Maths 12th Std

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Maths 12th Std

Chapter 1: Applications of Matrices and Determinants


=> Introduction
=> Inverse of a Non-Singular Square Matrix
=> Adjoint of a Square Matrix
=> Definition of inverse matrix of a square matrix
=> Properties of inverses of matrices
=> Application of matrices to Geometry
=> Application of matrices to Cryptography
=> Exercise 1.1: Inverse of a Non-Singular Square Matrix
=> Inverse of a Non-Singular Square Matrix: Solved Example Problems
=> Elementary Transformations of a Matrix
=> Row Echelon form
=> Rank of a Matrix
=> Gauss Jordan Method
=> Exercise 1.2: Elementary Transformations of a Matrix
=> Elementary Transformations of a Matrix: Solved Example Problems
=> Applications of Matrices: Solving System of Linear Equations
=> Formation of a System of Linear Equations
=> System of Linear Equations in Matrix Form
=> Solution to a System of Linear equations
=> Matrix Inversion Method
=> Exercise 1.3: Matrices linear equations by matrix inversion method
=> Matrices: Cramer’s Rule
=> Exercise 1.4: Matrices: Cramer’s Rule
=> Matrix: Gaussian Elimination Method
=> Exercise 1.5: Matrix: Gaussian Elimination Method
=> Solved Example Problems on Applications of Matrices: Solving System of Linear Equations
=> Matrix: Non-homogeneous Linear Equations
=> Exercise 1.6: Matrix: Non-homogeneous Linear Equations
=> Matrix: Homogeneous system of linear equations
=> Exercise 1.7: Matrix: Homogeneous system of linear equations
=> Choose the Correct Answers
=> Summary

Chapter 2: Complex Numbers


=> Introduction
=> Introduction to Complex Numbers
=> Exercise 2.1: Introduction to Complex Numbers
=> Complex Numbers
=> Exercise 2.2: Complex Numbers
=> Basic Algebraic Properties of Complex Numbers
=> Exercise 2.3: Properties of Complex Numbers
=> Conjugate of a Complex Number
=> Exercise 2.4: Conjugate of a Complex Number
=> Modulus of a Complex Number
=> Properties of Modulus of a complex number
=> Modulus of a Complex Number: Solved Example Problems
=> Square roots of a complex number
=> Exercise 2.5: Modulus of a Complex Number
=> Geometry and Locus of Complex Numbers
=> Exercise 2.6: Geometry and Locus of Complex Numbers
=> Polar form of a complex number
=> Euler’s Form of the complex number
=> Exercise 2.7: Polar and Euler form of a Complex Number
=> de Moivre’s Theorem and its Applications
=> de Moivre's Theorem
=> Finding nth roots of a complex number
=> The nth roots of unity
=> Exercise 2.8: de Moivre’s Theorem and its Applications
=> Solved Example Problems on de Moivre’s Theorem
=> Choose the correct Answers
=> Summary

Chapter 3: Theory of Equations


=> Introduction
=> Basics and types of Polynomial Equations
=> Vieta’s formula for Quadratic Equations
=> Vieta’s formula for Polynomial Equations
=> Exercise 3.1: Vieta’s Formulae and Formation of Polynomial Equations
=> Nature of Roots and Nature of Coefficients of Polynomial Equations
=> Imaginary Roots
=> Irrational Roots
=> Rational Roots
=> Applications of Polynomial Equation in Geometry
=> Exercise 3.2: Polynomial Equation in Geometry
=> Roots of Higher Degree Polynomial Equations
=> Polynomials with Additional Information
=> Exercise 3.3: Polynomials with Additional Information
=> Partly Factored Polynomial
=> Exercise 3.4: Partly Factored Polynomial
=> Rational Root Theorem
=> Reciprocal Equations
=> Non-polynomial Equations
=> Exercise 3.5: Polynomial Equations with no Additional Information
=> Descartes Rule
=> Exercise 3.6: Descartes Rule
=> Choose the correct Answers
=> Summary

