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# Class 12 Maths NCERT Solutions

## Mathematics Textbook for Class 12

Author: NCERT
Publisher: NCERT

Shaalaa provides solutions for NCERT Solutions for Class 12 Maths and has all the answers for the questions given in Mathematics Textbook for Class 12. Shaalaa is surely a site that most of your classmates are using to perform well in exams.

You can solve Mathematics Textbook for Class 12 textbook questions and use Shaalaa NCERT Solutions for Class 12 Maths to verify your answers. ## Chapters covered in NCERT Solutions for Class 12 Maths

#### Chapter 1: Relations and Functions

Shaalaa has a total of 101 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Relations and Functions are Composition of Functions and Invertible Function, Concept of Binary Operations, Introduction of Relations and Functions, Inverse of a Function, Types of Functions, Types of Relations

#### Chapter 2: Inverse Trigonometric Functions

Shaalaa has a total of 51 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Inverse Trigonometric Functions are Basic Concepts of Trigonometric Functions, Graphs of Inverse Trigonometric Functions, Inverse Trigonometric Functions - Principal Value Branch, Inverse Trigonometric Functions (Simplification and Examples), Properties of Inverse Trigonometric Functions

#### Chapter 3: Matrices

Shaalaa has a total of 111 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Matrices are Addition of Matrices, Concept of Transpose of a Matrix, Elementary Operation (Transformation) of a Matrix, Equality of Matrices, Introduction of Matrices, Introduction of Operations on Matrices, Inverse of a Nonsingular Matrix by Elementary Transformation, Invertible Matrices, Matrices Notation, Multiplication of a Matrix by a Scalar, Multiplication of Matrices, Multiplication of Two Matrices, Negative of Matrix, Order of a Matrix, Proof of the Uniqueness of Inverse, Properties of Matrix Addition, Properties of Multiplication of Matrices, Properties of Scalar Multiplication of a Matrix, Properties of Transpose of the Matrices, Subtraction of Matrices, Symmetric and Skew Symmetric Matrices, Types of Matrices

#### Chapter 4: Determinants

Shaalaa has a total of 101 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Determinants are Applications of Determinants and Matrices, Area of a Triangle, Determinant of a Matrix of Order 3 × 3, Determinant of a Square Matrix, Determinants of Matrix of Order One and Two, Elementary Transformations, Introduction of Determinant, Inverse of a Square Matrix by the Adjoint Method, Minors and Co-factors, Properties of Determinants, Rule A=KB

#### Chapter 5: Continuity and Differentiability

Shaalaa has a total of 148 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Continuity and Differentiability are Algebra of Continuous Functions, Concept of Continuity, Concept of Differentiability, Continuous Function of Point, Derivative - Exponential and Log, Derivatives of Composite Functions - Chain Rule, Derivatives of Functions in Parametric Forms, Derivatives of Implicit Functions, Derivatives of Inverse Trigonometric Functions, Exponential and Logarithmic Functions, Higher Order Derivative, Infinite Series, Logarithmic Differentiation, Mean Value Theorem, Proof Derivative X^n Sin Cos Tan, Second Order Derivative

#### Chapter 6: Application of Derivatives

Shaalaa has a total of 167 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Application of Derivatives are Approximations, Graph of Maxima and Minima, Increasing and Decreasing Functions, Introduction to Applications of Derivatives, Maxima and Minima, Maximum and Minimum Values of a Function in a Closed Interval, Rate of Change of Bodies Or Quantities, Simple Problems on Applications of Derivatives, Tangents and Normals

#### Chapter 7: Integrals

Shaalaa has a total of 273 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Integrals are Comparison Between Differentiation and Integration, Definite Integral as the Limit of a Sum, Definite Integrals Problems, Evaluation of Definite Integrals by Substitution, Evaluation of Simple Integrals of the Following Types and Problems, Fundamental Theorem of Calculus, Geometrical Interpretation of Indefinite Integral, Indefinite Integral by Inspection, Indefinite Integral Problems, Integrals of Some Particular Functions, Integration as an Inverse Process of Differentiation, Integration Using Trigonometric Identities, Introduction of Integrals, Methods of Integration - Integration by Parts, Methods of Integration - Integration by Substitution, Methods of Integration - Integration Using Partial Fractions, Properties of Definite Integrals, Properties of Indefinite Integral

