Notes for JEE Main & Advanced Mathematics

Recent Notes

Matrices of Rotation of Axes
Matrices
Geometrical Transformations
Matrices
Cayley-Hamilton Theorem
Matrices
Consistency of a System of Linear Equation \[\mathbf{AX=B,}\] where \[\mathbf{A}\] is a square matrix
Matrices
Homogeneous and Non-homogeneous Systems of Linear Equations
Matrices
Echelon Form of a Matrix
Matrices
Rank of Matrix
Matrices
Inverse of a Matrix
Matrices
Adjoint of a Square Matrix
Matrices
Special Types of Matrices
Matrices
Transpose of a Matrix
Matrices
Positive Integral Powers of a Matrix
Matrices
Multiplication of Matrices
Matrices
Scalar Multiplication of Matrices
Matrices
Addition and Subtraction of Matrices
Matrices
Trace of a Matrix
Matrices
Types of Matrices
Matrices
Equality of Matrices
Matrices
Order of a Matrix
Matrices
Definition
Matrices
Some Special Determinants
Determinants
Application of Determinants in Solving a System of Linear Equations
Determinants
Differentiation and Integration of Determinants
Determinants
Product of Two Determinants
Determinants
Minors and Cofactors
Determinants
Properties of Determinants
Determinants
Definition
Determinants
Lagrange's Mean Value Theorem
Applications of Derivatives
Rolle's Theorem
Applications of Derivatives
Greatest and Least Values of a Function Defined on an Interval \[[a,\,\,b]\]
Applications of Derivatives
Properties of Maxima and Minima
Applications of Derivatives
Higher Order Derivative Test
Applications of Derivatives
Sufficient Criteria for Extreme Values (1st Derivative Test)
Applications of Derivatives
Necessary Condition for Extreme Values
Applications of Derivatives
Definition
Applications of Derivatives
Definition
Applications of Derivatives
Length of Perpendicular from Origin to the Tangent
Applications of Derivatives
Length of Intercept Made on Axes by The Tangent
Applications of Derivatives
Length of Tangent, Normal, Subtangent, Subnormal
Applications of Derivatives
Angle of Intersection of Two Curves
Applications of Derivatives
Equation of the Tangent and Normal
Applications of Derivatives
Slope of the Tangent and Normal
Applications of Derivatives
Velocity and Acceleration in Rectilinear Motion
Applications of Derivatives
Derivative as the Rate of Change
Differentiation
Deduction of Euler?s Theorem
Differentiation
Euler's Theorem on Homogeneous Functions
Differentiation
Higher Partial Derivatives
Differentiation
Definition
Differentiation
Leibnitz?s Theorem
Differentiation
Differentiation of Integral Function
Differentiation
\[{{n}^{th}}\] Derivative Using Partial Fractions
Differentiation
Successive Differentiation or Higher Order Derivatives
Differentiation
Differentiation of a Function with Respect to Another Function
Differentiation
Methods of Differentiation
Differentiation
Theorems for Differentiation
Differentiation
Some Standard Differentiation
Differentiation
Introduction
Differentiation
Relation Between A.P., G.P. and H.P.
Geometric Progression
Properties of Arithmetic, Geometric, Harmonic Means Between Two Given Numbers
Geometric Progression
Special Series
Geometric Progression
Method of Difference
Geometric Progression
Method for Finding Sum
Geometric Progression
Sum of A.G.P.
Geometric Progression
\[{{n}^{th}}\]term of A.G.P.
Geometric Progression
Definition
Geometric Progression
Properties of H.P.
Other Series
Harmonic Mean
Other Series
General Term of an H.P.
Other Series
Definition
Other Series
Properties of G.P.
Geometric Progression
Geometric Mean
Geometric Progression
Sum of infinite terms of a G.P.
Geometric Progression
Sum of first 'n' terms of a G.P.
Geometric Progression
Selection of Terms in a G.P.
Geometric Progression
General term of a G.P.
