NCERT Solutions for Class 11 Maths 2024-25

Chapter 1 - Sets

A set is defined as the characterised accumulation of the various items. Sets are an integral part of modern-day Mathematics. The concepts in this chapter include different types of sets, various set operations and Venn diagrams. The concepts of relations and functions are characterised by using sets. Learning of sets also aids in the understanding of the concepts of sequences, probability, geometry and more. 

1. Exercise 1.1 Introduces you to the fundamental concepts of sets, including their formation and basic operations like union, intersection, and difference.

2. Exercise 1.2 Learn about roster form (listing the elements directly within curly braces), set-builder form (using a description to define the elements), and Venn diagrams (illustrating sets visually using circles).

3. Exercise 1.3 Explores relationships between sets, concepts like subset, proper subset, equal sets, and disjoint sets, and how to determine these relationships between two sets.

4. Exercise 1.4 This exercise ventures into more advanced set theory concepts. You'll be introduced to universal sets, complements of sets (elements that belong to the universal set but not the original set), and De Morgan's Laws, which are crucial properties that govern the relationships between complements of sets.

Topics Covered in Class 11 Maths Chapter 1 Sets

• A set is called a well-defined collection of objects.

• Representation of Sets:

We can represent a set in two methods:

• Roster form: In the roster form, we list all the objects of the set within curly brackets { } and separate by commas.

• Set-builder form: In this form, all the elements of the set should have a single property to be the member of that set.

• Types of Sets

• Empty Sets: A set which will not have any element is called an empty set. This is also called the void set or null set, and it is denoted by {} or Φ.

• Singleton Set: This is a set consisting of a single element.

• Finite and infinite Set: If a set consists of a finite number of elements, then it is called a finite set, if nor the set will be an infinite set.

• Equal Sets: Set A and Set B are said to be equal, only if all elements of A are also the elements of B i.e. two equal sets will have exactly the same element.

• Equivalent Sets: Two finite sets are said to be equal if the number of elements are equal.

• Every set will be a subset of itself.

• The empty set will always be a subset of every set.

• If a finite set contains n elements, then the total number of subsets is 2n.

• Power Set: The power set is a set which has all of the subsets, and also the empty set & the original set. It's commonly denoted with the letter P.

• Universal Set: The universal set is a set that contains all sets in a specific context.

• Venn diagrams: Venn diagrams are diagrams that show the relationship between two sets.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 1 of CBSE Class 11 Maths Solutions–

• Chapter 1: Sets Important Questions

• Chapter 1: Sets Important Formulas

• Chapter 1: Sets Revision Notes

• Chapter 1: Sets NCERT Exemplar Solutions

• Chapter 1: Sets RD Sharma Solutions

• Chapter 1: Sets RS Aggarwal Solutions

Chapter 2 - Relations and Functions

An upgrade on Sets, Relations and Functions explores the idea of linking pairs of objects from two different sets and then deriving relations between the said objects of the pair. Certain relations qualify as functions, a crucial concept in Mathematics for its capturing of the idea of two quantities corresponding with each other and the correspondence is mathematically precise.

1. Exercise 2.1 deals with identifying whether a relation is a function or not. The key concept to remember here is that a function assigns a unique output (range element) to every input (domain element). You'll be given a relation and asked to determine if it follows this rule.

2. Exercise 2.2 is about depicting a function using an arrow diagram. Arrow diagrams provide a visual representation of the connection between elements in a function's domain and range. Arrows point from the domain elements to their corresponding range elements.

3. Exercise 2.3 practices representing a function as a set of ordered pairs. Ordered pairs define the function by listing the input (domain element) and the corresponding output (range element) together. Each ordered pair shows the relationship between an input and its unique output.

• Ordered Pair: An ordered pair is formed by two objects or elements that are arranged in a specific order.

• Equality of Two Ordered Pairs: If a = c and b = d, two ordered pairs (a, b) and (c, d) are equal.

• Cartesian Product of Two Sets: The set of all ordered pairs (a, b) where a ∈ A and b ∈ B exist for any two non-empty sets A and B is termed the cartesian product of sets A and B and is denoted by A × B.

• Relations: A relation R which is from a non-empty set A to a non-empty set B will be a subset of the cartesian product set A × B. The subset can be derived by describing a relationship between the first element & the second element of the ordered pairs in A × B.

• Functions: A relation R from the sets A to B will be a function, if every element of set A has one and only image in set B. In simple words, a function f can be a relation if no two pairs in the relation has the first element.

