This book is a complete and comprehensive preparation resource for students of Class XII studying for the CBSE Board exams. It provides clear and concise explanations and coverage of all topics specified by NCERT, offers a multitude of problems drawn from the current and previous years' question papers as per the current NCERT Exam Pattern, and presents solutions to every single problem. With this, students are certain to be successful in achieving their ambitions.

*Salient features:*

- The entire curriculum has been divided into small, manageable chunks corresponding to 240 days so that students can complete the content for that day in 1–2 hours of study
- Solutions to all problems have been provided for conceptual understanding of the theoretical and numerical portions of each chapter (there is no unsolved exercise)
- As per the NCERT Exam Pattern, questions are divided into the following types: Very Short Answer (VSA): Objective: 1-Mark Questions; Short Answer (SA): 2-Mark Questions; Long Answer I (LA-I): 4-Mark Questions; Long Answer II (LA-II): 6-Mark Questions
- At the end of each chapter, a test is included, with complete, detailed solutions, exactly as per the NCERT Exam Pattern
- At the end of each chapter, a revision day is provided so that students can recapitulate all the topics they have studied in that chapter
- Detailed solutions and in-depth explanations of all NCERT unsolved exercises and NCERT Exemplar problems are given
- Solutions and step-by-step explanations of all CBSE questions are provided
- This book will also be very helpful for students of various state boards and provides a strong foundation for students preparing for IIT-JEE and other engineering entrance examinations
- The Android app accompanying this book contains CBSE questions and solutions from 2020 onwards and additional chapter-wise questions

**Vikash Khatri** obtained his MSc in Structural/Civil Engineering from the prestigious Indian Institute of Science, Bengaluru, and his PhD in Structural/Civil Engineering from Banaras Hindu University, Varanasi. He has more than a decade of teaching experience in various engineering colleges. He is the author of several test preparation books on mathematics and engineering.

*Preface *

*Acknowledgements *

**Chapter 1: Relations and Functions **

Day 1: Types of Relations

Day 2: NCERT Exercise 1.1 (With Solutions)

Day 3: Types of Functions

Day 4: NCERT Exercise 1.2 (With Solutions)

Day 5: Composition of Functions

Day 6: Invertible Functions

Day 7: NCERT Exercise 1.3 (With Solutions)

Day 8: NCERT Miscellaneous Exercises (With Solutions)

Day 9: NCERT Exemplar Problems: Solutions (Q1–Q27)

Day 10: NCERT Exemplar Problems: Solutions (Q28–Q61)

Day 11: CBSE Previous Years’ Questions – I

Day 12: CBSE Previous Years’ Questions – II

Day 13: Very Short Answer (VSA): 1-Mark and Short Answer (SA): 2-Mark Questions

Day 14: Long Answer - I (LA-I): 4-Mark and Long Answer - II (LA-II): 6-Mark Questions

Day 15: Revision

Day 16: Chapter Test

Day 17: Chapter Test Solutions

Chapter 2: Inverse Trigonometric Functions

Day 18: Basic Concepts and Principal Value of Inverse Trigonometric Functions

Day 19: NCERT Exercise 2.1 (With Solutions)

Day 20: Properties of Inverse Trigonometric Functions

Day 21: NCERT Exercise 2.2 (With Solutions)

Day 22: NCERT Miscellaneous Exercises (With Solutions)

Day 23: NCERT Exemplar Problems: Solutions (Q1–Q19)

Day 24: NCERT Exemplar Problems: Solutions (Q20–Q55)

Day 25: CBSE Previous Years’ Questions

Day 26: Very Short Answer (VSA): 1-Mark and Short Answer (SA): 2-Mark Questions

Day 27: Long Answer - I (LA-I): 4-Mark and Long Answer - II (LA-II): 6-Mark Questions

Day 28: Revision

Day 29: Chapter Test

Day 30: Chapter Test Solutions

Chapter 3: Matrices

Day 31: Concept, Notation and Order of Matrices

Day 32: Types and Equality of Matrices

Day 33: NCERT Exercise 3.1 (With Solutions)

Day 34: Addition and Scalar Multiplication

Day 35: Multiplication of Matrices – I

Day 36: Multiplication of Matrices – II

Day 37: NCERT Exercise 3.2 (With Solutions)

Day 38: Transpose of a Matrix and Symmetric and Skew-Symmetric Matrices

Day 39: NCERT Exercise 3.3 (With Solutions)

Day 40: Inverse of a Matrix by Elementary Operations

Day 41: NCERT Exercise 3.4 (With Solutions)

Day 42: NCERT Miscellaneous Exercises (With Solutions)