Geometric Progression
Definition
Geometric Progression
Properties of A.P.
Arithmetic Progressions
Arithmetic Mean
Arithmetic Progressions
Sum of n terms of an A.P.
Arithmetic Progressions
Selection of Terms in an A.P.
Arithmetic Progressions
General Term of an A.P.
Arithmetic Progressions
Definition
Arithmetic Progressions
Some Important Results
Trigonometric Equations
Some Properties Related to Circle
Trigonometric Equations
Some Terminology Related to Height and Distance
Trigonometric Equations
Solutions of Triangles
Trigonometric Equations
Regular Polygon
Trigonometric Equations
Cyclic Quadrilateral
Trigonometric Equations
Ex-central Triangle
Trigonometric Equations
Pedal Triangle
Trigonometric Equations
Circle Connected With Triangle
Trigonometric Equations
Half Angle Formulae
Trigonometric Equations
Area of Triangle
Trigonometric Equations
Napier's Analogy (Law of Tangents)
Trigonometric Equations
Theorem of The Medians: (Apollonius Theorem)
Trigonometric Equations
Projection Formulae
Trigonometric Equations
The Law of Cosines or Cosine Rule
Trigonometric Equations
Relation Between Sides and Angles
Trigonometric Equations
Periodic Functions
Trigonometric Equations
Important Points to be Taken in Case of While Solving Trigonometrical Equations
Trigonometric Equations
Method for Finding Principal Value
Trigonometric Equations
General Solution of The Form \[\mathbf{acos}\,\mathbf{\theta +bsin}\,\mathbf{\theta =c}\]
Trigonometric Equations
Trigonometrical Equations With Their General Solution
Trigonometric Equations
Trigonometrical Equations and Inequations Definition
Trigonometric Equations
Differentiability of a Function at a Point
Functions
Discontinuous Function
Functions
Continuity From Left and Right
Functions
Continuity of a Function at a Point
Functions
Introduction
Functions
Methods of Evaluation of Limits
Functions
Fundamental Theorems on Limits
Functions
Limit of a Function
Functions
Inverse Function
Functions
Composite Function
Functions
Periodic Function
Functions
Even and Odd Function
Functions
Conditional Trigonometrical Identities
Trigonometrical Ratios and Identities
Kinds of function
Functions
Algebra of Functions
Functions
Domain, Co-domain and Range of Function
Functions
Definition of Function
Functions
Intervals
Functions
Maximum and Minimum Value of a \[\mathbf{cos}\,\,\mathbf{\theta }\,\,\mathbf{+}\,\mathbf{b}\,\,\mathbf{sin}\,\,\mathbf{\theta }\]
Trigonometrical Ratios and Identities
Some Important Definitions
Functions
Trigonometric Ratio of Sub-multiple of an Angle
Trigonometrical Ratios and Identities
Trigonometric Ratio of Multiple of an Angle
Trigonometrical Ratios and Identities
Formulae to Rransform The Product Into Sum or Difference
Trigonometrical Ratios and Identities
Trigonometrical Ratios In Terms of Each Other
Trigonometrical Ratios and Identities
Trigonometrical Ratios for Some Special Angles
Trigonometrical Ratios and Identities
Trigonometrical Ratios for Various Angles
Trigonometrical Ratios and Identities
Trigonometrical Ratios of Allied Angles
Trigonometrical Ratios and Identities
Trigonometrical Ratios or Functions
Trigonometrical Ratios and Identities
Domain and Range of a Trigonometrical Function
Trigonometrical Ratios and Identities
Angle of Intersection of Two Spheres
Three Dimensional Geometry
Intersection of Straight Line and a Sphere
Three Dimensional Geometry
Condition of Tangency of a Plane to a Sphere
Three Dimensional Geometry
Relation Between an arc and an Angle
Trigonometrical Ratios and Identities
Relation Between Three Systems of Measurement of an Angle
Trigonometrical Ratios and Identities
System of Measurement of Angles   
Trigonometrical Ratios and Identities
Section of a Sphere by a Plane
Three Dimensional Geometry
Equation in Sphere in Various Forms
Three Dimensional Geometry
General Equation of Sphere
Three Dimensional Geometry
Projection of a Line on a Plane
Three Dimensional Geometry
Angle Between Line and Plane
Three Dimensional Geometry
Intersection Point of a Line and Plane
Three Dimensional Geometry
Introduction
Trigonometrical Ratios and Identities
Equation of Plane Through a Given Line
Three Dimensional Geometry
Coplanar Lines
Three Dimensional Geometry
Image of a Point in a Plane
Three Dimensional Geometry
Equation of Planes Bisecting Angle Between Two Given Planes
Three Dimensional Geometry
Locus
Angle Between Two Planes
Three Dimensional Geometry
Foot of Perpendicular from a Point \[\mathbf{A(\alpha ,}\,\,\mathbf{\beta ,}\,\,\mathbf{\gamma )}\]to a given plane \[\mathbf{ax+by+cz+d=0}\].