• Types of Functions: 

• One One Function

• Many One Function

• Onto Function

• One One and Onto Function

• Into Function

• Constant Function

• Identity Function

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 2 of CBSE Class 11 Maths Solutions–

• Chapter 2: Relations and Functions Important Questions

• Chapter 2: Relations and Functions Important Formulas

• Chapter 2: Relations and Functions Revision Notes

• Chapter 2: Relations and Functions NCERT Exemplar Solutions

• Chapter 2: Relations and Functions RD Sharma Solutions

• Chapter 2: Relations and Functions RS Aggarwal Solutions

Class 11 Maths NCERT Solutions Chapter 3 - Trigonometric Functions

This chapter generalises the concepts of trigonometric ratios to trigonometric functions, along with the study of their properties. Students get to explore the dynamic world of trigonometry as they attempt and solve the various numerical problems provided in this chapter.

1. Exercise 3.1 focuses on understanding degrees and radians as units to measure angles. It involves converting between these units and solving problems related to angles and their corresponding measures.

2. Exercise 3.2 explores the relationship between angles and arc lengths in a circle. You'll likely solve problems finding the angle measure based on a given arc length or vice versa.

3. Exercise 3.3 dives into the concept of finding the values of trigonometric functions (sine, cosine, tangent) for a given angle. You might be provided with the angle in degrees or radians and asked to determine the trigonometric function's value.

4. Exercise 3.4 introduces you to some basic trigonometric identities. You might encounter problems that require using these identities to simplify expressions or solve equations involving trigonometric functions.

Topics Covered in Class 11 Maths Chapter 3 Trigonometric Functions:

• Introduction to Trigonometric Functions

• Angles and Their Measurements

• Trigonometric Ratios

• Trigonometric Functions

• Trigonometric Identities

• Heights and Distances

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 3 of CBSE Class 11 Maths Solutions–

• Chapter 3: Trigonometric Functions Important Questions

• Chapter 3: Trigonometric Functions Important Formulas

• Chapter 3: Trigonometric Functions Revision Notes

• Chapter 3: Trigonometric Functions NCERT Exemplar Solutions 

• Chapter 3: Trigonometric Functions RD Sharma Solutions

• Chapter 3: Trigonometric Functions RS Aggarwal Solutions

Chapter - Principle of Mathematical Induction (Not available in current syllabus) 

In this chapter, we explore the fundamental idea of mathematical induction, a powerful technique used in mathematics to demonstrate statements concerning natural numbers. Mathematical induction is built on the principle that if a statement is true for a particular natural number, and if it's also true for the next natural number, then it's true for all natural numbers equal to or greater than the initial number.

We start by grasping the basic concepts of induction and the principle itself. Then, we examine various uses of mathematical induction, showing how it's helpful in proving a wide array of mathematical statements and theorems. By following a structured approach, this chapter provides students with the skills to effectively apply mathematical induction to establish the accuracy of mathematical statements involving natural numbers.

Topics Covered in Class 11 Maths Chapter Principle of Mathematical Induction:

• Basic Concepts of Induction

• The Principle of Mathematical Induction

• Applications of Mathematical Induction

• Applications and Proof of sine and cosine formulae.

• Deducing the identities like following:

$\begin{array}{l}cosx + cosy =2cos\frac{1}{2}(x + y )cos\frac{1}{2}(x – y )\end{array} $

$\begin{array}{l}tan(x\pm y)=\frac{tanx\pm tany}{1\mp tanxtany},cot(x\pm y)=\frac{cotxcoty\mp 1}{cotx\pm coty}\end{array} $

$\begin{array}{l}cosx – cosy =-2sin\frac{1}{2}(x + y )sin\frac{1}{2}(x – y)\end{array} $

Along with this, students can also download additional study materials provided by Vedantu, for Chapter of CBSE Class 11 Maths Solutions

• Principle of Mathematical Induction Important Questions

• Principle of Mathematical Induction Important Formulas

• Principle of Mathematical Induction Revision Notes

• Principle of Mathematical Induction NCERT Exemplar Solutions

Chapter 4 - Complex Numbers and Quadratic Equations

This chapter introduces students to the concept of complex numbers and their relation to quadratic equations. It explores the properties of complex numbers, including algebraic operations and graphical representation. Additionally, it covers the solutions of quadratic equations involving complex roots, along with the fundamental theorem of algebra. 

1. Exercise 4.1 focuses on basic operations and properties of complex numbers. This might involve simplifying expressions, finding conjugates, and performing arithmetic operations like addition, subtraction, multiplication, and division.

2. Exercise 4.2 delve into concepts like modulus and argument of complex numbers. You might find problems calculating distances, angles, or converting complex numbers to polar forms.

3. Exercise 4.3 explores applications of complex numbers in solving quadratic equations. This involves finding complex roots of quadratic equations and understanding their relationship with the discriminant.