Day 43: NCERT Exemplar Problems: Solutions (Q1–Q25)

Day 44: NCERT Exemplar Problems: Solutions (Q26–Q52)

Day 45: NCERT Exemplar Problems: Solutions (Q53–Q101)

Day 46: CBSE Previous Years’ Questions – I

Day 47: CBSE Previous Years’ Questions – II

Day 48: CBSE Previous Years’ Questions – III

Day 49: Very Short Answer (VSA) and Objective: 1-Mark Questions

Day 50: Short Answer (SA): 2-Mark Questions

Day 51: Long Answer - I (LA-I): 4-Mark Questions

Day 52: Long Answer - II (LA-II): 6-Mark Questions

Day 53: Revision

Day 54: Chapter Test

Day 55: Chapter Test Solutions

Chapter 4: Determinants

Day 56: Introduction

Day 57: NCERT Exercise 4.1 (With Solutions)

Day 58: Properties of Determinants

Day 59: NCERT Exercise 4.2 (With Solutions)

Day 60: Area of a Triangle

Day 61: NCERT Exercise 4.3 (With Solutions)

Day 62: Minors and Cofactors

Day 63: NCERT Exercise 4.4 (With Solutions)

Day 64: Adjoint and Inverse of a Matrix – I

Day 65: Adjoint and Inverse of a Matrix – II

Day 66: NCERT Exercise 4.5 (With Solutions)

Day 67: Applications of Determinants and Matrices

Day 68: NCERT Exercise 4.6 (With Solutions)

Day 69: NCERT Miscellaneous Exercises (With Solutions)

Day 70: NCERT Exemplar Problems: Solutions (Q1–Q23)

Day 71: NCERT Exemplar Problems: Solutions (Q24–Q58)

Day 72: CBSE Previous Years’ Questions – I

Day 73: CBSE Previous Years’ Questions – II

Day 74: Very Short Answer (VSA): 1-Mark Questions

Day 75: Short Answer (SA): 2-Mark Questions

Day 76: Long Answer - I (LA-I): 4-Mark Questions

Day 77: Long Answer (LA-II): 6-Mark Questions

Day 78: Revision

Day 79: Chapter Test

Day 80: Chapter Test Solutions

Chapter 5: Continuity and Differentiability

Day 81: Continuity

Day 82: NCERT Exercise 5.1 (With Solutions)

Day 83: Differentiability

NCERT Exercise 5.2 (With Solutions)

Day 84: Derivatives of Implicit and Inverse Trigonometric Functions

NCERT Exercise 5.3 (With Solutions)

Day 85: Derivatives of Exponential and Logarithmic Functions

NCERT Exercise 5.4 (With Solutions)

Day 86: Logarithmic Differentiation

NCERT Exercise 5.5 (With Solutions)

Day 87: Derivatives of Functions in Parametric Forms

NCERT Exercise 5.6 (With Solutions)

Day 88: Second-Order Derivatives

NCERT Exercise 5.7 (With Solutions)

Day 89: Rolle’s Theorem and Mean Value Theorem

NCERT Exercise 5.8 (With Solutions)

Day 90: NCERT Miscellaneous Exercises (With Solutions)

Day 91: NCERT Exemplar Problems: Solutions (Q1–Q42)

Day 92: NCERT Exemplar Problems: Solutions (Q43–Q78)

Day 93: NCERT Exemplar Problems: Solutions (Q79–Q106)

Day 94: CBSE Previous Years’ Questions – I

Day 95: CBSE Previous Years’ Questions – II

Day 96: Very Short Answer (VSA): 1-Mark and Short Answer (SA): 2-Mark Questions

Day 97: Long Answer - I (LA-I): 4-Mark and Long Answer - II (LA-II): 6-Mark Questions

Day 98: Revision

Day 99: Chapter Test

Day 100: Chapter Test Solutions

Chapter 6: Application of Derivatives

Day 101: Rate of Change of Quantities

NCERT Exercise 6.1 (With Solutions)

Day 102: Increasing and Decreasing Functions

NCERT Exercise 6.2 (With Solutions)

Day 103: Tangents and Normals

NCERT Exercise 6.3 (With Solutions)

Day 104: Approximations

NCERT Exercise 6.4 (With Solutions)

Day 105: Maxima and Minima

Day 106: NCERT Exercise 6.5 (With Solutions)

Day 107: NCERT Miscellaneous Exercises (With Solutions)

Day 108: NCERT Exemplar Problems: Solutions (Q1–Q24)

Day 109: NCERT Exemplar Problems: Solutions (Q25–Q40)

Day 110: NCERT Exemplar Problems: Solutions (Q41–Q64)