Three Dimensional Geometry
Transformation of Axes
Equation of Plane Passing Through the Given Point
Three Dimensional Geometry
Area of Some Geometrical Figures
Rectangular Cartesian Coordinates
Definition of Plane and Its Equations
Three Dimensional Geometry
Shortest Distance Between two Straight Lines
Three Dimensional Geometry
Foot of Perpendicular from a Point to The Line
Three Dimensional Geometry
Intersection of Two Lines
Three Dimensional Geometry
Changing Unsymmetrical form to Symmetrical Form
Three Dimensional Geometry
Some Points of a Triangle
Rectangular Cartesian Coordinates
Straight Line in Space
Three Dimensional Geometry
Angle Between Two Lines
Three Dimensional Geometry
Projection
Three Dimensional Geometry
Direction Cosines and Direction Ratios
Three Dimensional Geometry
Triangle and Tetrahedron
Three Dimensional Geometry
Section Formulae
Rectangular Cartesian Coordinates
Section Formula
Three Dimensional Geometry
Distance Formula
Three Dimensional Geometry
Properties of Some Geometrical Figures
Rectangular Cartesian Coordinates
Co-ordinates of a Point in Space
Three Dimensional Geometry
Distance Formula
Rectangular Cartesian Coordinates
Polar Co-ordinates
Rectangular Cartesian Coordinates
Cartesian Co-ordinates of a Point
Rectangular Cartesian Coordinates
Introduction
Rectangular Cartesian Coordinates
Binomial Distribution
Probability
Total Probability and Baye's Rule
Probability
Conditional Probability
Probability
Addition Theorems on Probability
Probability
Odds in Favour and Odds Against an Event
Probability
Problems Based on Combination and Permutation
Probability
Classical Definition of Probability
Probability
Definitions of Various Terms
Probability
Probability
Distance Between The Pair of Parallel Straight Lines     
Pair of 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
Pair of Straight Lines
Removal of First Degree Terms
Pair of Straight Lines
Equation of the Lines Joining the Origin to the Points of Intersection of a Given Line and a Given Curve
Pair of Straight Lines
Bisectors of the Angles Between the Lines
Pair of Straight Lines
Angle Between the Pair of Lines
Pair of Straight Lines
Point of Intersection of Lines Represented by \[\mathbf{a}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+ 2hxy+b}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+ 2gx+ 2fy+c= 0}\]
Pair of Straight Lines
Equation of Pair of Straight Lines
Pair of Straight Lines
Logic Gates
Mathematical Logic and Boolean Algebra
Switching Circuits
Mathematical Logic and Boolean Algebra
Boolean Functions
Mathematical Logic and Boolean Algebra
Introduction
Mathematical Logic and Boolean Algebra
Duality
Mathematical Logic and Boolean Algebra
Algebra of Statements
Mathematical Logic and Boolean Algebra
Tautologies and Contradictions
Mathematical Logic and Boolean Algebra
Negation of Compound Statements
Mathematical Logic and Boolean Algebra
Logical Equivalence
Mathematical Logic and Boolean Algebra
Basic Logical Connectives or Logical Operators
Mathematical Logic and Boolean Algebra
Truth Tables
Mathematical Logic and Boolean Algebra
Types of Statements
Mathematical Logic and Boolean Algebra
Use of Venn Diagrams in Checking Truth and Falsity of Statements
Mathematical Logic and Boolean Algebra
Statements or Propositions
Mathematical Logic and Boolean Algebra
Introduction
Mathematical Logic and Boolean Algebra
Advantages and Limitations of L.P.P.
