# NCERT Solutions For Class 11 Maths

**NCERT Solutions For Class 11 Maths Updated 2022-23 Edition**

**NCERT Solutions for Class 11 Maths** has answers to all of the problems in the **Class 11 NCERT textbook**. These **Ncert Solutions** given by utopper experts with step by step according latest **CBSE Syllabus**. Students can use the links at the bottom of this page to get access of solutions to these problems for each chapter. These **NCERT Solutions Class 11 Maths** covers all of the 16 Chapters.

Every solution is explained in detail. If these solutions are put together carefully, they can clear up all of the students’ questions by giving a thorough explanation of complicated topics. Our experts at Utopper have looked at and reviewed all of the **NCERT solutions for Class 11** by chapter. Students will be able to solve problems better if they practise questions from their textbooks and look up the answers.

**Class 11 Maths Ncert Solutions All Chapters**

The exercises in the NCERT Solutions for Class 11 Math subject cover the 16 chapters in the textbook. Sets, trigonometric functions, sequences and series, three-dimensional geometry, relations and functions, statistics, the binomial theorem, probability, and other topics are all covered in these chapters. The answers to these chapters are available in detail and free, so students can easily access and study them when it’s most convenient for them.

Our subject experts put together the **NCERT Solutions for Class 11 Maths** to answer all of your questions in all 16 chapters in detail. Students who want to do well on the **CBSE Class 11 Exam** will find that these Solutions for **Class 11 NCERT** are a great way to learn all of the Maths, Physics, Chemistry, and Biology concepts on the **syllabus**. The **NCERT Solutions** are clearly explained with clear graphs and worked-out examples that make it easy to learn. It helps students build a strong understanding of ideas, which is a big part of how well they do on competitive exams later on.

- Chapter 1 Sets
- Chapter 2 Relations and Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations and Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences and Series
- Chapter 10 Straight lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction to Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability

**Chapterwise Brief NCERT Solutions for Class 11 Maths**

Students who are having trouble with hard math problems can use these CBSE Maths Class 11 Solutions of NCERT to get help and quickly review. If you do the exercises at the end of each chapter, you will get good results.

In addition, when preparing for the exam, they can use our **Class 11 Maths revision notes**, which provide an overview of all the relevant topics. To have extra practise** sample papers** and critical questions are supplied on **Utopper**. Click on the below links to obtain the necessary materials for class 11.

**NCERT Solutions for Class 11 Maths – All Chapters**

The chapter-by-chapter **NCERT Solutions for Class 11 Maths** provide students with the key to unlocking their problem-solving skills. Students’ academic careers might be significantly affected by adopting an appropriate learning method. Students can use these solutions not just to get the proper solution but also to determine whether their answers are correct. The ultimate goal of delivering the best **NCERT Solutions** is to aid students in gaining a thorough understanding of the themes and concepts.

**NCERT Solutions Class 11 Maths Chapter 1 Sets**

A set is a group of items that all have the same characteristics. Sets are a very important part of modern math. This chapter talks about different kinds of sets, different ways to work with sets, and Venn diagrams. Sets are used to describe the ideas of relations and functions. Learning about sets can also help you understand sequences, probability, geometry, and other ideas.

This chapter gives you some ideas for how to deal with sets in a consistent way. For students to understand more complicated ideas, they need to know a lot about this chapter.

**Topics that are important in Class 11 Chapter 1 Sets:**

- A set is a group of objects with clear boundaries.

**Representation of Sets:**

- There are two ways to show a set:
- Roster form: In roster form, we list all the objects in the set between curly brackets () and separate them with commas.
- Set-builder form: In this form, each element of the set should have a single property in order to be a member of the set.