Day 111: CBSE Previous Years’ Questions – I

Day 112: CBSE Previous Years’ Questions – II

Day 113: Very Short Answer (VSA): 1-Mark and Short Answer (SA): 2-Mark Questions

Day 114: Long Answer - I (LA-I): 4-Mark and Long Answer - II (LA-II): 6-Mark Questions

Day 115: Revision

Day 116: Chapter Test

Day 117: Chapter Test Solutions

Chapter 7: Integrals

Day 118: Properties of Indefinite Integrals

NCERT Exercise 7.1 (With Solutions)

Day 119: Integration by Substitution

NCERT Exercise 7.2 (With Solutions)

Day 120: Integration Using Trigonometric Identities

NCERT Exercise 7.3 (With Solutions)

Day 121: Integration of Particular Functions

NCERT Exercise 7.4 (With Solutions)

Day 122: Integration by Partial Fractions

NCERT Exercise 7.5 (With Solutions)

Day 123: Integration by Parts

NCERT Exercise 7.6 (With Solutions)

Day 124: Integration of Some Important Functions

NCERT Exercise 7.7 (With Solutions)

Day 125: Definite Integral as the Limit of a Sum

NCERT Exercise 7.8 (With Solutions)

Day 126: Fundamental Theorem of Calculus: Area Function

NCERT Exercise 7.9 (With Solutions)

Day 127: Evaluation of Definite Integrals by Substitution

NCERT Exercise 7.10 (With Solutions)

Day 128: Properties of Definite Integrals

NCERT Exercise 7.11 (With Solutions)

Day 129: NCERT Miscellaneous Exercises (With Solutions)

Day 130: NCERT Exemplar Problems: Solutions (Q1–Q37)

Day 131: NCERT Exemplar Problems: Solutions (Q38–Q62)

Day 132: CBSE Previous Years’ Questions – I

Day 133: CBSE Previous Years’ Questions – II

Day 134: Very Short Answer (VSA): 1-Mark and Short Answer (SA): 2-Mark Questions

Day 135: Long Answer - I (LA-I): 4-Mark and Long Answer - II (LA-II): 6-Mark Questions

Day 136: Revision

Day 137: Chapter Test

Day 138: Chapter Test Solutions

Chapter 8: Application of Integrals

Day 139: Area under Simple Curves and Lines

NCERT Exercise 8.1 (With Solutions)

Day 140: Area between Two Curves

NCERT Exercise 8.2 (With Solutions)

Day 141: NCERT Miscellaneous Exercises (With Solutions)

Day 142: NCERT Exemplar Problems: Solutions

Day 143: CBSE Previous Years’ Questions

Day 144: Chapter Test

Day 145: Chapter Test Solutions

Chapter 9: Differential Equations

Day 146: Order and Degree of a Differential Equation

NCERT Exercise 9.1 (With Solutions)

Day 147: General and Particular Solutions of a Differential Equation

NCERT Exercise 9.2 (With Solutions)

Day 148: Formation of a Differential Equation whose General Solution is Given

NCERT Exercise 9.3 (With Solutions)

Day 149: Differential Equation with Variable Separable

NCERT Exercise 9.4 (With Solutions)

Day 150: Homogeneous Differential Equations

NCERT Exercise 9.5 (With Solutions)

Day 151: Linear Differential Equations

NCERT Exercise 9.6 (With Solutions)

Day 152: NCERT Miscellaneous Exercises (With Solutions)

Day 153: NCERT Exemplar Problems: Solutions (Q1–Q33)

Day 154: NCERT Exemplar Problems: Solutions (Q34–Q77)

Day 155: CBSE Previous Years’ Questions

Day 156: Very Short Answer (VSA): 1-Mark and Short Answer (SA): 2-Mark Questions

Day 157: Long Answer - I (LA-I): 4-Mark and Long Answer - II (LA-II): 6-Mark Questions

Day 158: Revision

Day 159: Chapter Test

Day 160: Chapter Test Solutions

Chapter 10: Vector Algebra

Day 161: Basics of Vectors

NCERT Exercise 10.1 (With Solutions)

Day 162: Algebra of Vectors

NCERT Exercise 10.2 (With Solutions)

Day 163: Scalar (or Dot) Product of Two Vectors

NCERT Exercise 10.3 (With Solutions)

Day 164: Vector (or Cross) Product of Two Vectors

NCERT Exercise 10.4 (With Solutions)

Day 165: Scalar Triple Product of Vectors

NCERT Exercise 10.5 (With Solutions)

Day 166: NCERT Miscellaneous Exercises (With Solutions)

Day 167: NCERT Exemplar Problems: Solutions (Q1–Q18)