Linear Programming
To Find The Vertices of Simple Feasible Region Without Drawing a Graph
Linear Programming
Graphical Solution of Two Variable Linear Programming Problem
Linear Programming
Mathematical Formulation of a Linear Programming Problem
Linear Programming
Terms of Linear Programming
Linear Programming
Linear Inequations
Linear Programming
Inverse Trigonometric Ratios of Multiple Angles
Inverse Trigonometric Functions
Formulae for Sum, Difference of Inverse Trigonometric Function
Inverse Trigonometric Functions
Properties of inverse trigonometric functions
Inverse Trigonometric Functions
Domain and Range of Inverse Trigonometric Functions
Inverse Trigonometric Functions
Graphs of Inverse Trigonometric Functions
Inverse Trigonometric Functions
Integration of Hyperbolic Functions
Indefinite Integrals
Integration of Trigonometric Functions
Indefinite Integrals
Integration of Rational Functions by Using Partial Fractions
Indefinite Integrals
Integrals of the form \[\int{\frac{a sinx+b cosx}{c sinx+d cosx} }\]and \[\int{\frac{a\,sinx+bcos\,x+q}{c\,sinx+d\,cosx+r}}\]
Indefinite Integrals
Integrals of the form \[\int_{{}}^{{}}{\frac{dx}{a+b\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}x},\,\int_{{}}^{{}}{\frac{dx}{a+b\,\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}x},}}\]\[\int_{{}}^{{}}{\frac{dx}{a\,\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}x+b\,\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}x}\mathbf{,}}\]\[\int_{{}}^{{}}{\frac{dx}{{{\mathbf{(}a\,\sin x+b\,\mathbf{cos}\,x\mathbf{)}}^{\mathbf{2}}}}\mathbf{,}}\int_{{}}^{{}}{\frac{dx}{a\,+b\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}x+c\,\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}x}}\]
Indefinite Integrals
Integrals of the Form \[\int{\frac{dx}{a+bcosx+csinx}}\,,\,\,\int{\frac{dx}{asinx+bcosx}}\]
Indefinite Integrals
Integrals of the Form \[\int{\frac{dx}{a+b\,cos\,x}}\] and \[\int{\frac{dx}{a+b\,sin\,x}}\]
Indefinite Integrals
Evaluation of the Various Forms of Integrals by Use of Standard Results
Indefinite Integrals
Position of Centre of Gravity in Some Special Cases
Statistics
Integration by Parts
Indefinite Integrals
Centre of Gravity of a Compound Body and Remainder
Statistics
Centre of Gravity
Statistics
Limiting Equilibrium on an Inclined Plane
Statistics
Coefficient of Friction
Statistics
Friction
Statistics
Equilibrium of Coplanar Forces
Statistics
Triangle Theorem of Couples
Statistics
Integration By Substitution
Indefinite Integrals
Couples
Statistics
Moment
Statistics
Parallel Forces
Statistics
Lami's Theorem
Statistics
Polygon Law of Forces
Statistics
Triangle Law of Forces
Statistics
Parallelogram Law of Forces
Statistics
Fundamental Integration Formulae
Indefinite Integrals
Introduction
Statistics
Definition
Indefinite Integrals
Image of a Point in Different Cases
Straight Line
Reflection on The Surface
Straight Line
Concurrent Lines
Straight Line
Position of Two Points with Respect to a Line
Straight Line
Position of a Point with Respect to a Line
Straight Line
Length of Perpendicular
Straight Line
Equations of the Bisectors of The Angles Between two Straight Lines
Straight Line
Equation of Straight Line Through a Given Point Making a Given Angle With a Given Line
Straight Line
Angle Between two Non-parallel Lines
Straight Line
General Equation of Lines Through the Intersection of Two Given Lines
Straight Line
Point of Intersection of Two Lines
Straight Line
General Equation of a Straight Line and its Transformation in Standard Forms
Straight Line
