RD Sharma Solutions for Class 12 Maths Chapterwise List - Free
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Mathematics for Class 12 (Set of 2 Volume)
Author: R.D. SharmaPublisher: Dhanpat Rai PublicationsLanguage: EnglishShaalaa 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.
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Chapters covered in RD Sharma Solutions for Class 12 Maths
RD Sharma Class 12 Mathematics Chapter 1: Relations solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 1.1 | 34 | 10 to 11 |
| Exercise 1.2 | 18 | 26 to 27 |
| Exercise 1.3 | 24 | 29 to 30 |
| Exercise 1.4 | 34 | 31 to 33 |
RD Sharma Class 12 Mathematics Chapter 2: Functions solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 2.1 | 46 | 31 to 32 |
| Exercise 2.2 | 21 | 46 to 54 |
| Exercise 2.3 | 20 | 54 to 69 |
| Exercise 2.4 | 27 | 68 to 69 |
RD Sharma Class 12 Mathematics Chapter 3: Binary Operations solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 3.1 | 21 | 4 to 5 |
| Exercise 3.2 | 31 | 12 to 13 |
| Exercise 3.3 | 4 | 15 |
| Exercise 3.4 | 19 | 25 |
| Exercise 3.5 | 11 | 33 to 34 |
| Exercise 3.6 | 20 | 35 to 36 |
| Exercise 3.7 | 29 | 36 to 39 |
RD Sharma Class 12 Mathematics Chapter 4: Inverse Trigonometric Functions solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 4.1 | 29 | 6 to 66 |
| Exercise 4.11 | 15 | 82 |
| Exercise 4.12 | 6 | 89 |
| Exercise 4.13 | 4 | 92 |
| Exercise 4.14 | 30 | 115 to 116 |
| Exercise 4.15 | 60 | 116 to 119 |
| Exercise 4.16 | 35 | 119 to 122 |
| Exercise 4.2 | 9 | 10 |
| Exercise 4.3 | 9 | 14 |
| Exercise 4.4 | 8 | 18 |
| Exercise 4.5 | 9 | 21 |
| Exercise 4.6 | 9 | 24 |
| Exercise 4.7 | 56 | 42 to 43 |
| Exercise 4.8 | 14 | 54 |
| Exercise 4.9 | 7 | 58 to 59 |
RD Sharma Class 12 Mathematics Chapter 5: Algebra of Matrices solutions
Concepts covered in Algebra of Matrices are Addition of Matrices, Concept of Transpose of a Matrix, Elementary Transformations, 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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 5.1 | 38 | 5 to 8 |
| Exercise 5.2 | 33 | 18 to 19 |
| Exercise 5.3 | 106 | 41 to 48 |
| Exercise 5.4 | 16 | 54 to 55 |
| Exercise 5.5 | 8 | 60 to 61 |
| Exercise 5.6 | 68 | 62 to 65 |
| Exercise 5.7 | 45 | 38 to 69 |
RD Sharma Class 12 Mathematics Chapter 6: Determinants solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 6.1 | 27 | 10 to 11 |
| Exercise 6.2 | 84 | 57 to 62 |
| Exercise 6.3 | 21 | 71 to 72 |
| Exercise 6.4 | 32 | 84 to 85 |
| Exercise 6.5 | 5 | 89 |
RD Sharma Class 12 Mathematics Chapter 7: Adjoint and Inverse of a Matrix solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 7.1 | 55 | 22 to 25 |
| Exercise 7.2 | 16 | 34 |
| Exercise 7.3 | 30 | 35 to 36 |
| Exercise 7.4 | 31 | 37 to 39 |
RD Sharma Class 12 Mathematics Chapter 8: Solution of Simultaneous Linear Equations solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 8.1 | 55 | 14 to 18 |
| Exercise 8.2 | 16 | 20 to 21 |
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RD Sharma Class 12 Mathematics Chapter 9: Continuity solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 9.1 | 62 | 16 to 21 |
| Exercise 9.2 | 38 | 34 to 37 |
RD Sharma Class 12 Mathematics Chapter 10: Differentiability solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 10.1 | 11 | 10 to 11 |
| Exercise 10.2 | 12 | 16 |
RD Sharma Class 12 Mathematics Chapter 11: Differentiation solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 11.1 | 10 | 17 |
| Exercise 11.2 | 74 | 37 to 38 |
| Exercise 11.3 | 49 | 62 to 64 |
| Exercise 11.4 | 31 | 74 to 75 |
| Exercise 11.5 | 69 | 88 to 90 |
| Exercise 11.6 | 8 | 98 to 99 |
| Exercise 11.7 | 28 | 103 to 104 |
| Exercise 11.8 | 24 | 112 to 113 |
RD Sharma Class 12 Mathematics Chapter 12: Higher Order Derivatives solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 12.1 | 61 | 16 to 18 |
RD Sharma Class 12 Mathematics Chapter 13: Derivative as a Rate Measurer solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 13.1 | 10 | 4 |
| Exercise 13.2 | 33 | 19 to 21 |
RD Sharma Class 12 Mathematics Chapter 14: Differentials, Errors and Approximations solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 14.1 | 45 | 9 to 12 |