Topics Covered in Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations:

• Introduction to Complex Numbers

• Algebra of Complex Numbers

• Quadratic Equations in One Variable

• Solutions of Quadratic Equations

• Graphical Representation of Complex Numbers

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 5 of CBSE Class 11 Maths Solutions–

• Chapter 4: Complex Numbers and Quadratic Equations Important Questions

• Chapter 4: Complex Numbers and Quadratic Equations Important Formulas

• Chapter 4: Complex Numbers and Quadratic Equations Revision Notes

• Chapter 4: Complex Numbers and Quadratic Equations NCERT Exemplar Solutions

• Chapter 4: Complex Numbers RD Sharma Solutions

• Chapter 4: Quadratic Equations RD Sharma Solutions

• Chapter 4: Complex Numbers and Quadratic Equations RS Aggarwal Solutions

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 5 of CBSE Class 11 Maths Solutions–

• Chapter 5: Linear Inequalities Important Questions

• Chapter 5: Linear Inequalities Revision Notes

• Chapter 5: Linear Inequalities NCERT Exemplar Solutions

• Chapter 5: Linear Inequalities RD Sharma Solutions

• Chapter 5: Linear Inequalities (In One Variable) RS Aggarwal Solutions

• Chapter 5: Linear Inequalities (In Two Variable) RS Aggarwal Solutions

Chapter 6 - Permutations and Combinations

Chapter 6, "Permutations and Combinations," introduces students to advanced mathematical concepts with applications in various fields. This chapter consists of 4 exercises with 31 questions covering permutations and combinations. It includes fundamental principles of counting, basic arrangements and selections, permutations under certain conditions, division of objects, permutations of alike objects, distribution of alike objects, circular permutations, selection of objects, number of divisors, sum of divisors, and rearrangements.

1. Exercise 6.1 deals with finding the number of ways to arrange distinct objects in a row. This is a fundamental concept of permutations.

2. Exercise 6.2 introduces selection of objects. You'll need to find the number of ways to choose a specific number of objects from a larger collection. This is related to combinations.

3. Exercise 6.3 applies the concept of combinations to selecting a group of members from a set of people.

4. Exercise 6.4 introduces a constraint into arrangements. You'll need to find the number of arrangements considering two objects that must always be together. This requires applying permutation formulas with some modifications.

Topics Covered in Class 11 Maths Chapter 6 Permutations and Combinations:

• Fundamental Principle of Counting

• Factorial Notation

• Permutations

• Linear Arrangement

• Circular Arrangement

• Permutations when Objects are Repeated

• Combinations

• Selections of Objects

• Combinations with Repetition

• Mathematical Induction

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 6 of CBSE Class 11 Maths Solutions–

• Chapter 6: Permutations and Combinations Important Questions

• Chapter 6: Permutations and Combinations Important Formulas

• Chapter 6: Permutations and Combinations Revision Notes

• Chapter 6: Permutations and Combinations NCERT Exemplar Solutions

• Chapter 6: Permutations RD Sharma Solutions

• Chapter 6: Combinations RD Sharma Solutions

• Chapter 6: Permutations RS Aggarwal Solutions

• Chapter 6: Combinations RS Aggarwal Solutions

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 7 of CBSE Class 11 Maths Solutions:

• Chapter 7: Binomial Theorem Important Questions

• Chapter 7: Binomial Theorem Important Formulas

• Chapter 7: Binomial Theorem Revision Notes

• Chapter 7: Binomial Theorem NCERT Exemplar Solutions

• Chapter 7: Binomial Theorem RD Sharma Solutions

• Chapter 7: Binomial Theorem RS Aggarwal Solutions

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 8 of CBSE Class 11 Maths Solutions–

• Chapter 8: Sequences and Series Important Questions

• Chapter 8: Sequences and Series Revision Notes

• Chapter 8: Sequences and Series NCERT Exemplar Solutions

• Chapter 8: Sequences and Series RD Sharma Solutions

• Chapter 8: Sequences and Series RS Aggarwal Solutions

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 10 of CBSE Class 11 Maths Solutions–

• Chapter 9: Straight Lines Important Questions

• Chapter 9: Straight Lines Important Formulas

• Chapter 9: Straight Lines Revision Notes

• Chapter 9: Straight Lines NCERT Exemplar Solutions

• Chapter 9: Straight Lines RD Sharma Solutions

• Chapter 9: Straight Lines RS Aggarwal Solutions

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 10 of CBSE Class 11 Maths Solutions:

• Chapter 10: Conic Sections Important Questions

• Chapter 10: Conic Sections Important Formulas

• Chapter 10: Conic Sections Revision Notes

• Chapter 10: Conic Sections NCERT Exemplar Solutions

• Chapter 10: Conic Sections RD Sharma Solutions

• Chapter 10: Conic Sections RS Aggarwal Solutions

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 11 of CBSE Class 11 Maths Solutions

• Chapter 11: Introduction to Three Dimensional Geometry Important Questions

• Chapter 11: Introduction to Three Dimensional Geometry Important Formulas

• Chapter 11: Introduction to Three Dimensional Geometry Revision Notes

• Chapter 11: Introduction to Three Dimensional Geometry NCERT Exemplar Solutions

• Chapter 11: Introduction to Three Dimensional Geometry RD Sharma Solutions

• Chapter 11: Introduction to Three Dimensional Geometry RS Aggarwal Solutions

Chapter 12 - Limits and Derivatives

Calculus, a very important concept of Mathematics, associated with the study of change in the value of a function with the change of points in the domain is explained in this chapter. Students, through this chapter, are introduced to the vast world of calculus, which finds a host of applications across various fields. 