Equation of Parallel and Perpendicular Lines to a Given Line
Straight Line
Equations of Straight Line in Different Forms
Straight Line
Slope (Gradient) of a Line
Straight Line
Definition
Straight Line
Miscellaneous Differential Equation
Differential Equations
Application of Differential Equation
Differential Equations
Linear Differential Equation
Differential Equations
Solution by Inspection
Differential Equations
Exact Differential Equation
Differential Equations
Homogeneous Differential Equation
Differential Equations
Variable Separable Type Differential Equation
Differential Equations
Formation of Differential Equation
Differential Equations
Definition
Differential Equations
Symmetrical Area
Definite Integrals
Application of Vectors in 3-dimensional Geometry
Vector Algebra
Rotation of a Vector About an Axis
Vector Algebra
Vector Product of Four Vectors
Vector Algebra
Area of Bounded Regions
Definite Integrals
Scalar Product of Four Vectors
Vector Algebra
Vector Triple Product
Vector Algebra
Integration of Piecewise Continuous Functions
Definite Integrals
Scalar Triple Product
Vector Algebra
Volumes and Surfaces of Solids of Revolution
Definite Integrals
Some Important Results of Definite Integral
Definite Integrals
Area Between Two Curves
Definite Integrals
Vector or Cross Product
Vector Algebra
Scalar or Dot Product
Vector Algebra
Linear Independence and Dependence of Vectors
Vector Algebra
Linear Combination of Vectors
Vector Algebra
Position Vector
Vector Algebra
Leibnitz's Rule
Definite Integrals
Properties of Vectors
Vector Algebra
Walli's Formula
Definite Integrals
Types of Vector
Vector Algebra
Reduction Formulae for Definite Integration
Definite Integrals
Gamma Function
Definite Integrals
Summation of Series by Integration
Definite Integrals
Representation of Vectors
Vector Algebra
Introduction
Vector Algebra
Properties of Definite Integral
Definite Integrals
Evaluation of Definite Integral by Substitution
Definite Integrals
Definition
Definite Integrals
Rectangular or Equilateral Hyperbola
Conic Section
Asymptotes of a Hyperbola
Conic Section
Subtangent and Subnormal of the Hyperbola
Conic Section
Diameter of The Hyperbola
Conic Section
Pole and Polar
Conic Section
Equation of The Chord Joining Two Points on The Hyperbola
Conic Section
Equation of the Chord of the Hyperbola Whose mid point \[\mathbf{(}{{\mathbf{x}}_{\mathbf{1}}}\mathbf{,}\,\,{{\mathbf{y}}_{\mathbf{1}}}\mathbf{)}\] is given
Conic Section
Equation of Chord of Contact of Tangents Drawn from a Point to a Hyperbola
Conic Section
Equations of Normal in Different Forms
Conic Section
Equation of Pair of Tangents
Conic Section
Equations of Tangent in Different Forms
Conic Section
Intersection of a Line and a Hyperbola
Conic Section
Position of a Point With Respect to a Hyperbola
Conic Section
Parametric Equations of Hyperbola
Conic Section
Auxiliary Circle of Hyperbola
Conic Section
Special form of Hyperbola
Conic Section
Conjugate Hyperbola
Conic Section
Standard Equation of the Hyperbola
Conic Section
Definition
Conic Section
Subtangent and Subnormal
Conic Section
Diameter of The Ellipse
Conic Section
Pole and Polar
Conic Section
Equation of The Chord Joining Two Points on an Ellipse
Conic Section
Equation of Chord With Mid Point \[\mathbf{(}{{\mathbf{x}}_{\mathbf{1}}}\mathbf{,}{{\mathbf{y}}_{\mathbf{1}}}\mathbf{)}\]
Conic Section
Chord of Contact
Conic Section
Auxiliary Circle
Conic Section
Equations of Normal in Different Forms
Conic Section
Equation of Pair of Tangents \[\mathbf{S}{{\mathbf{S}}_{\mathbf{1}}}\mathbf{=}{{\mathbf{T}}^{\mathbf{2}}}\]
