# RD Sharma Class 12 Maths Chapter Wise Solutions

## CBSE, Karnataka Board PUC Class 12 Maths Solutions Guide

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## CBSE, Karnataka Board PUC Class 12 Maths Textbook Solutions

Questions and answers for the Class 12 Maths Textbook on this page. RD Sharma Solutions for Class 12 Maths Digest CBSE, Karnataka Board PUC will help students understand the concepts better.

## RD Sharma Solutions for Class 12 Maths Chapterwise List | Class 12 Maths Digest

The answers to the RD Sharma books are the best study material for students. Listed below are the chapter-wise RD Sharma Maths Class 12 Solutions CBSE, Karnataka Board PUC.

### Appears in ## Chapters covered in RD Sharma Solutions for Class 12 Maths

### RD Sharma Solutions for Class 12 Mathematics Chapter 1: Relations

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

#### RD Sharma Class 12 Mathematics Chapter 1: Relations exercises

ExerciseNo. of questionsPages
Exercise 1.13410 to 11
Exercise 1.21826 to 27
Exercise 1.32429 to 30
Exercise 1.43431 to 33

### RD Sharma Solutions for Class 12 Mathematics Chapter 2: Functions

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

#### RD Sharma Class 12 Mathematics Chapter 2: Functions exercises

ExerciseNo. of questionsPages
Exercise 2.14631 to 32
Exercise 2.22146 to 54
Exercise 2.31954 to 55
Exercise 2.42868 to 69
Exercise 2.54572 to 74
Exercise 2.65575 to 79

### RD Sharma Solutions for Class 12 Mathematics Chapter 3: Binary Operations

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

#### RD Sharma Class 12 Mathematics Chapter 3: Binary Operations exercises

ExerciseNo. of questionsPages
Exercise 3.1214 to 5
Exercise 3.23112 to 13
Exercise 3.3415
Exercise 3.41925
Exercise 3.51133 to 34
Exercise 3.62035 to 36
Exercise 3.72936 to 39

### RD Sharma Solutions for Class 12 Mathematics Chapter 4: Inverse Trigonometric Functions

Concepts covered in Inverse Trigonometric Functions are Basic Concepts of Inverse Trigonometric Functions, Graphs of Inverse Trigonometric Functions, Inverse Trigonometric Functions - Principal Value Branch, Inverse Trigonometric Functions (Simplification and Examples), Properties of Inverse Trigonometric Functions

#### RD Sharma Class 12 Mathematics Chapter 4: Inverse Trigonometric Functions exercises

ExerciseNo. of questionsPages
Exercise 4.01146 to 7
Exercise 4.021010
Exercise 4.03914
Exercise 4.04818
Exercise 4.05921
Exercise 4.06924
Exercise 4.075642 to 43
Exercise 4.081454
Exercise 4.09758 to 59
Exercise 4.101466
Exercise 4.111582
Exercise 4.12689
Exercise 4.13492
Exercise 4.1430115 to 116
Exercise 4.1560116 to 119
Exercise 4.1635119 to 122

### RD Sharma Solutions for Class 12 Mathematics Chapter 5: Algebra of Matrices

Concepts covered in Algebra of Matrices are Addition of Matrices, Elementary Transformations, Equality of Matrices, Introduction of Matrices, Introduction of Operations on Matrices, Inverse of a 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, Transpose of a Matrix, Types of Matrices

#### RD Sharma Class 12 Mathematics Chapter 5: Algebra of Matrices exercises

ExerciseNo. of questionsPages
Exercise 5.1385 to 8
Exercise 5.23318 to 19
Exercise 5.310641 to 48
Exercise 5.41654 to 55
Exercise 5.5860 to 61
Exercise 5.66862 to 65
Exercise 5.74538 to 69

### RD Sharma Solutions for Class 12 Mathematics Chapter 6: Determinants

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

#### RD Sharma Class 12 Mathematics Chapter 6: Determinants exercises

ExerciseNo. of questionsPages
Exercise 6.12710 to 11
Exercise 6.28457 to 62
Exercise 6.32171 to 72
Exercise 6.43284 to 85
Exercise 6.5589
Exercise 6.65690 to 95
Exercise 6.73393 to 96

### RD Sharma Solutions for Class 12 Mathematics Chapter 7: Adjoint and Inverse of a Matrix

Concepts covered in Adjoint and Inverse of a Matrix 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

#### RD Sharma Class 12 Mathematics Chapter 7: Adjoint and Inverse of a Matrix exercises

ExerciseNo. of questionsPages
Exercise 7.15522 to 25
Exercise 7.21634
Exercise 7.33035 to 36
Exercise 7.43137 to 39