Chapter 4: Inverse Trigonometric Functions


=> Introduction
=> Some Fundamental Concepts of Inverse Trigonometric Functions
=> Sine Function and Inverse Sine Function
=> Exercise 4.1: Sine Function and Inverse Sine Function
=> The Cosine Function and Inverse Cosine Function
=> Exercise 4.2: Cosine Function and Inverse Cosine Function
=> The Tangent Function and the Inverse Tangent Function
=> Exercise 4.3: Tangent Function and the Inverse Tangent Function
=> Cosecant Function and the Inverse Cosecant Function
=> The Secant Function and Inverse Secant Function
=> The Cotangent Function and the Inverse Cotangent Function
=> Principal Value of Inverse Trigonometric Functions
=> Exercise 4.4: Principal Value of Inverse Trigonometric Functions
=> Properties of Inverse Trigonometric Functions
=> Solved Example Problems on Inverse Trigonometric Functions
=> Exercise 4.5: Inverse Trigonometric Functions
=> Choose the correct answers
=> Summary

Chapter 5: Two Dimensional Analytical Geometry II


=> Introduction
=> Circle
=> Equation of a circle in standard form
=> Equations of tangent and normal at a point P on a given circle
=> Condition for the line y = mx + c to be a tangent to the circle and finding the point of contact
=> Circle: Solved Example Problems
=> Exercise 5.1: Circle
=> Conics
=> The general equation of a Conic
=> Parabola
=> Ellipse
=> Hyperbola
=> Exercise 5.2: Conics
=> Conic Sections
=> Exercise 5.3: Conic Sections
=> Parametric form of Conics
=> Tangents and Normals to Conics
=> Exercise 5.4: Tangents and Normals to Conics
=> Real life Applications of Conics
=> Exercise 5.5: Real life Applications of Conics
=> Solved Example Problems on Real life Applications of Conics
=> Choose the correct Answer
=> Summary

Chapter 6: Applications of Vector Algebra


=> Introduction
=> Geometric introduction to vectors
=> Scalar Product and Vector Product
=> Exercise 6.1: Scalar Product and Vector Product
=> Scalar triple product
=> Exercise 6.2: Scalar triple product
=> Vector triple product
=> Jacobi’s Identity and Lagrange’s Identity
=> Exercise 6.3: Vector triple product, Jacobi’s Identity and Lagrange’s Identity
=> Application of Vectors to 3-Dimensional Geometry
=> Exercise 6.4: Application of Vectors to 3-Dimensional Geometry
=> A point on the straight line and the direction of the straight line
=> Straight Line passing through two given points
=> Angle between two straight lines
=> Point of intersection of two straight lines
=> Shortest distance between two straight lines
=> Exercise 6.5: Point of intersection of two straight lines
=> Different forms of Equation of a plane
=> Equation of a plane when a normal to the plane
=> Equation of a plane perpendicular to a vector and passing through a given point
=> Intercept form of the equation of a plane
=> Exercise 6.6: Equation of a plane
=> Equation of a plane passing through three given non-collinear points
=> Equation of a plane passing through a given point and parallel to two given non-parallel vectors
=> Equation of a plane passing through two given distinct points and is parallel to a non-zero vector
=> Exercise 6.7: Equation of a plane
=> Condition for a line to lie in a plane
=> Condition for coplanarity of two lines
=> Equation of plane containing two non-parallel coplanar lines
=> Exercise 6.8: Equation of a plane
=> Angle between two planes
=> Angle between a line and a plane
=> Distance of a point from a plane
=> Distance between two parallel planes
=> Equation of line of intersection of two planes
=> Equation of a plane passing through the line of intersection of two given planes
=> Image of a Point in a Plane
=> Meeting Point of a Line and a Plane
=> Exercise 6.9: Equation of intersection of the planes
=> Choose the correct answer
=> Summary



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