**Types of Sets**

**Empty Sets:**A set with no elements is called an empty set. This is also known as the void set or the null set, and or are used to show it.**Singleton Set:**This is a group with only one member.**Finite and infinite sets:**A set is said to be finite if it has a finite number of elements, and infinite if it has an infinite number of elements.**Equal Sets:**Sets A and B are said to be equal if all of the elements in Set A are also in Set B. This means that two equal sets will have exactly the same element.**Equivalent Sets:**Two finite sets are the same if they have the same number of parts.- There will be a subset of every set.
- Every set will always have the empty set as a part of it.
- If there are n elements in a finite set, then there are 2n subsets.

**Power Set:**The power set is a set that has all of the subsets, as well as the empty set and the original set. It’s usually shown by the letter P.**Universal Set:**A set that includes all other sets in a certain situation.**Venn diagrams**are pictures that show how two sets are related to each other.

Chapter 1 – Sets Exercises | |

Exercise 1.1 Finite and Infinite Sets | 6 Questions & Solutions |

Exercise 1.2 Finite and Infinite Sets | 6 Questions & Solutions |

Exercise 1.3 Subsets | 9 Questions & Solutions |

Exercise 1.4 Operations on Sets | 12 Questions & Solutions |

Exercise 1.5 Complement of a Set | 7 Questions & Solutions |

Exercise 1.6 Union and Intersection of Two Sets | 8 Questions & Solutions |

**NCERT Solutions Class 11 Maths Chapter 2 Relations and Functions**

In an update to Sets, Relations, and Functions, the idea of linking pairs of objects from two different sets and then figuring out how those objects relate to each other is explored. Some relationships can be thought of as functions, which is an important idea in mathematics because it shows how two numbers can be related in a way that is mathematically exact. This chapter explained all of this and much more in a fun and creative way.

**Important topics covered in Class 11 Chapter 2 Relations and Functions:**

- Ordered Pair: An ordered pair is made up of two things that are put together in a certain way.
- Equality of Two Ordered Pairs: If a = c and b = d, then two ordered pairs (a, b) and (c, d) are equal.
- Cartesian Product of Two Sets: The cartesian product of two sets A and B is the set of all ordered pairs (a, b) where a A and b B for any two non-empty sets A and B. It is written as A B.
- Relationships: If a relation R goes from a non-empty set A to a non-empty set B, then A B is a subset of R. You can get to the subset by saying what the relationship is between the first and second elements of the ordered pairs in A B.
- Functions: A relationship R between two sets A and B is a function if every item in set A has only one image in set B. In simple terms, a function f can be a relation if no two pairs in the relation share the same first element.

**Types of Functions:**

- One One Function
- Many One Function
- Onto Function
- One One and Onto Function
- Into Function
- Constant Function
- Identity Function

**Class 11 Maths NCERT Solutions Chapter 2 Exercises**

Chapter 2 – Relations and Functions Exercises | |

Exercise 2.1 Cartesian Products of Sets | 10 Questions & Solutions |

Exercise 2.2 Relations | 9 Questions & Solutions |

Exercise 2.3 Real functions | 5 Questions & Solutions |

**Class 11 Maths NCERT Solutions Chapter 3 Trigonometric Functions**

This chapter takes the ideas of trigonometric ratios and applies them to trigonometric functions. It also looks at the properties of these functions. As students try to solve the different math problems in this chapter, they can learn more about the exciting world of trigonometry.

**Class 11 Maths NCERT Solutions Chapter 3 Exercises**

Chapter 3 – Trigonometric Functions Exercises | |

Exercise 3.1 Angles | 7 Questions & Solutions |

Exercise 3.2 Trigonometric Functions | 10 Questions & Solutions |

Exercise 3.3 Sum and Difference of Two Angles | 25 Questions & Solutions |

Exercise 3.4 Trigonometric Equations | 9 Questions & Solutions |

**NCERT Solutions Class 11 Maths Chapter 4 Principle of Mathematical Induction**

For students who are good at mathematical induction, this chapter can be quite interesting with just one exercise. Make sure you understand the ideas, as they will help you in your future studies as well.