RD Sharma Class 12 Mathematics Chapter 15: Mean Value Theorems solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 15.1 | 40 | 8 to 17 |
| Exercise 15.2 | 26 | 9 to 20 |
RD Sharma Class 12 Mathematics Chapter 16: Tangents and Normals solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 16.1 | 32 | 10 to 11 |
| Exercise 16.2 | 45 | 27 to 29 |
| Exercise 16.3 | 23 | 40 to 41 |
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RD Sharma Class 12 Mathematics Chapter 17: Increasing and Decreasing Functions solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 17.1 | 9 | 10 |
| Exercise 17.2 | 69 | 33 to 35 |
RD Sharma Class 12 Mathematics Chapter 18: Maxima and Minima solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 18.1 | 9 | 7 |
| Exercise 18.2 | 14 | 16 |
| Exercise 18.3 | 21 | 31 |
| Exercise 18.4 | 8 | 37 |
| Exercise 18.5 | 47 | 72 to 74 |
RD Sharma Class 12 Mathematics Chapter 19: Indefinite Integrals solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 19.1 | 25 | 4 to 65 |
| Exercise 19..11 | 1 | 69 |
| Exercise 19.11 | 11 | 69 |
| Exercise 19.12 | 13 | 73 |
| Exercise 19.13 | 5 | 79 |
| Exercise 19.14 | 10 | 83 |
| Exercise 19.15 | 5 | 86 |
| Exercise 19.16 | 15 | 90 |
| Exercise 19.17 | 9 | 93 |
| Exercise 19.18 | 18 | 98 to 99 |
| Exercise 19.19 | 17 | 104 |
| Exercise 19.2 | 59 | 14 to 106 |
| Exercise 19.21 | 18 | 110 to 111 |
| Exercise 19.22 | 11 | 114 |
| Exercise 19.23 | 15 | 117 |
| Exercise 19.24 | 11 | 122 |
| Exercise 19.25 | 60 | 133 to 134 |
| Exercise 19.26 | 24 | 14 to 143 |
| Exercise 19.27 | 12 | 149 |
| Exercise 19.3 | 19 | 23 to 24 |
| Exercise 19.4 | 6 | 30 |
| Exercise 19.5 | 10 | 33 |
| Exercise 19.6 | 8 | 3 to 36 |
| Exercise 19.7 | 6 | 38 |
| Exercise 19.8 | 50 | 47 to 48 |
| Exercise 19.85 | 1 | 48 |
| Exercise 19.9 | 72 | 57 to 59 |
| MCQ | 34 | 199 to 203 |
| Revision Excercise | 130 | 203 to 205 |
| Very Short Answers | 62 | 179 to 198 |
RD Sharma Class 12 Mathematics Chapter 20: Definite Integrals solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 20.1 | 68 | 16 to 18 |
| Exercise 20.2 | 62 | 38 to 40 |
| Exercise 20.3 | 30 | 55 to 56 |
| Exercise 20.4 | 16 | 61 |
| Exercise 20.5 | 50 | 94 to 96 |
| Exercise 20.6 | 34 | 110 to 111 |
| MCQ | 42 | 117 to 120 |
| Revision Exercise | 69 | 12 to 123 |
| Very Short Answers | 45 | 111 to 116 |
RD Sharma Class 12 Mathematics Chapter 21: Areas of Bounded Regions solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 21.1 | 29 | 14 to 16 |
| Exercise 21.2 | 5 | 24 |
| Exercise 21.3 | 52 | 51 to 53 |
| Exercise 21.4 | 5 | 61 |
| MCQ | 33 | 62 to 64 |
RD Sharma Class 12 Mathematics Chapter 22: Differential Equations solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 22.1 | 91 | 4 to 108 |
| Exercise 22.11 | 34 | 134 to 136 |
| Exercise 22.2 | 33 | 16 to 17 |
| Exercise 22.3 | 25 | 24 to 25 |
| Exercise 22.4 | 9 | 28 |
| Exercise 22.5 | 26 | 34 |
| Exercise 22.6 | 4 | 38 |
| Exercise 22.7 | 71 | 55 to 57 |
| Exercise 22.8 | 11 | 66 |
| Exercise 22.9 | 48 | 83 to 84 |
| MCQ | 54 | 139 to 144 |
| Revision Exercise | 113 | 144 to 148 |
| Very Short Answers | 29 | 137 to 139 |
RD Sharma Class 12 Mathematics Chapter 23: Algebra of Vectors solutions
Concepts covered in Algebra of Vectors are Addition of Vectors, Basic Concepts of Vector Algebra, Components of a 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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 23.1 | 9 | 4 |
| Exercise 23.2 | 15 | 17 to 24 |
| Exercise 23.3 | 4 | 23 to 24 |
| Exercise 23.4 | 11 | 36 to 42 |
| Exercise 23.5 | 11 | 42 to 43 |
| Exercise 23.6 | 20 | 48 to 49 |
| Exercise 23.7 | 14 | 60 to 61 |
| Exercise 23.8 | 17 | 65 to 66 |
| Exercise 23.9 | 16 | 73 to 74 |
| MCQ | 19 | 78 to 79 |
| Very Short Answers | 52 | 75 to 77 |
RD Sharma Class 12 Mathematics Chapter 24: Scalar Or Dot Product solutions
Concepts covered in Scalar Or Dot Product are Addition of Vectors, Basic Concepts of Vector Algebra, Components of a 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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 24.1 | 66 | 29 to 33 |
| Exercise 24.2 | 10 | 46 |
