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 are 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.
- • 1: Relations
- • 2: Functions
- • 3: Binary Operations
- • 4: Inverse Trigonometric Functions
- • 5: Algebra of Matrices
- • 6: Determinants
- • 7: Adjoint and Inverse of a Matrix
- • 8: Solution of Simultaneous Linear Equations
- • 9: Continuity
- • 10: Differentiability
- • 11: Differentiation
- • 12: Higher Order Derivatives
- • 13: Derivative as a Rate Measurer
- • 14: Differentials, Errors and Approximations
- • 15: Mean Value Theorems
- • 16: Tangents and Normals
- • 17: Increasing and Decreasing Functions
- • 18: Maxima and Minima
- • 19: Indefinite Integrals
- • 20: Definite Integrals
- • 21: Areas of Bounded Regions
- • 22: Differential Equations
- • 23: Algebra of Vectors
- • 24: Scalar Or Dot Product
- • 25: Vector or Cross Product
- • 26: Scalar Triple Product
- • 27: Direction Cosines and Direction Ratios
- • 28: Straight Line in Space
- • 29: The Plane
- • 30: Linear programming
- • 31: Probability
- • 32: Mean and Variance of a Random Variable
- • 33: Binomial Distribution
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Chapters covered in RD Sharma Solutions for Mathematics [English] Class 12
RD Sharma Solutions for Class 12 Mathematics 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 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 Solutions for Class 12 Mathematics 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 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 | 19 | 54 to 55 |
| Exercise 2.4 | 28 | 68 to 69 |
| Exercise 2.5 | 45 | 72 to 74 |
| Exercise 2.6 | 55 | 75 to 79 |
RD Sharma Solutions for Class 12 Mathematics 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 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 Solutions for Class 12 Mathematics 4: Inverse Trigonometric Functions
Concepts covered in Inverse Trigonometric Functions are Graphs of Inverse Trigonometric Functions, 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 4: Inverse Trigonometric Functions exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 4.01 | 14 | 6 to 7 |
| Exercise 4.02 | 10 | 10 |
| Exercise 4.03 | 9 | 14 |
| Exercise 4.04 | 8 | 18 |
| Exercise 4.05 | 9 | 21 |
| Exercise 4.06 | 9 | 24 |
| Exercise 4.07 | 56 | 42 to 43 |
| Exercise 4.08 | 14 | 54 |
| Exercise 4.09 | 7 | 58 to 59 |
| Exercise 4.10 | 14 | 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 |
RD Sharma Solutions for Class 12 Mathematics 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 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 Solutions for Class 12 Mathematics 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 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 |
| Exercise 6.6 | 56 | 90 to 95 |
| Exercise 6.7 | 33 | 93 to 96 |
RD Sharma Solutions for Class 12 Mathematics 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 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 Solutions for Class 12 Mathematics 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 8: Solution of Simultaneous Linear Equations exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 8.1 | 55 | 14 to 18 |
| Exercise 8.2 | 8 | 20 to 21 |
| Exercise 8.3 | 6 | 21 |
| Exercise 8.4 | 10 | 21 to 23 |
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RD Sharma Solutions for Class 12 Mathematics 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 9: Continuity exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 9.1 | 62 | 16 to 21 |
| Exercise 9.2 | 38 | 34 to 37 |
| Exercise 9.3 | 12 | 41 to 42 |
| Exercise 9.4 | 42 | 42 to 47 |
RD Sharma Solutions for Class 12 Mathematics 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 10: Differentiability exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 10.1 | 11 | 10 to 11 |
| Exercise 10.2 | 12 | 16 |
| Exercise 10.3 | 13 | 17 |
| Exercise 10.4 | 26 | 17 to 20 |
RD Sharma Solutions for Class 12 Mathematics 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 11: Differentiation exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 11.01 | 10 | 17 |