In Chapter 4 of the NCERT Maths Book for Class 11, Solutions PDF, there are sections on deduction, induction, the steps of the mathematical induction principle, and examples to show how these steps work.

**Class 11 Maths NCERT Solutions Chapter 4 Exercises**

Chapter 4 – Mathematical Induction Exercises | |

Exercise 4.1 Principle of Mathematical Induction | 24 Questions & Solutions |

**NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations**

To account for the square root of negative numbers, the rules for real numbers are stretched to include complex numbers. In higher math, the idea of complex numbers is very important, so make sure you understand all of the ideas in this chapter. The fifth chapter of Class 11 Maths is called “Complex Numbers and Quadratic Equations.”

This chapter talks about things like the definition of complex numbers, the conjugate of a complex number, the algebra of complex numbers, the argand plane, the modulus and argument of a complex number, polar form, De-theorem, Moivre’s the cube root and square root of a complex number, loci in the complex plane, the vectorial representation of a complex number, quadratic expression, the nature of roots and graphs, and more.

**Class 11 Maths NCERT Solutions Chapter 5 Exercises**

Chapter 5 – Complex Numbers and Quadratic Equations Exercises | |

Exercise 5.1 Complex Numbers | 14 Questions & Solutions |

Exercise 5.2 Argand Plane and Polar Representation | 8 Questions & Solutions |

Exercise 5.3 Quadratic Equations | 10 Questions & Solutions |

**NCERT Solutions Class 11 Maths Chapter 6 Linear Inequalities**

This chapter is very important for the test, and if you understand all the ideas, it can also be very interesting. Most of the time, two amounts are not the same. The ideas and activities in this chapter will help you see how inequality is a normal part of life. “Linear Inequalities” is Chapter 6 of NCERT Maths Book Class 11 Solutions PDF.

This chapter covers an introduction to linear inequalities, examples of inequality in everyday life, notations, types of inequalities, the solution and solution set for a linear inequality with one variable, rules of inequality, and a graphical solution for a linear inequality with two variables. It also talks about linear inequalities with one variable, linear inequalities with two variables, and quadratic inequalities.

**Class 11 Maths NCERT Solutions Chapter 6 Exercises**

Chapter 6 – Linear Inequalities Exercises | |

Exercise 6.1 Inequalities | 26 Questions & Solutions |

Exercise 6.2 Graphical Solution of Linear Inequalities in Two Variables | 10 Questions & Solutions |

Exercise 6.3 Solution of System of Linear Inequalities in Two Variables | 15 Questions & Solutions |

**NCERT Solutions for Class 11 Maths Chapter 7 – Permutations and Combinations**

Students can find all of the Free NCERT Solutions for Class 11 Maths Chapter 7 “Permutations and Combinations” exercises here. If you have any questions about the NCERT Solutions for Class 11 Maths Chapter 7 sums, these are the best way to make sure you understand everything. Chapter 7 talks about the basic idea of counting, the factorial, how formulas are made, and how it can be used in permutations and combinations.

**Class 11 Maths NCERT Solutions Chapter 7 Exercises**

Chapter 7 – Permutations and Combinations Exercises | |

Exercise 7.1 Fundamental Principle of Counting | 6 Questions & Solutions |

Exercise 7.2 Permutations | 5 Questions & Solutions |

Exercise 7.3 Derivation of the formula | 11 Questions & Solutions |

Exercise 7.4 Combinations | 9 Questions & Solutions |

**NCERT Solutions for Class 11 Maths Chapter 8 – Binomial Theorem**

Math teacher with many years of experience in this subject explains and solves NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem with all exercise sums. Math experts look over and check all of the answers very carefully.