Conic Section
Equations of Tangent in Different Forms
Conic Section
Intersection of a Line and an Ellipse
Conic Section
Position of a Point with Respect to an Ellipse
Conic Section
Special Forms of an Ellipse
Conic Section
Parametric Form of The Ellipse
Conic Section
Standard Equation of the Ellipse
Conic Section
Definition
Conic Section
Pole and Polar
Conic Section
Length of Tangent, Subtangent, Normal and Subnormal to \[{{\mathbf{y}}^{\mathbf{2}}}\mathbf{= 4ax}\,\,\mathbf{at }\,\mathbf{(a}{{\mathbf{t}}^{\mathbf{2}}}\mathbf{,2at)}\]
Conic Section
Length of Tangent, Subtangent, Normal, Subnormal
Conic Section
Diameter of a Parabola
Conic Section
Equation of the Chord Joining any Two Points on the Parabola 
Conic Section
Equation of the Chord of the Parabola Which is Bisected at a Given Point  
Conic Section
Equation of The Chord of Contact of Tangents to a Parabola 
Conic Section
Co-normal Points
Conic Section
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 \[\mathbf{'}{{\mathbf{t}}_{\mathbf{2}}}\mathbf{'}\]
Conic Section
Point of Intersection of Normals at Any Two Points on The Parabola
Conic Section
Equations of Normal in Different Forms
Conic Section
Equation of Pair of Tangents From a Point to a Parabola
Conic Section
Point of Intersection of Tangents at Any Two Points on The Parabola
Conic Section
Equations of Tangent in Different Forms
Conic Section
Position of a Point and a Line With Respect to a Parabola
Conic Section
Parametric Equations of a Parabola
Conic Section
Special form of Parabola \[{{\mathbf{(yk)}}^{\mathbf{2~}}}\mathbf{= 4a}\,\,\mathbf{(xh)= a}\]
Conic Section
Standard Equation of The Parabola
Conic Section
Definition
Conic Section
Recognisation of Conics
Conic Section
General Equation of a Conic Section When Its Focus, Directrix and Eccentricity are Given
Conic Section
Definitions of Various Important Terms
Conic Section
Definition
Conic Section
Image of The Circle by The Line Mirror
Circle and System of Circles
Limiting Points
Circle and System of Circles
Co-axial System of Circles
Circle and System of Circles
Radical Centre
Circle and System of Circles
Radical Axis
Circle and System of Circles
Family of Circles
Circle and System of Circles
Angle of Intersection of Two Circles
Circle and System of Circles
Common Tangents to Two Circles
Circle and System of Circles
Pole and Polar
Circle and System of Circles
Diameter of a Circle
Circle and System of Circles
Common Chord of Two Circles
Circle and System of Circles
Chord of Contact of Tangents
Circle and System of Circles
Normal to a Circle at a Given Point
Circle and System of Circles
Power of Point with Respect to a Circle
Circle and System of Circles
Director Circle
Circle and System of Circles
Pair of Tangents
Circle and System of Circles
Length of Tangent
Circle and System of Circles
Tangent to a Circle at a Given Point
Circle and System of Circles
Intersection of a Line and a Circle
Circle and System of Circles
Position of a Point With Respect to a Circle
Circle and System of Circles
Intercepts on the Axes
Circle and System of Circles
Equation of a Circle in Some Special Cases
Circle and System of Circles
Standard Forms of Equation of a Circle
Circle and System of Circles
Definition
Circle and System of Circles
Divisibility Problems
Binomial Theorem and Mathematical Induction
Second Principle of Mathematical Induction
Binomial Theorem and Mathematical Induction
First Principle of Mathematical Induction
Binomial Theorem and Mathematical Induction