#### Chapter 8: Application of Integrals

Shaalaa has a total of 40 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Application of Integrals are Area Between Two Curves, Area of the Region Bounded by a Curve and a Line, Area Under Simple Curves

#### Chapter 9: Differential Equations

Shaalaa has a total of 118 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Differential Equations are Basic Concepts of Differential Equation, Differential Equations with Variables Separable Method, Formation of a Differential Equation Whose General Solution is Given, General and Particular Solutions of a Differential Equation, Homogeneous Differential Equations, Linear Differential Equations, Order and Degree of a Differential Equation, Procedure to Form a Differential Equation that Will Represent a Given Family of Curves, Solutions of Linear Differential Equation

#### Chapter 10: Vector Algebra

Shaalaa has a total of 76 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Vector Algebra are Addition of Vectors, Basic Concepts of Vector Algebra, Components of a Vector, Concept of Direction Cosines, Geometrical Interpretation of Scalar, Introduction of Product of Two Vectors, Introduction of Vector, Magnitude and Direction of a Vector, Multiplication of a Vector by a Scalar, Position Vector of a Point Dividing a Line Segment in a Given Ratio, Projection of a Vector on a Line, Properties of Vector Addition, Scalar (Or Dot) Product of Two Vectors, Scalar Triple Product of Vectors, Section formula, Types of Vectors, Vector Joining Two Points, Vector (Or Cross) Product of Two Vectors, Vectors Examples and Solutions

#### Chapter 11: Three Dimensional Geometry

Shaalaa has a total of 78 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Three Dimensional Geometry are Angle Between Line and a Plane, Angle Between Two Lines, Angle Between Two Planes, Coplanarity of Two Lines, Direction Cosines and Direction Ratios of a Line, Distance of a Point from a Plane, Equation of a Line in Space, Equation of a Plane in Normal Form, Equation of a Plane Passing Through Three Non Collinear Points, Equation of a Plane Perpendicular to a Given Vector and Passing Through a Given Point, Intercept Form of the Equation of a Plane, Introduction of Three Dimensional Geometry, Plane Passing Through the Intersection of Two Given Planes, Relation Between Direction Ratio and Direction Cosines, Shortest Distance Between Two Lines, Three - Dimensional Geometry Examples and Solutions, Vector and Cartesian Equation of a Plane

#### Chapter 12: Linear Programming

Shaalaa has a total of 32 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Linear Programming are Different Types of Linear Programming Problems, Graphical Method of Solving Linear Programming Problems, Introduction of Linear Programming, Linear Programming Problem and Its Mathematical Formulation, Mathematical Formulation of Linear Programming Problem

#### Chapter 13: Probability

Shaalaa has a total of 122 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Probability are Baye'S Theorem, Bernoulli Trials and Binomial Distribution, Conditional Probability, Independent Events, Introduction of Probability, Mean of a Random Variable, Multiplication Theorem on Probability, Probability Examples and Solutions, Properties of Conditional Probability, Random Variables and Its Probability Distributions, Variance of a Random Variable

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## NCERT Solutions for Class 12 Maths

Class 12 NCERT solutions answers all the questions given in the NCERT textbooks in a step-by-step process. Our Maths tutors have helped us put together this for our Class 12 Students. The solutions on Shaalaa will help you solve all the NCERT Class 12 Mathematics questions without any problems. Every chapter has been broken down systematically for the students, which gives fast learning and easy retention.

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Our NCERT solutions for Class 12 Maths cover everything from Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Linear Programming, Probability and the other topics. Yes, these are the best NCERT 12 Maths solution options on the market. You get to fully prepare for the exam in a reliable and comprehensive manner. You just have to check it out for yourself and the experience can be really impressive.

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