| Exercise 11.02 | 74 | 37 to 38 |
| Exercise 11.03 | 49 | 62 to 64 |
| Exercise 11.04 | 31 | 74 to 75 |
| Exercise 11.05 | 69 | 88 to 90 |
| Exercise 11.06 | 8 | 98 to 99 |
| Exercise 11.07 | 28 | 103 to 104 |
| Exercise 11.08 | 24 | 112 to 113 |
| Exercise 11.09 | 28 | 116 to 118 |
| Exercise 11.10 | 33 | 119 to 122 |
RD Sharma Solutions for Class 12 Mathematics 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 12: Higher Order Derivatives exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 12.1 | 61 | 16 to 18 |
| Exercise 12.2 | 9 | 22 |
| Exercise 12.3 | 25 | 22 to 24 |
RD Sharma Solutions for Class 12 Mathematics 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 13: Derivative as a Rate Measurer exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 13.1 | 10 | 4 |
| Exercise 13.2 | 33 | 19 to 21 |
| Exercise 13.3 | 10 | 24 |
| Exercise 13.4 | 26 | 24 to 26 |
RD Sharma Solutions for Class 12 Mathematics 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 14: Differentials, Errors and Approximations exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 14.1 | 45 | 9 to 12 |
| Exercise 14.2 | 5 | 12 |
| Exercise 14.3 | 12 | 13 |
RD Sharma Solutions for Class 12 Mathematics 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 15: Mean Value Theorems exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 15.1 | 39 | 8 to 9 |
| Exercise 15.2 | 26 | 17 to 18 |
| Exercise 15.3 | 5 | 19 |
| Exercise 15.4 | 11 | 19 to 20 |
RD Sharma Solutions for Class 12 Mathematics 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 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 |
| Exercise 16.4 | 18 | 41 to 42 |
| Exercise 16.5 | 29 | 42 to 44 |
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RD Sharma Solutions for Class 12 Mathematics 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 17: Increasing and Decreasing Functions exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 17.1 | 9 | 10 |
| Exercise 17.2 | 69 | 33 to 35 |
| Exercise 17.3 | 14 | 39 to 40 |
| Exercise 17.4 | 30 | 40 to 42 |
RD Sharma Solutions for Class 12 Mathematics 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 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 |
| Exercise 18.6 | 10 | 80 |
| Exercise 18.7 | 29 | 80 to 82 |
RD Sharma Solutions for Class 12 Mathematics 19: Indefinite Integrals
Concepts covered in Indefinite Integrals are Comparison Between Differentiation and Integration, Definite Integral as the Limit of a Sum, Definite Integrals, 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 19: Indefinite Integrals exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 19.01 | 15 | 4 |
| Exercise 19.02 | 48 | 14 to 15 |
| Exercise 19.03 | 19 | 23 to 24 |
| Exercise 19.04 | 6 | 30 |
| Exercise 19.05 | 10 | 33 |
| Exercise 19.06 | 8 | 3 to 36 |
| Exercise 19.07 | 6 | 38 |
| Exercise 19.08 | 51 | 47 to 48 |
| Exercise 19.09 | 72 | 57 to 59 |
| Exercise 19.10 | 10 | 65 |
| Exercise 19.11 | 12 | 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 | 11 | 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 19.28 | 18 | 154 to 155 |
| Exercise 19.29 | 14 | 158 to 159 |
| Exercise 19.30 | 69 | 17 to 178 |
| Exercise 19.31 | 11 | 190 |
| Exercise 19.32 | 14 | 176 to 196 |
| Very Short Answers | 62 | 179 to 198 |
| MCQ | 34 | 199 to 203 |
| Revision Excercise | 130 | 203 to 205 |
RD Sharma Solutions for Class 12 Mathematics 20: Definite Integrals
Concepts covered in Definite Integrals are Comparison Between Differentiation and Integration, Definite Integral as the Limit of a Sum, Definite Integrals, 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 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 |
| Very Short Answers | 45 | 111 to 116 |
| MCQ | 42 | 117 to 120 |
| Revision Exercise | 69 | 12 to 123 |
RD Sharma Solutions for Class 12 Mathematics 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 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 Solutions for Class 12 Mathematics 22: Differential Equations
