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

Definition

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

Definition

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

Necessary Condition for Extreme Values

Definition

Definition

Length of Perpendicular from Origin to the Tangent

Length of Tangent, Normal, Subtangent, Subnormal

Angle of Intersection of Two Curves

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

Definition

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

Introduction

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.

Definition

Properties of H.P.

Harmonic Mean

General Term of an H.P.

Definition

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.

Definition

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.

Definition

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

Introduction

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

Intervals

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 AnglesÂ Â

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

Introduction

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

Locus

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

Projection

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

Introduction

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 LinesÂ Â Â Â Â

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

Introduction

Duality

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

Introduction

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

Friction

Equilibrium of Coplanar Forces

Triangle Theorem of Couples

Integration By Substitution

Couples

Moment

Parallel Forces

Lami's Theorem

Polygon Law of Forces

Triangle Law of Forces

Parallelogram Law of Forces

Fundamental Integration Formulae

Introduction

Definition

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

Definition

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

Definition

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

Introduction

Properties of Definite Integral

Evaluation of Definite Integral by Substitution

Definition

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

Definition

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

Definition

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 ParabolaÂ

Equation of the Chord of the Parabola Which is Bisected at a Given PointÂ Â

Equation of The Chord of Contact of Tangents to a ParabolaÂ

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

Definition

Recognisation of Conics

General Equation of a Conic Section When Its Focus, Directrix and Eccentricity are Given

Definitions of Various Important Terms

Definition

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

Definition

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

Derangement

Division Into Groups

Conditional Combinations

Number of Combinations With Repetition and All Possible Selections

Number of Combinations Without Repetition

Definition

Circular Permutations

Conditional Permutations

Number of permutations with repetition

Number of Permutations Without Repetition

Definition of Permutation

Introduction

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

Polynomial

Composition of Relations

Equivalence Classes of An Equivalence Relation

Types of Relations

Inverse Relation

Definition

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

Introduction

Nomenclature Of Simple Aromatic CompoundsÂ

Nomenclature Of Spiro Compounds

Nomenclature Of Special Compounds

Nomenclature Of Bicyclic Compounds

Bond-Line Notation Of Organic Compounds

IUPAC System Of Nomenclature Of Complex CompoundsÂ Â Â Â Â Â

General Rules For Naming Organic Compounds

Alkyl groups

Classification Of Carbon Atoms In Organic Compounds

Nomenclature Of Organic Compounds

New High Performance Materials

Detergents

Plant Growth Hormones

Pheromones, Sex Attractants

Chemicals in food

Â Chemical in cosmetics

Rocket Propellant

Drugs and Chemotherapy

Dyes

Classification Of Organic CompoundsÂ Â Â

Organometallic Compounds

Some More Important Halogen Derivatives

Halo-Arenes Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

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

Alloys

Refractory Materials

Furnaces

Main Types Of Metallurgical Processes

Extraction of Metals: Metallurgy

Metals in Biology

Occurrence of Metals

Liquefaction Of GasesÂ

Specific And Molar Heat Capacity Of Gases

Degrees Of Freedom Of A Gaseous MoleculeÂ

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

Vitamins

Digestion of food

Energy cycle or metabolism

Â LipidsÂ Â Â Â Â Â Â Â Â Â Â Â Â Â

Nucleic acids

Amino acids

Polysaccharide (Starch and cellulose)

Disaccharides

Advance Level Information

Molecular Masses of Polymers

Biodegradable Polymers

Some Important Polymer and Their Uses

Rubber

General Methods and Mechanism of Polymerisation

Classification of Polymers

Diazonium salts Â

Some important conversions

Aniline

Amines

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-hexoseÂ

Carbohydrates

Aromatic Carboxylic Acids

Substituted Carboxylic Acids

Higher Fatty Acids

Unsaturated Dicarboxylic Acids

Dicarboxylic Acids

Interconversions

Individual Members Of Monocarboxylic Acids

Chemical Properties Of Monocarboxylic Acids

Acidic Nature Of Monocarboxylic Acids

Methods Of Preparation Of Monocarboxylic Acid

Classification

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

Introduction

Ether

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

Dienes

Cycloalkene

Distinction Between Alkanes, Alkenes And Alkynes

Separation of alkane, alkene and alkyne Â

Alkynes

Alkenes

Individual members of alkanes

Alkanes [Paraffines] Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Characteristics Of Hydrocarbons