Some Important Points
Binomial Theorem and Mathematical Induction
Three / Four Consecutive Terms or Coefficients
Binomial Theorem and Mathematical Induction
Binomial Theorem for any Index
Binomial Theorem and Mathematical Induction
Multinomial Theorem (for Positive Integral Index)
Binomial Theorem and Mathematical Induction
An Important Theorem
Binomial Theorem and Mathematical Induction
Use of Differentiation and Integration in Binomial Theorem
Binomial Theorem and Mathematical Induction
Properties of Binomial Coefficients
Binomial Theorem and Mathematical Induction
Greatest Term and Greatest Coefficient
Binomial Theorem and Mathematical Induction
To Determine a Particular Term in the Expansion
Binomial Theorem and Mathematical Induction
Middle Term
Binomial Theorem and Mathematical Induction
Number of Terms In The Expansion of \[{{(a+b+c)}^{n}}\] and \[{{(a+b+c+d)}^{n}}\]
Binomial Theorem and Mathematical Induction
Independent Term or Constant Term
Binomial Theorem and Mathematical Induction
General Term
Binomial Theorem and Mathematical Induction
Some Important Expansions
Binomial Theorem and Mathematical Induction
Binomial Theorem for Positive Integral Index
Binomial Theorem and Mathematical Induction
Binomial Expression
Binomial Theorem and Mathematical Induction
Number of Divisors
Permutations and Combinations
Multinomial Theorem
Permutations and Combinations
Some Important Results For Geometrical Problems
Permutations and Combinations
Derangement
Permutations and Combinations
Division Into Groups
Permutations and Combinations
Conditional Combinations
Permutations and Combinations
Number of Combinations With Repetition and All Possible Selections
Permutations and Combinations
Number of Combinations Without Repetition
Permutations and Combinations
Definition
Permutations and Combinations
Circular Permutations
Permutations and Combinations
Conditional Permutations
Permutations and Combinations
Number of permutations with repetition
Permutations and Combinations
Number of Permutations Without Repetition
Permutations and Combinations
Definition of Permutation
Permutations and Combinations
Introduction
Permutations and Combinations
Some Important Result
Quadratic Equations
Equations Which Can Be Reduced to Linear, Quadratic and Biquadratic Equations
Quadratic Equations
Rational Algebraic Inequations
Quadratic Equations
Descarte's Rule of Signs
Quadratic Equations
Position of Roots
Quadratic Equations
Wavy Curve Method
Quadratic Equations
The Quadratic Expression
Quadratic Equations
Properties of Quadratic Equation
Quadratic Equations
Condition for Common Roots
Quadratic Equations
Higher Degree Equations
Quadratic Equations
Relations Between Roots and Coefficients
Quadratic Equations
Nature of Roots
Quadratic Equations
Solution of Quadratic Equation
Quadratic Equations
Types of Quadratic Equation
Quadratic Equations
Polynomial
Quadratic Equations
Composition of Relations
Set Theory and Relations
Equivalence Classes of An Equivalence Relation
Set Theory and Relations
Types of Relations
Set Theory and Relations
Inverse Relation
Set Theory and Relations
Definition
Set Theory and Relations
Cartesian Product of Sets
Set Theory and Relations
Laws of Algebra of Sets
Set Theory and Relations
Some important results on number of elements in sets
Set Theory and Relations
Operations on sets
Set Theory and Relations
Venn-Euler Diagrams
Set Theory and Relations
Types of Sets
Set Theory and Relations
Introduction
Set Theory and Relations



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