Concepts covered in Differential Equations are Differential Equations, 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 22: Differential Equations exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 22.01 | 26 | 4 to 5 |
| Exercise 22.02 | 33 | 16 to 17 |
| Exercise 22.03 | 25 | 24 to 25 |
| Exercise 22.04 | 9 | 28 |
| Exercise 22.05 | 26 | 34 |
| Exercise 22.06 | 4 | 38 |
| Exercise 22.07 | 71 | 55 to 57 |
| Exercise 22.08 | 11 | 66 |
| Exercise 22.09 | 48 | 83 to 84 |
| Exercise 22.10 | 65 | 106 to 108 |
| Exercise 22.11 | 34 | 134 to 136 |
| Very Short Answers | 29 | 137 to 139 |
| MCQ | 54 | 139 to 144 |
| Revision Exercise | 113 | 144 to 148 |
RD Sharma Solutions for Class 12 Mathematics 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 23: Algebra of Vectors exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 23.1 | 9 | 4 |
| Exercise 23.2 | 13 | 17 |
| Exercise 23.3 | 6 | 23 to 24 |
| Exercise 23.4 | 6 | 36 to 37 |
| Exercise 23.4 | 16 | 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 |
| Very Short Answers | 52 | 75 to 77 |
| MCQ | 19 | 78 to 79 |
RD Sharma Solutions for Class 12 Mathematics 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 24: Scalar Or Dot Product exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 24.1 | 66 | 29 to 33 |
| Exercise 24.2 | 10 | 46 |
| very short answer | 42 | 46 to 48 |
| MCQ | 26 | 49 to 51 |
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RD Sharma Solutions for Class 12 Mathematics 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 25: Vector or Cross Product exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 25.1 | 47 | 29 to 31 |
| very short answers | 31 | 33 to 34 |
| MCQ | 15 | 34 to 36 |
RD Sharma Solutions for Class 12 Mathematics 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 26: Scalar Triple Product exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 26.1 | 25 | 16 to 17 |
| Exercise 26.1 | 11 | 17 to 18 |
| MCQ | 15 | 18 to 20 |
RD Sharma Solutions for Class 12 Mathematics 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 27: Direction Cosines and Direction Ratios exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 27.1 | 19 | 23 |
| Very Short Answers | 21 | 24 to 25 |
| MCQ | 12 | 25 to 26 |
RD Sharma Solutions for Class 12 Mathematics 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 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 |
| Very Short Answers | 21 | 41 to 42 |
| MCQ | 14 | 42 to 43 |
RD Sharma Solutions for Class 12 Mathematics 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 29: The Plane exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 29.01 | 9 | 4 to 5 |
| Exercise 29.02 | 7 | 7 |
| Exercise 29.03 | 25 | 13 to 14 |
| Exercise 29.04 | 11 | 19 |
| Exercise 29.05 | 5 | 22 to 23 |
| Exercise 29.06 | 24 | 29 |
| Exercise 29.07 | 8 | 33 |
| Exercise 29.08 | 19 | 39 to 40 |
| Exercise 29.09 | 13 | 49 |
| Exercise 29.10 | 4 | 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 |
| Very Short Answers | 23 | 83 to 84 |
| MCQ | 18 | 84 to 86 |
RD Sharma Solutions for Class 12 Mathematics 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 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 Solutions for Class 12 Mathematics 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 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 |
| Very Short Answers | 18 | 102 to 103 |
| MCQ | 59 | 103 to 108 |
RD Sharma Solutions for Class 12 Mathematics 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 32: Mean and Variance of a Random Variable exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 32.1 | 34 | 14 to 16 |
| Exercise 32.2 | 29 | 42 to 44 |
| Very Short Answers | 7 | 45 |
| MCQ | 9 | 45 to 47 |
RD Sharma Solutions for Class 12 Mathematics 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 33: Binomial Distribution exercises
| Exercise | No. of questions | Pages |
|---|---|---|
| Exercise 33.1 | 72 | 12 to 15 |
| Exercise 33.2 | 27 | 25 to 26 |
| Very Short Answers | 12 | 27 |
| MCQ | 30 | 27 to 30 |
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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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