**Class 11 Maths NCERT Solutions Chapter 8 Exercises**

Chapter 8 – Binomial Theorem Exercises | |

Exercise 8.1 Binomial Theorem | 14 Questions & Solutions |

Exercise 8.2 General and Middle Terms | 2 Questions & Solutions |

**NCERT Solutions for Class 11 Maths Chapter 9 – Sequences and Series**

This Free NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series for all exercises is very helpful for Class 11 students. In chapter 9, there are a total of four exercises that are based on the 11th Class Maths Book Solution.

**Class 11 Maths NCERT Solutions Chapter 9 Exercises**

Chapter 9 – Sequences and Series Exercises | |

Exercise 9.1 Sequences | 14 Questions & Solutions |

Exercise 9.2 Arithmetic Progression | 8 Questions & Solutions |

Exercise 9.3 Geometric Progression | 32 Questions & Solutions |

Exercise 9.4 Sum to n Terms of Special Series | 10 Questions & Solutions |

**NCERT Solutions for Class 11 Maths Chapter 10 – Straight Lines**

Chapter 10 of Class 11 Maths NCERT Solutions Straight Lines helps students remember what they learned in class about two-dimensional geometry. Shifting of origin, many forms of equations for lines parallel to the axis, angle between two lines, slope of a line, point-slope form, slope intercept form, two-point form, intercept, etc.

**Class 11 Maths NCERT Solutions Chapter 10 Exercises**

Chapter 10 – Straight Lines Exercises | |

Exercise 10.1 Slope of a Line | 14 Questions & Solutions |

Exercise 10.2 Various Forms of the Equation of a Line | 20 Questions & Solutions |

Exercise 10.3 General Equation of a Line | 18 Questions & Solutions |

**NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections**

This chapter goes into detail about the idea of conic sections. A conic section is a curve in math that is made when the surface of a cone meets a flat plane. The sections of a cone, such as a circle, an ellipse, a parabola, a hyperbola, a point, a straight line, and two intersecting lines as a degenerate case of a conic section, are all covered.

The chapter also has standard equations and simple properties for circles, parabolas, ellipses, and hyperbolas. In this chapter of 11 Maths NCERT Solutions PDF, there are 4 exercises and one other exercise that, when done, help students learn about the above topics.

**Class 11 Maths NCERT Solutions Chapter 11 Exercises**

Chapter 11 – Conic Sections Exercises | |

Exercise 11.1 Sections of a Cone | 15 Questions & Solutions |

Exercise 11.2 Parabola | 12 Questions & Solutions |

Exercise 11.3 Ellipse | 20 Questions & Solutions |

Exercise 11.4 Hyperbola | 15 Questions & Solutions |

**NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three-dimensional Geometry**

Three numbers are used to describe a place in space. Students in Class 11 will learn the basics of geometry in three-dimensional space in this chapter. The chapter goes into detail about the idea of coordinate axes and coordinate planes in three dimensions, as well as the coordinates of a point, the distance between two points, and the section formula.

There are three exercises in the chapter to help students solve problems and get a better grasp of the idea.

**Class 11 Maths NCERT Solutions Chapter 12 Exercises**

Chapter 12 – Introduction to Three Dimensional Geometry | |

Exercise 12.1 Coordinate Planes | 4 Questions & Solutions |

Exercise 12.2 Distance between Two Points | 5 Questions & Solutions |

Exercise 12.3 Section Formula | 5 Questions & Solutions |

**NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives**

The chapter, “Limits and Derivatives,” explains what Calculus is all about. Calculus is a branch of math that looks at how the points in the domain change the value of a function. In the beginning of this chapter, students get a sense of what derivatives are (without actually defining it). Later in the chapter, a simple definition of a limit is given, as well as some algebra about limits. Lastly, the chapter goes back to what a derivative is and how it works in algebra.

**Class 11 Maths NCERT Solutions Chapter 13 Exercises**

Chapter 13 – Limits and Derivatives Exercises | |

Exercise 13.1 Limits | 32 Questions & Solutions |

Exercise 13.2 Derivatives | 11 Questions & Solutions |

**NCERT Solutions for Class 11 Maths Chapter 14 – Mathematical Reasoning**

You can find some basic ideas about Mathematical Reasoning in this NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning. This chapter goes over some of the basics of reasoning by deduction. In NCERT Solutions for Class 11 Maths Chapter 14, there are five exercises that go into detail about inductions and deductions in math.

