# RD Sharma Class 12 Maths Chapter Wise Solutions

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

Author: R.D. Sharma
Publisher: Dhanpat Rai Publications

Shaalaa provides solutions for RD Sharma Class 12 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 well in exams.

You can solve Mathematics for Class 12 (Set of 2 Volume) textbook questions and use Shaalaa RD Sharma Solutions for Class 12 Maths to verify your answers. ## Chapters covered in RD Sharma Solutions for Class 12 Maths

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

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

#### 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 Class 12 Mathematics Chapter 2: Functions solutions

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

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

ExerciseNo. of questionsPages
Exercise 2.14631 to 32
Exercise 2.22146 to 54
Exercise 2.32054 to 69
Exercise 2.42768 to 69

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

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

#### 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 Class 12 Mathematics Chapter 4: Inverse Trigonometric Functions solutions

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

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

ExerciseNo. of questionsPages
Exercise 4.1296 to 66
Exercise 4.111582
Exercise 4.12689
Exercise 4.13492
Exercise 4.1430115 to 116
Exercise 4.1560116 to 119
Exercise 4.1635119 to 122
Exercise 4.2910
Exercise 4.3914
Exercise 4.4818
Exercise 4.5921
Exercise 4.6924
Exercise 4.75642 to 43
Exercise 4.81454
Exercise 4.9758 to 59

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

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 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

#### 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 Class 12 Mathematics Chapter 6: Determinants solutions

Shaalaa has a total of 258 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

#### 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

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

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 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 Class 12 Mathematics Chapter 8: Solution of Simultaneous Linear Equations solutions

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 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 8.21620 to 21

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

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

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

ExerciseNo. of questionsPages
Exercise 9.16216 to 21
Exercise 9.23834 to 37

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

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

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

ExerciseNo. of questionsPages
Exercise 10.11110 to 11
Exercise 10.21216

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

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

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

ExerciseNo. of questionsPages
Exercise 11.11017
Exercise 11.27437 to 38
Exercise 11.34962 to 64
Exercise 11.43174 to 75
Exercise 11.56988 to 90
Exercise 11.6898 to 99
Exercise 11.728103 to 104
Exercise 11.824112 to 113

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

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

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

ExerciseNo. of questionsPages
Exercise 12.16116 to 18

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

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

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

ExerciseNo. of questionsPages
Exercise 13.1104
Exercise 13.23319 to 21

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

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

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

ExerciseNo. of questionsPages
Exercise 14.1459 to 12

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

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

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

ExerciseNo. of questionsPages
Exercise 15.1408 to 17
Exercise 15.2269 to 20

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

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

#### 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

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

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

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

ExerciseNo. of questionsPages
Exercise 17.1910
Exercise 17.26933 to 35

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

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

#### 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

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

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

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

ExerciseNo. of questionsPages
Exercise 19.1254 to 65
Exercise 19..11169
Exercise 19.111169
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 19.25914 to 106
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 19.31923 to 24
Exercise 19.4630
Exercise 19.51033
Exercise 19.683 to 36
Exercise 19.7638
Exercise 19.85047 to 48
Exercise 19.85148
Exercise 19.97257 to 59
MCQ34199 to 203
Revision Excercise130203 to 205

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

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

#### 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 Class 12 Mathematics Chapter 21: Areas of Bounded Regions solutions

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

#### 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 Class 12 Mathematics Chapter 22: Differential Equations solutions

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 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 22.1914 to 108
Exercise 22.1134134 to 136
Exercise 22.23316 to 17
Exercise 22.32524 to 25
Exercise 22.4928
Exercise 22.52634
Exercise 22.6438
Exercise 22.77155 to 57
Exercise 22.81166
Exercise 22.94883 to 84
MCQ54139 to 144
Revision Exercise113144 to 148

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

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

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

ExerciseNo. of questionsPages
Exercise 23.194
Exercise 23.21517 to 24
Exercise 23.3423 to 24
Exercise 23.41136 to 42
Exercise 23.51142 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 Class 12 Mathematics Chapter 24: Scalar Or Dot Product solutions

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

#### 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 Class 12 Mathematics Chapter 25: Vector or Cross Product solutions

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

#### 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 Class 12 Mathematics Chapter 26: Scalar Triple Product solutions

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

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

ExerciseNo. of questionsPages
Exercise 26.12916 to 17
MCQ1518 to 20

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

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

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

ExerciseNo. of questionsPages
Exercise 27.11923
MCQ1225 to 26

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

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

#### 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 Class 12 Mathematics Chapter 29: The Plane solutions

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

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

ExerciseNo. of questionsPages
Exercise 29.1134 to 51
Exercise 29.112561 to 62
Exercise 29.12865
Exercise 29.131873 to 74
Exercise 29.14377
Exercise 29.151581 to 82
Exercise 29.277
Exercise 29.32513 to 14
Exercise 29.41119
Exercise 29.5522 to 23
Exercise 29.62429
Exercise 29.7833
Exercise 29.81939 to 40
Exercise 29.91349
MCQ1884 to 86

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

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

#### 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 Class 12 Mathematics Chapter 31: Probability solutions

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

#### 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
MCG1105
MCQ55103 to 108

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

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

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

ExerciseNo. of questionsPages
Exercise 32.114
Exercise 32.13314 to 16
Exercise 32.22942 to 44
MCQ945 to 47

### RD Sharma Class 12 Mathematics Chapter 33: Binomial Distribution solutions

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 Class 12 Mathematics Chapter 33: Binomial Distribution exercises

ExerciseNo. of questionsPages
Exercise 33.114
Exercise 33.17112 to 15
Exercise 33.22725 to 26
MCQ3027 to 30

## RD Sharma Solutions for Class 12 Maths

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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