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# RD Sharma Class 12 Maths Chapter Wise Solutions

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## Solutions for Mathematics for Class 12 (Set of 2 Volume)

Shaalaa provides RD Sharma Solutions for Class 12 Maths and has all the answers for the questions given in Mathematics for Class 12 (Set of 2 Volume). Shaalaa is surely a site that most of your classmates are using to perform in exams.

You can solve Mathematics for Class 12 (Set of 2 Volume) and use Shaalaa RD Sharma Solutions for Class 12 Maths to check your answers.

## Chapters covered in RD Sharma Solutions for Mathematics for Class

#### Chapter 1: Relations

Shaalaa has a total of 110 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Relations 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: Functions

Shaalaa has a total of 214 questions with solutions for this chapter in Class 12 Maths. Concepts covered in 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 3: Binary Operations

Shaalaa has a total of 135 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Binary Operations 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 4: Inverse Trigonometric Functions

Shaalaa has a total of 300 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 5: Algebra of Matrices

Shaalaa has a total of 314 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Algebra of 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 Matrix by Elementary Operations, 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 6: Determinants

Shaalaa has a total of 258 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Determinants are Adjoint and Inverse of a Matrix, 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, Minors and Co-factors, Properties of Determinants, Rule A=KB

#### Chapter 7: Adjoint and Inverse of a Matrix

Shaalaa has a total of 132 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Adjoint and Inverse of a Matrix are Adjoint and Inverse of a Matrix, 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, Minors and Co-factors, Properties of Determinants, Rule A=KB

#### Chapter 8: Solution of Simultaneous Linear Equations

Shaalaa has a total of 79 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Solution of Simultaneous Linear Equations are Adjoint and Inverse of a Matrix, 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, Minors and Co-factors, Properties of Determinants, Rule A=KB

#### Chapter 9: Continuity

Shaalaa has a total of 154 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Continuity 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 10: Differentiability

Shaalaa has a total of 62 questions with solutions for this chapter in Class 12 Maths. Concepts covered in 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 11: Differentiation

Shaalaa has a total of 354 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Differentiation 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 12: Higher Order Derivatives

Shaalaa has a total of 95 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Higher Order 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 13: Derivative as a Rate Measurer

Shaalaa has a total of 79 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Derivative as a Rate Measurer 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 14: Differentials, Errors and Approximations

Shaalaa has a total of 62 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Differentials, Errors and Approximations 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 15: Mean Value Theorems

Shaalaa has a total of 81 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Mean Value Theorems 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 16: Tangents and Normals

Shaalaa has a total of 147 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Tangents and Normals 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 17: Increasing and Decreasing Functions

Shaalaa has a total of 122 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Increasing and Decreasing Functions 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 18: Maxima and Minima

Shaalaa has a total of 138 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Maxima and Minima 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 19: Indefinite Integrals

Shaalaa has a total of 863 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Indefinite 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 20: Definite Integrals

Shaalaa has a total of 416 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Definite 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 21: Areas of Bounded Regions

Shaalaa has a total of 124 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Areas of Bounded Regions are Area Between Two Curves, Area of the Region Bounded by a Curve and a Line, Area Under Simple Curves

#### Chapter 22: Differential Equations

Shaalaa has a total of 548 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, 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 23: Algebra of Vectors

Shaalaa has a total of 188 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Algebra of Vectors 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 24: Scalar Or Dot Product

Shaalaa has a total of 144 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Scalar Or Dot Product 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 25: Vector or Cross Product

Shaalaa has a total of 93 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Vector or Cross Product 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 26: Scalar Triple Product

Shaalaa has a total of 51 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Scalar Triple Product 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 27: Direction Cosines and Direction Ratios

Shaalaa has a total of 52 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Direction Cosines and Direction Ratios 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 28: Straight Line in Space

Shaalaa has a total of 137 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Straight Line in Space 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 29: The Plane

Shaalaa has a total of 235 questions with solutions for this chapter in Class 12 Maths. Concepts covered in The Plane 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 30: Linear programming

Shaalaa has a total of 133 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 31: Probability

Shaalaa has a total of 269 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

#### Chapter 32: Mean and Variance of a Random Variable

Shaalaa has a total of 79 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Mean and Variance of a Random Variable 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

#### Chapter 33: Binomial Distribution

Shaalaa has a total of 141 questions with solutions for this chapter in Class 12 Maths. Concepts covered in Binomial Distribution 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

## RD Sharma Solutions for Mathematics for Class

Class 12 RD Sharma solutions answers all the questions given in the RD Sharma 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 RD Sharma 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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