**Class 11 Maths NCERT Solutions Chapter 14 Exercises**

Chapter 14 – Mathematical Reasoning Exercises | |

Exercise 14.1 Statements | 2 Questions & Solutions |

Exercise 14.2 New Statements from Old | 3 Questions & Solutions |

Exercise 14.3 Special Words/Phrases | 4 Questions & Solutions |

Exercise 14.4 Implications | 4 Questions & Solutions |

Exercise 14.5 Validating Statements | 5 Questions & Solutions |

**NCERT Solutions for Class 11 Maths Chapter 15- Statistics**

Statistics is the study of the information that is gathered for specific reasons. This NCERT Solutions for Class 11 Maths Chapter 15 Statistics gives you some of the most important ways to measure dispersion. In the NCERT Solutions for Class 11 Maths Chapter 15, there are three exercises.

**Class 11 Maths NCERT Solutions Chapter 15 Exercises**

Chapter 15 – Statistics Exercises | |

Exercise 15.1 Measures of Dispersion | 12 Questions & Solutions |

Exercise 15.2 Variance and Standard Deviation | 10 Questions & Solutions |

Exercise15.3 Analysis of Frequency Distributions | 5 Questions & Solutions |

**NCERT Solutions for Class 11 Maths Chapter 16 Probability**

The chapter talks about the idea of probability as a way to measure the uncertainty of different things or, more simply, the chances that something will happen. In this chapter, students will learn about random experiments, their results, sample spaces (representations of sets), and events, including “not,” “and,” and “or” events, exhaustive events, and events that can’t happen together.

**Class 11 Maths NCERT Solutions Chapter 16 Exercises**

Chapter 16 – Probability Exercises | |

Exercise 16.1 Random Experiments | 16 Questions & Solutions |

Exercise 16.2 Event | 7 Questions & Solutions |

Exercise 16.3 Axiomatic Approach to Probability | 21 Questions & Solutions |

NCERT Solutions Class 11 Maths All Chapters |

Chapter 1 – Sets |

Chapter 2 Relations and Functions |

Chapter 3 Trigonometric Functions |

Chapter 4 Principle of Mathematical Induction |

Chapter 5 Complex Numbers and Quadratic Equations |

Chapter 6 Linear Inequalities |

Chapter 7 Permutations and Combinations |

Chapter 8 Binomial Theorem |

Chapter 9 Sequences and Series |

Chapter 10 Straight lines |

Chapter 11 Conic Sections |

Chapter 12 Introduction to Three Dimensional Geometry |

Chapter 13 Limits and Derivatives |

Chapter 14 Mathematical Reasoning |

Chapter 15 Statistics |

Chapter 16 Probability |

**Importance of Class 11 Maths NCERT Solutions **

Class 11 students have a great deal of homework to complete. Their curriculum comprises of numerous subjects, including mathematics, physics, Chemistry and , Biology. In order to outperform the rest of the class, pupils must have a solid understanding of these disciplines. After finishing the chapters, students might seek out extra study materials to further their understanding. Choosing Utopper’s **NCERT solutions** will assist students to solve difficult questions and gain an understanding of the curriculum. In addition, students will be able to comprehend the essential concepts taught in **Class 11 NCERT Solutions**. Thus, individuals can develop a study plan that will aid them throughout their final exams.

These **NCERT solutions** are unquestionably of great assistance to students who wish to complete the **Class 11 curriculum** and do well on their tests. These solutions were developed by subject matter specialists at Utopper in accordance with **CBSE guidelines**. Therefore, students can utilise these solutions as references to enhance their own skills in order to perform well on exams.