| MCQ | 26 | 49 to 51 |
| very short answer | 42 | 46 to 48 |
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RD Sharma Class 12 Mathematics Chapter 25: Vector or Cross Product solutions
Concepts covered in Vector or Cross Product are Addition of Vectors, Basic Concepts of Vector Algebra, Components of a 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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 25.1 | 47 | 29 to 31 |
| MCQ | 15 | 34 to 36 |
| very short answers | 31 | 33 to 34 |
RD Sharma Class 12 Mathematics Chapter 26: Scalar Triple Product solutions
Concepts covered in Scalar Triple Product are Addition of Vectors, Basic Concepts of Vector Algebra, Components of a 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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 26.1 | 29 | 16 to 17 |
| MCQ | 15 | 18 to 20 |
| Very Short Answers | 7 | 18 |
RD Sharma Class 12 Mathematics Chapter 27: Direction Cosines and Direction Ratios solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 27.1 | 19 | 23 |
| MCQ | 12 | 25 to 26 |
| Very Short Answers | 21 | 24 to 25 |
RD Sharma Class 12 Mathematics Chapter 28: Straight Line in Space solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 28.1 | 18 | 9 to 10 |
| Exercise 28.2 | 34 | 15 to 17 |
| Exercise 28.3 | 10 | 22 to 23 |
| Exercise 28.4 | 14 | 29 to 30 |
| Exercise 28.5 | 26 | 37 to 38 |
| MCQ | 14 | 42 to 43 |
| Very Short Answers | 21 | 41 to 42 |
RD Sharma Class 12 Mathematics Chapter 29: The Plane solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 29.1 | 13 | 4 to 51 |
| Exercise 29.11 | 25 | 61 to 62 |
| Exercise 29.12 | 8 | 65 |
| Exercise 29.13 | 18 | 73 to 74 |
| Exercise 29.14 | 3 | 77 |
| Exercise 29.15 | 15 | 81 to 82 |
| Exercise 29.2 | 7 | 7 |
| Exercise 29.3 | 25 | 13 to 14 |
| Exercise 29.4 | 11 | 19 |
| Exercise 29.5 | 5 | 22 to 23 |
| Exercise 29.6 | 24 | 29 |
| Exercise 29.7 | 8 | 33 |
| Exercise 29.8 | 19 | 39 to 40 |
| Exercise 29.9 | 13 | 49 |
| MCQ | 18 | 84 to 86 |
| Very Short Answers | 23 | 83 to 84 |
RD Sharma Class 12 Mathematics Chapter 30: Linear programming solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 30.1 | 16 | 14 to 17 |
| Exercise 30.2 | 28 | 32 to 33 |
| Exercise 30.3 | 15 | 38 to 40 |
| Exercise 30.4 | 55 | 50 to 57 |
| Exercise 30.5 | 2 | 65 |
| MCQ | 17 | 67 to 68 |
RD Sharma Class 12 Mathematics Chapter 31: Probability solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 31.1 | 9 | 17 |
| Exercise 31.2 | 16 | 22 |
| Exercise 31.3 | 33 | 34 to 35 |
| Exercise 31.4 | 42 | 53 to 55 |
| Exercise 31.5 | 40 | 68 to 70 |
| Exercise 31.6 | 13 | 81 to 82 |
| Exercise 31.7 | 39 | 95 to 99 |
| MCG | 1 | 105 |
| MCQ | 55 | 103 to 108 |
| Very Short Answers | 17 | 102 to 103 |
| Very Short AnswersVery Short Answers | 1 | 103 |
RD Sharma Class 12 Mathematics Chapter 32: Mean and Variance of a Random Variable solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 32. | 1 | 14 |
| Exercise 32.1 | 33 | 14 to 16 |
| Exercise 32.2 | 29 | 42 to 44 |
| MCQ | 9 | 45 to 47 |
| Very Short Answers | 7 | 45 |
RD Sharma Class 12 Mathematics Chapter 33: Binomial Distribution solutions
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
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 33. | 1 | 14 |
| Exercise 33.1 | 71 | 12 to 15 |
| Exercise 33.2 | 27 | 25 to 26 |
| MCQ | 30 | 27 to 30 |
| Very Short Answers | 12 | 27 |
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.
Shaalaa provides free RD Sharma solutions for Class 12 Maths. Shaalaa has carefully crafted RD Sharma solutions for Class 12 Mathematics that can help you understand the concepts and learn how to answer properly in your board exams. You can also share our link for free Class 12 Mathematics RD Sharma solutions with your classmates.
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Comprehensive RD Sharma solutions for Class 12 Maths
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Our RD Sharma solutions for Class 12 Maths 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. Yes, these are the best RD Sharma 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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