Day 168: NCERT Exemplar Problems: Solutions (Q19–Q45)

Day 169: CBSE Previous Years’ Questions – I

Day 170: CBSE Previous Years’ Questions – II

Day 171: Very Short Answer (VSA): 1-Mark and Short Answer (SA): 2-Mark Questions

Day 172: Long Answer - I (LA-I): 4-Mark and Long Answer - II (LA-II): 6-Mark Questions

Day 173: Revision

Day 174: Chapter Test

Day 175: Chapter Test Solutions

**Chapter 11: Three-Dimensional Geometry **

Day 176: Direction Cosines and Direction Ratios of a Line

NCERT Exercise 11.1 (With Solutions)

Day 177: Line in Space

Day 178: NCERT Exercise 11.2 (With Solutions)

Day 179: Plane in Space

Day 180: NCERT Exercise 11.3 (With Solutions)

Day 181: NCERT Miscellaneous Exercises (With Solutions)

Day 182: NCERT Exemplar Problems: Solutions (Q1–Q20)

Day 183: NCERT Exemplar Problems: Solutions (Q21–Q49)

Day 184: CBSE Previous Years’ Questions – I

Day 185: CBSE Previous Years’ Questions – II

Day 186: Very Short Answer (VSA): 1-Mark and Short Answer (SA): 2-Mark Questions

Day 187: Long Answer - I (LA-I): 4-Mark and Long Answer - II (LA-II): 6-Mark Questions

Day 188: Revision

Day 189: Chapter Test

Day 190: Chapter Test Solutions

Chapter 12: Linear Programming

Day 191: Linear Programming Problem (LPP)

Day 192: NCERT Exercise 12.1 (With Solutions)

Day 193: NCERT Exercise 12.2 (With Solutions Q1–Q6)

Day 194: NCERT Exercise 12.2 (With Solutions Q7–Q11)

Day 195: NCERT Miscellaneous Exercises (With Solutions Q1–Q5)

Day 196: NCERT Miscellaneous Exercises (With Solutions Q6–Q10)

Day 197: NCERT Exemplar Problems: Solutions (Q1–Q10)

Day 198: NCERT Exemplar Problems: Solutions (Q11–Q20)

Day 199: NCERT Exemplar Problems: Solutions (Q21–Q25)

Day 200: NCERT Exemplar Problems: Solutions (Q26–Q45)

Day 201: CBSE Previous Years’ Questions – I

Day 202: CBSE Previous Years’ Questions – II

Day 203: CBSE Previous Years’ Questions – III

Day 204: CBSE Previous Years’ Questions – IV

Day 205: Very Short Answer (VSA): 1-Mark and Short Answer (SA): 2-Mark Questions

Day 206: Long Answer - I (LA-I): 4-Mark Questions

Day 207: Long Answer - II (LA-II): 6-Mark Questions

Day 208: Revision

Day 209: Chapter Test

Day 210: Chapter Test Solutions

Chapter 13: Probability

Day 211: Probability Basics – I

Day 212: Probability Basics – II

Day 213: Conditional Probability

Day 214: NCERT Exercise 13.1 (With Solutions)

Day 215: Multiplication Theorem and Independent Events

Day 216: NCERT Exercise 13.2 (With Solutions)

Day 217: Bayes’ Theorem

Day 218: NCERT Exercise 13.3 (With Solutions)

Day 219: Random Variables and their Probability Distribution

Day 220: NCERT Exercise 13.4 (With Solutions)

Day 221: Bernoulli Trials and Binomial Distribution

Day 222: NCERT Exercise 13.4 (With Solutions)

Day 223: NCERT Miscellaneous Exercises (With Solutions)

Day 224: NCERT Exemplar Problems: Solutions (Q1–Q22)

Day 225: NCERT Exemplar Problems: Solutions (Q23–Q40)

Day 226: NCERT Exemplar Problems: Solutions (Q41–Q55)

Day 227: NCERT Exemplar Problems: Solutions (Q56–Q108)

Day 228: CBSE Previous Years’ Questions – I

Day 229: CBSE Previous Years’ Questions – II

Day 230: CBSE Previous Years’ Questions – III

Day 231: CBSE Previous Years’ Questions – IV

Day 232: Very Short Answer – Objective (VSA): 1-Mark Questions

Day 233: Short Answer (SA): 2-Mark Questions

Day 234: Long Answer - I (LA-I): 4-Mark Questions

Day 235: Long Answer - II (LA-II): 6-Mark Questions

Day 236: Revision

Day 237: Chapter Test I

Day 238: Chapter Test I Solutions

Day 239: Chapter Test II

Day 240: Chapter Test II Solutions