### RD Sharma Solutions for Class 12 Mathematics Chapter 8: Solution of Simultaneous Linear Equations

Concepts covered in Solution of Simultaneous Linear Equations 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

#### RD Sharma Class 12 Mathematics Chapter 8: Solution of Simultaneous Linear Equations exercises

ExerciseNo. of questionsPages
Exercise 8.15514 to 18
Exercise 8.2820 to 21
Exercise 8.3621
Exercise 8.41021 to 23

### RD Sharma Solutions for Class 12 Mathematics Chapter 9: Continuity

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

#### RD Sharma Class 12 Mathematics Chapter 9: Continuity exercises

ExerciseNo. of questionsPages
Exercise 9.16216 to 21
Exercise 9.23834 to 37
Exercise 9.31241 to 42
Exercise 9.44242 to 47

### RD Sharma Solutions for Class 12 Mathematics Chapter 10: Differentiability

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

#### RD Sharma Class 12 Mathematics Chapter 10: Differentiability exercises

ExerciseNo. of questionsPages
Exercise 10.11110 to 11
Exercise 10.21216
Exercise 10.31317
Exercise 10.42617 to 20

### RD Sharma Solutions for Class 12 Mathematics Chapter 11: Differentiation

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

#### RD Sharma Class 12 Mathematics Chapter 11: Differentiation exercises

ExerciseNo. of questionsPages
Exercise 11.011017
Exercise 11.027437 to 38
Exercise 11.034962 to 64
Exercise 11.043174 to 75
Exercise 11.056988 to 90
Exercise 11.06898 to 99
Exercise 11.0728103 to 104
Exercise 11.0824112 to 113
Exercise 11.0928116 to 118
Exercise 11.1033119 to 122

### RD Sharma Solutions for Class 12 Mathematics Chapter 12: Higher Order Derivatives

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

#### RD Sharma Class 12 Mathematics Chapter 12: Higher Order Derivatives exercises

ExerciseNo. of questionsPages
Exercise 12.16116 to 18
Exercise 12.2922
Exercise 12.32522 to 24

### RD Sharma Solutions for Class 12 Mathematics Chapter 13: Derivative as a Rate Measurer

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

#### RD Sharma Class 12 Mathematics Chapter 13: Derivative as a Rate Measurer exercises

ExerciseNo. of questionsPages
Exercise 13.1104
Exercise 13.23319 to 21
Exercise 13.31024
Exercise 13.42624 to 26

### RD Sharma Solutions for Class 12 Mathematics Chapter 14: Differentials, Errors and Approximations

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

#### RD Sharma Class 12 Mathematics Chapter 14: Differentials, Errors and Approximations exercises

ExerciseNo. of questionsPages
Exercise 14.1459 to 12
Exercise 14.2512
Exercise 14.31213

### RD Sharma Solutions for Class 12 Mathematics Chapter 15: Mean Value Theorems

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

#### RD Sharma Class 12 Mathematics Chapter 15: Mean Value Theorems exercises

ExerciseNo. of questionsPages
Exercise 15.1398 to 9
Exercise 15.22617 to 18
Exercise 15.3519
Exercise 15.41119 to 20

### RD Sharma Solutions for Class 12 Mathematics Chapter 16: Tangents and Normals

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

#### RD Sharma Class 12 Mathematics Chapter 16: Tangents and Normals exercises

ExerciseNo. of questionsPages
Exercise 16.13210 to 11
Exercise 16.24527 to 29
Exercise 16.32340 to 41
Exercise 16.41841 to 42
Exercise 16.52942 to 44

### RD Sharma Solutions for Class 12 Mathematics Chapter 17: Increasing and Decreasing Functions

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

#### RD Sharma Class 12 Mathematics Chapter 17: Increasing and Decreasing Functions exercises

ExerciseNo. of questionsPages
Exercise 17.1910
Exercise 17.26933 to 35
Exercise 17.31439 to 40
Exercise 17.43040 to 42

### RD Sharma Solutions for Class 12 Mathematics Chapter 18: Maxima and Minima

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

#### RD Sharma Class 12 Mathematics Chapter 18: Maxima and Minima exercises

ExerciseNo. of questionsPages
Exercise 18.197
Exercise 18.21416
Exercise 18.32131
Exercise 18.4837
Exercise 18.54772 to 74
Exercise 18.61080
Exercise 18.72980 to 82

### RD Sharma Solutions for Class 12 Mathematics Chapter 19: Indefinite Integrals

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 Integrals, 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, Some Properties of Indefinite Integral