Aliphatic Hydrocarbon

Conformational Isomerism Â

Monosaccharides

Â LipidsÂ Â Â Â Â Â Â Â Â Â Â Â Â Â

Optical Isomerism

Geometrical Or Cis-Trans Isomerism

Constitutional or structural isomerism

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 Â Â

Oxygen Family

Noble Gases

Halogen Family

Nitrogen Family

Carbon Family

Boron Family

Alkaline Earth Metals and Their CompoundsÂ

Alkali Metals And Their Compounds

Hydrogen Peroxide

Hydrogen Peroxide

Water

Isotopes of Hydrogen

Hydrogen

Furnaces

Alloys

Refractory Materials

Main Types Of Metallurgical Processes

Extraction of Metals: Metallurgy

Metals in Biology

Occurrence of Metals

Diagonal relationship

Some other periodic properties

Electronegativity

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

Transistor

P-N Junction Diode as a Rectifier

Special Purpose Diodes

Reverse Breakdown

Biasing

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

Solids

Fresnel's Biprims

Semiconductor electronics

Lloyd's Mirror

Interference in Thin Films

Transformer

dc GeneratorÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

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

Coherence

Resultant Amplitude and Intensity

Important Terms

Super Position of Waves

Reflection and Refraction of Wavefront

Wavefront

Huygen's Wave Theory

Newton's Corpuscular Theory

Photometry

Resolving Limit and Resolving Power

Binocular

Reflecting Telescope

Galilean Telescope

Terrestrial Telescope

Astronomical Telescope (Refracting Type)

Microscope

Lens Camera

Defects in Eye

Human Eye

Spectrum

Colours of Objects

Rainbow

Scattering of Light

Dispersion Through a Prism

Prism

Defects in Lens

Silvering of Lens

Combination of Lens

Self Induction

Cutting of Lens

Displacement Method

Lens Immersed in a Liquid

Inductance

Newton's Formula

Periodic EMI

Magnification

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

Lens

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 Â

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

Demodulation

Pulse Code Modulation

Pulse Modulation

Frequency Modulation (FM)

Amplitude Modulation (AM)

Modulation

Analog and Digital Signals

Types of Communication System

Basic Communication System

Communication

Uses of Radioactive Isotopes

Successive Disintegration and Radioactive Equilibrium

Radioactive Series

Radioactive Disintegration

Nuclear Radiations

Radioactivity

Nuclear Fusion

Nuclear Reactor

Difficulties in Chain ReactionÂ Â Â Â Â Â Â Â Â Â

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

Neutron

Nucleus

Electronic Configurations of Atoms

Quantum Numbers

Hydrogen Spectrum and Spectral Series

Transition of Electron

Energy

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

X-Rays

Compton Effect

Important Formulae for Photoelectric Effect

Effect of Intensity and Frequency of Light

Experimental Setup for Photoelectric Effect

Photo-Electric Effect

Photon

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

Phase

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

Magnetism

Force On a Current Carrying Conductor In Magnetic Field

Hall Effect

Cyclotron

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

Toroid

Solenoid

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

Potentiometer

Different Measuring Instruments

Kirchoff's Laws

Grouping of Cells

Cell in Various Positions

Cell

Grouping of Resistance

Colour Coding of Resistance

Electrical Conducting Materials For Specific Use

Stretching of Wire

Resistivity (p), Conductivity and Conductance (C)

Resistance

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

Dielectric

Capacitor or Condenser

Redistribution of Charges and Loss of Energy

Combination of Charged Drops

Capacitance

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 SpheresÂ

Electric Field and Potential Due to Various Charge Distribution

Electric Potential

Electric Field

Coulomb's Law

Electroscope

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

Beats

Kundt's Tube

Resonance Tube

End Correction

Tuning Fork

Standing Wave in a Organ Pipe

Vibration of Composite Strings

Sonometer

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

Echo

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

Waves

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

Radiation

Convection

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

Conduction

Transmission of Heat

Entropy

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

Thermodynamics

Gaseous Mixture

Specific Heat in Terms of Degree of Freedom

Mayer's FormulaÂ Â Â Â Â Â Â Â Â Â

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

MaxwellÃs 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)

Gas

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

Heat

Expansion of Gases

Variation of Density with Temperature

Thermal Expansion in Liquids

Application of Thermal Expansion in Solids

Scales of Temperature

Thermal Expansion

Thermometers

Thermometry

Temperature

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

Â Equation of Continuity

Critical Velocity and Reynold's Number

Streamline, Laminar and Turbulent Flow

Floatation

Archimedes Principle

Pascal's Law

Density

Pressure

Introduction

Useful Facts and Formulae

Shape of Drops

Ascent Formula

Capillarity

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

Strain

Stress

Elastic Property of Matter

Types of Solids

States of Matter

Comparison Between Interatomic and Intermolecular Forces

Intermolecular Forces

Interatomic Forces

Weightlessness in a Satellite

Weightlessness

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

Introduction

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

Collision

Position and Velocity of an Automobile w.r.t Time

Important Points

Power

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

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

Introduction

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

Introduction

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

Impulse

Frame of Reference

Newton's Third Law

Â Equilibrium of Concurrent Force

Force

Newton's Second Law

Newton's First Law

Linear Momentum

Inertia

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

Skidding of Object on A Rotating Platform

Skidding of Vehicle on A Level Road

Work Done by Centripetal Force

Centrifugal Force

Centripetal force

Centripetal Acceleration

Variables of Circular Motion

Circular Motion

Projectile Motion on An Inclined Plane

Horizontal Projectile

Oblique Projectile

Types of Projectile Motion

Principle of Physical Independence of Motions

Assumptions of Projectile Motion

Projectile