# Notes for JEE Main & Advanced Mathematics

## 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
Special Types of Matrices
Transpose of a Matrix
Positive Integral Powers of a Matrix
Multiplication of Matrices
Scalar Multiplication 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
Sufficient Criteria for Extreme Values (1st Derivative Test)
Necessary Condition for Extreme Values
Definition
Definition
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
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
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 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
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