#### RD Sharma Class 12 Mathematics Chapter 19: Indefinite Integrals exercises

ExerciseNo. of questionsPages
Exercise 19.01154
Exercise 19.024814 to 15
Exercise 19.031923 to 24
Exercise 19.04630
Exercise 19.051033
Exercise 19.0683 to 36
Exercise 19.07638
Exercise 19.085147 to 48
Exercise 19.097257 to 59
Exercise 19.101065
Exercise 19.111269
Exercise 19.121373
Exercise 19.13579
Exercise 19.141083
Exercise 19.15586
Exercise 19.161590
Exercise 19.17993
Exercise 19.181898 to 99
Exercise 19.1917104
Exercise 19.211106
Exercise 19.2118110 to 111
Exercise 19.2211114
Exercise 19.2315117
Exercise 19.2411122
Exercise 19.2560133 to 134
Exercise 19.262414 to 143
Exercise 19.2712149
Exercise 19.2818154 to 155
Exercise 19.2914158 to 159
Exercise 19.306917 to 178
Exercise 19.3111190
Exercise 19.3214176 to 196
MCQ34199 to 203
Revision Excercise130203 to 205

### RD Sharma Solutions for Class 12 Mathematics Chapter 20: Definite Integrals

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 Integrals, 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, Some Properties of Indefinite Integral

#### RD Sharma Class 12 Mathematics Chapter 20: Definite Integrals exercises

ExerciseNo. of questionsPages
Exercise 20.16816 to 18
Exercise 20.26238 to 40
Exercise 20.33055 to 56
Exercise 20.41661
Exercise 20.55094 to 96
Exercise 20.634110 to 111
MCQ42117 to 120
Revision Exercise6912 to 123

### RD Sharma Solutions for Class 12 Mathematics Chapter 21: Areas of Bounded Regions

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

#### RD Sharma Class 12 Mathematics Chapter 21: Areas of Bounded Regions exercises

ExerciseNo. of questionsPages
Exercise 21.12914 to 16
Exercise 21.2524
Exercise 21.35251 to 53
Exercise 21.4561
MCQ3362 to 64

### RD Sharma Solutions for Class 12 Mathematics Chapter 22: Differential Equations

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

#### RD Sharma Class 12 Mathematics Chapter 22: Differential Equations exercises

ExerciseNo. of questionsPages
Exercise 22.01264 to 5
Exercise 22.023316 to 17
Exercise 22.032524 to 25
Exercise 22.04928
Exercise 22.052634
Exercise 22.06438
Exercise 22.077155 to 57
Exercise 22.081166
Exercise 22.094883 to 84
Exercise 22.1065106 to 108
Exercise 22.1134134 to 136
MCQ54139 to 144
Revision Exercise113144 to 148

### RD Sharma Solutions for Class 12 Mathematics Chapter 23: Algebra of Vectors

Concepts covered in Algebra of Vectors are Addition of Vectors, Basic Concepts of Vector Algebra, Components of Vector, 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, Vector Joining Two Points, Vector (Or Cross) Product of Two Vectors, Vectors and Their Types, Vectors Examples and Solutions

#### RD Sharma Class 12 Mathematics Chapter 23: Algebra of Vectors exercises

ExerciseNo. of questionsPages
Exercise 23.194
Exercise 23.21317
Exercise 23.3623 to 24
Exercise 23.4636 to 37
Exercise 23.41642 to 43
Exercise 23.62048 to 49
Exercise 23.71460 to 61
Exercise 23.81765 to 66
Exercise 23.91673 to 74
MCQ1978 to 79

### RD Sharma Solutions for Class 12 Mathematics Chapter 24: Scalar Or Dot Product

Concepts covered in Scalar Or Dot Product are Addition of Vectors, Basic Concepts of Vector Algebra, Components of Vector, 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, Vector Joining Two Points, Vector (Or Cross) Product of Two Vectors, Vectors and Their Types, Vectors Examples and Solutions

#### RD Sharma Class 12 Mathematics Chapter 24: Scalar Or Dot Product exercises

ExerciseNo. of questionsPages
Exercise 24.16629 to 33
Exercise 24.21046
MCQ2649 to 51

### RD Sharma Solutions for Class 12 Mathematics Chapter 25: Vector or Cross Product

Concepts covered in Vector or Cross Product are Addition of Vectors, Basic Concepts of Vector Algebra, Components of Vector, 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, Vector Joining Two Points, Vector (Or Cross) Product of Two Vectors, Vectors and Their Types, Vectors Examples and Solutions

#### RD Sharma Class 12 Mathematics Chapter 25: Vector or Cross Product exercises

ExerciseNo. of questionsPages
Exercise 25.14729 to 31
MCQ1534 to 36

### RD Sharma Solutions for Class 12 Mathematics Chapter 26: Scalar Triple Product

Concepts covered in Scalar Triple Product are Addition of Vectors, Basic Concepts of Vector Algebra, Components of Vector, 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, Vector Joining Two Points, Vector (Or Cross) Product of Two Vectors, Vectors and Their Types, Vectors Examples and Solutions

