational Field
Inertial and Gravitational Masses
Mass and Density of Earth
Variation in g Due to Rotation of Earth
Variation in g With Depth
Variation in g With Height
Variation in g Due to Shape of Earth
Acceleration Due to Gravity
Properties of Gravitational Force
Newton's law of Gravitation
Collision Between Bullet and Vertically Suspended Block
Perfectly Inelastic Collision
Rebounding of Ball After Collision With Ground
Head on Inelastic Collision
Perfectly Elastic Oblique Collision
Perfectly elastic head on collision
Position and Velocity of an Automobile w.r.t Time
Important Points
Law of Conservation of Energy
Velocity of Chain While Leaving the Table
Work Done in Pulling the Chain Against Gravity
Gravitational Potential Energy
Electrical Potential Energy
Elastic Potential Energy
Potential Energy
Stopping of Vehicle by Retarding Force
Kinetic Energy
Work Depends on Frame of Reference
Work Done in Conservative and Non-conservative Field
Work Done Calculation by Force Displacement Graph
Work Done by a Variable Force
Dimension and Units of Work
Nature of Work Done
Work Done by a Constant Force
Sticking of a Person with the Wall of Rotor
Sticking of a Block With Accelerated Cart
Velocity at the Bottom of Rough Wedge
Stopping of Two Blocks Due to Friction
Stopping of Block Due to Friction
Coefficient of Friction Between a Body and Wedge
Maximum Length of Hung Chain
Minimum Mass Hung from the String to Just Start the Motion
Motion of an Insect in the Rough Bowl
Motion of Two Bodies one Resting on the Other
Work done against friction
Acceleration of a Block Against Friction
Calculation of Required Force in Different Situation
Angle of Repose
Resultant Force Exerted by Surface on Block
Angle of Friction
Methods of Changing Friction
Advantages and Disadvantages of Friction
Friction is a Cause of Motion
Graph Between Applied Force and Force of Friction
Types of Friction
Modification of Newton's Laws of motion
Spring Balance and Physical Balance
Motion of Connected Block Over A Pulley
Motion of Blocks Connected by Mass Less String
Motion of Blocks In Contact
Acceleration of Block on Smooth Inclined Plane
Acceleration of Block on Horizontal Smooth Surface
Apparent Weight of a Body in a Lift
Free Body Diagram
Law of Conservation of Linear Momentum
Frame of Reference
Newton's Third Law
 Equilibrium of Concurrent Force
Newton's Second Law
Newton's First Law
Linear Momentum
Point Mass
Conical Pendulum
Motion in vertical circle
Equations of Circular Motion
Non-Uniform Circular Motion
Reaction of Road On Car
Motion of Charged Particle In Magnetic Field
Overturning of Vehicle
Banking of A Road
Bending of A Cyclist