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

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

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

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

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

- • Chapter 1: Relations
- • Chapter 2: Functions
- • Chapter 3: Binary Operations
- • Chapter 4: Inverse Trigonometric Functions
- • Chapter 5: Algebra of Matrices
- • Chapter 6: Determinants
- • Chapter 7: Adjoint and Inverse of a Matrix
- • Chapter 8: Solution of Simultaneous Linear Equations
- • Chapter 9: Continuity
- • Chapter 10: Differentiability
- • Chapter 11: Differentiation
- • Chapter 12: Higher Order Derivatives
- • Chapter 13: Derivative as a Rate Measurer
- • Chapter 14: Differentials, Errors and Approximations
- • Chapter 15: Mean Value Theorems
- • Chapter 16: Tangents and Normals
- • Chapter 17: Increasing and Decreasing Functions
- • Chapter 18: Maxima and Minima
- • Chapter 19: Indefinite Integrals
- • Chapter 20: Definite Integrals
- • Chapter 21: Areas of Bounded Regions
- • Chapter 22: Differential Equations
- • Chapter 23: Algebra of Vectors
- • Chapter 24: Scalar Or Dot Product
- • Chapter 25: Vector or Cross Product
- • Chapter 26: Scalar Triple Product
- • Chapter 27: Direction Cosines and Direction Ratios
- • Chapter 28: Straight Line in Space
- • Chapter 29: The Plane
- • Chapter 30: Linear programming
- • Chapter 31: Probability
- • Chapter 32: Mean and Variance of a Random Variable
- • Chapter 33: Binomial Distribution

### Appears in

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

**RD Sharma Solutions for Class 12 Mathematics Chapter 1: 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 Solutions for Class 12 Mathematics Chapter 2: Functions**

#### 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 | 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 Chapter 3: Binary Operations**

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

#### RD Sharma Class 12 Mathematics Chapter 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 Chapter 5: Algebra 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 Solutions for Class 12 Mathematics Chapter 6: Determinants**

#### 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 |

Exercise 6.6 | 56 | 90 to 95 |

Exercise 6.7 | 33 | 93 to 96 |

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

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

#### 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 | 8 | 20 to 21 |

Exercise 8.3 | 6 | 21 |

Exercise 8.4 | 10 | 21 to 23 |

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

#### 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 |

Exercise 9.3 | 12 | 41 to 42 |

Exercise 9.4 | 42 | 42 to 47 |

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

#### 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 |

Exercise 10.3 | 13 | 17 |

Exercise 10.4 | 26 | 17 to 20 |

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

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

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

#### 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 |

Exercise 13.3 | 10 | 24 |

Exercise 13.4 | 26 | 24 to 26 |

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

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

#### RD Sharma Class 12 Mathematics Chapter 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 Chapter 16: 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 |

Exercise 16.4 | 18 | 41 to 42 |

Exercise 16.5 | 29 | 42 to 44 |

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

#### 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 |

Exercise 17.3 | 14 | 39 to 40 |

Exercise 17.4 | 30 | 40 to 42 |

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

#### 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 |

Exercise 18.6 | 10 | 80 |

Exercise 18.7 | 29 | 80 to 82 |

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

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

#### 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 |

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 Chapter 21: Areas of Bounded Regions**

#### 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 Solutions for Class 12 Mathematics Chapter 22: Differential Equations**

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

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

#### 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 |

very short answer | 42 | 46 to 48 |

MCQ | 26 | 49 to 51 |

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

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

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

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

#### 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 |

Very Short Answers | 21 | 41 to 42 |

MCQ | 14 | 42 to 43 |

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

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

#### 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 Solutions for Class 12 Mathematics Chapter 31: Probability**

#### 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 |

Very Short Answers | 18 | 102 to 103 |

MCQ | 59 | 103 to 108 |

**RD Sharma Solutions for Class 12 Mathematics Chapter 32: Mean and 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 | 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 Chapter 33: Binomial Distribution**

#### RD Sharma Class 12 Mathematics Chapter 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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