#### RD Sharma Class 12 Mathematics Chapter 26: Scalar Triple Product exercises

ExerciseNo. of questionsPages
Exercise 26.12516 to 17
Exercise 26.11117 to 18
MCQ1518 to 20

### RD Sharma Solutions for Class 12 Mathematics Chapter 27: Direction Cosines and Direction Ratios

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

#### RD Sharma Class 12 Mathematics Chapter 27: Direction Cosines and Direction Ratios exercises

ExerciseNo. of questionsPages
Exercise 27.11923
MCQ1225 to 26

### RD Sharma Solutions for Class 12 Mathematics Chapter 28: Straight Line in Space

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

#### RD Sharma Class 12 Mathematics Chapter 28: Straight Line in Space exercises

ExerciseNo. of questionsPages
Exercise 28.1189 to 10
Exercise 28.23415 to 17
Exercise 28.31022 to 23
Exercise 28.41429 to 30
Exercise 28.52637 to 38
MCQ1442 to 43

### RD Sharma Solutions for Class 12 Mathematics Chapter 29: The Plane

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

#### RD Sharma Class 12 Mathematics Chapter 29: The Plane exercises

ExerciseNo. of questionsPages
Exercise 29.0194 to 5
Exercise 29.0277
Exercise 29.032513 to 14
Exercise 29.041119
Exercise 29.05522 to 23
Exercise 29.062429
Exercise 29.07833
Exercise 29.081939 to 40
Exercise 29.091349
Exercise 29.10451
Exercise 29.112561 to 62
Exercise 29.12865
Exercise 29.131873 to 74
Exercise 29.14377
Exercise 29.151581 to 82
MCQ1884 to 86

### RD Sharma Solutions for Class 12 Mathematics Chapter 30: Linear programming

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

#### RD Sharma Class 12 Mathematics Chapter 30: Linear programming exercises

ExerciseNo. of questionsPages
Exercise 30.11614 to 17
Exercise 30.22832 to 33
Exercise 30.31538 to 40
Exercise 30.45550 to 57
Exercise 30.5265
MCQ1767 to 68

### RD Sharma Solutions for Class 12 Mathematics Chapter 31: Probability

Concepts covered in Probability are Bayes’ 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 Class 12 Mathematics Chapter 31: Probability exercises

ExerciseNo. of questionsPages
Exercise 31.1917
Exercise 31.21622
Exercise 31.33334 to 35
Exercise 31.44253 to 55
Exercise 31.54068 to 70
Exercise 31.61381 to 82
Exercise 31.73995 to 99
MCQ59103 to 108

### RD Sharma Solutions for Class 12 Mathematics Chapter 32: Mean and Variance of a Random Variable

Concepts covered in Mean and Variance of a Random Variable are Bayes’ 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 Class 12 Mathematics Chapter 32: Mean and Variance of a Random Variable exercises

ExerciseNo. of questionsPages
Exercise 32.13414 to 16
Exercise 32.22942 to 44
MCQ945 to 47

### RD Sharma Solutions for Class 12 Mathematics Chapter 33: Binomial Distribution

Concepts covered in Binomial Distribution are Bayes’ 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 Class 12 Mathematics Chapter 33: Binomial Distribution exercises

ExerciseNo. of questionsPages
Exercise 33.17212 to 15
Exercise 33.22725 to 26
MCQ3027 to 30

## RD Sharma Solutions for Class 12 Maths

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## RD Sharma Solutions for Class 12 Maths CBSE, Karnataka Board PUC

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

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## Comprehensive RD Sharma Solutions for CBSE, Karnataka Board PUC Maths Class 12 Guide

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Our CBSE, Karnataka Board PUC RD Sharma solutions for Maths Class 12 cover everything from Relations, Functions, Binary Operations, Inverse Trigonometric Functions, Algebra of Matrices, Determinants, Adjoint and Inverse of a Matrix, Solution of Simultaneous Linear Equations, Continuity, Differentiability, Differentiation, Higher Order Derivatives, Derivative as a Rate Measurer, Differentials, Errors and Approximations, Mean Value Theorems, Tangents and Normals, Increasing and Decreasing Functions, Maxima and Minima, Indefinite Integrals, Definite Integrals, Areas of Bounded Regions, Differential Equations, Algebra of Vectors, Scalar Or Dot Product, Vector or Cross Product, Scalar Triple Product, Direction Cosines and Direction Ratios, Straight Line in Space, The Plane, Linear programming, Probability, Mean and Variance of a Random Variable, Binomial Distribution and the other topics.

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