1. Exercise 12.1 likely focuses on the concept of derivatives, which are fundamental tools in calculus for understanding how a function's output changes with respect to its input. It might involve finding the derivatives of simple algebraic expressions using the basic differentiation rules.

2. Exercise 12.2 introduce the differentiation of exponential functions, specifically the derivative of the function e^x (where e is the mathematical constant approximately equal to 2.71828).

Topics Covered in Class 11 Maths Chapter 12 - Limits and Derivatives

• Finding limits by direct substitution (when possible)

• Techniques for finding limits of indeterminate forms

• Finding one-sided limits (left-hand limit and right-hand limit)

• Introduction to the concept of derivatives and their applications (rate of change)

• Finding the derivative of a function using the first principle

• Differentiation formulas for basic functions (like sin(x), cos(x), etc.)

• Product rule and quotient rule for differentiation

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 12 of CBSE Class 11 Maths Solutions:

• Chapter 12: Limits and Derivatives Important Questions

• Chapter 12: Limits and Derivatives Important Formulas

• Chapter 12: Limits and Derivatives Revision Notes

• Chapter 12: Limits and Derivatives NCERT Exemplar Solutions

• Chapter 12: Limits RD Sharma Solutions

• Chapter 12: Derivatives RD Sharma Solutions

• Chapter 12: Limits RS Aggarwal Solutions

• Chapter 12: Derivatives RS Aggarwal Solutions

Along with this, students can also download additional study materials provided by Vedantu, for Chapter of CBSE Class 11 Maths Solutions–

• Mathematical Reasoning Important Questions

• Mathematical Reasoning Important Formulas

• Mathematical Reasoning Revision Notes

• Mathematical Reasoning NCERT Exemplar Solutions

Chapter 13 - Statistics

Statistics is an important part of higher mathematics, covering topics like range, mean deviation, measures of dispersion, standard deviation, and mean deviation for ungrouped data. This chapter introduces key terms such as statistics, class limit, class interval, primary and secondary data, variable, frequency, and types of frequency distributions. It also explains graphical representation methods like histograms, bar diagrams, pie charts, frequency polygons, and cumulative frequency curves.

1. Exercise 13.1 revisits the idea of organizing data into a frequency table. It emphasizes how to group data points into classes (intervals) and record the frequency (number of occurrences) for each class.

2. Exercise 13.2 builds on frequency tables by introducing histograms. It guides you through the process of constructing a histogram, which visually represents the distribution of data using bars. You'll learn how to divide data into classes, calculate the width of each class, and determine the frequency density (number of observations per unit width) for each class.

3. Exercise 13.3 dives into cumulative frequency distribution. It explains how to calculate the cumulative frequency for each class. The cumulative frequency refers to the total number of observations less than or equal to a specific class. You'll also learn how to represent the cumulative frequency distribution graphically using a cumulative frequency curve.

Topics Covered in Class 11 Maths Chapter 13 - Statistics

• Measures of Central Tendency: Mean (average), Median, Mode

• Measures of Dispersion: Range, Quartile deviation, Variance, Standard deviation

• Frequency Distribution

• Additional Concepts (depending on your specific textbook):

• Correlation: Studying the relationship between two variables

• Regression analysis: Modelling the relationship between variables

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 13 of CBSE Class 11 Maths Solutions–

• Chapter 13: Statistics Exercises Important Questions

• Chapter 13: Statistics Exercises Important Formulas

• Chapter 13: Statistics Exercises Revision Notes

• Chapter 13: Statistics Exercises NCERT Exemplar Solutions

• Chapter 13: Statistics RD Sharma Solutions

• Chapter 13: Statistics RS Aggarwal Solutions

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 14 of CBSE Class 11 Maths Solutions–

• Chapter 14: Probability Important Questions

• Chapter 14: Probability Important Formulas

• Chapter 14: Probability Revision Notes

• Chapter 14: Probability NCERT Exemplar Solutions

• Chapter 14: Probability RD Sharma Solutions

• Chapter 14: Probability RS Aggarwal Solutions

CBSE Class 11 Maths Weightage 2024-25

CBSE Class 11 Maths Exam Pattern for 2024-25

The CBSE Class 11 Maths exam pattern for 2024-25 is likely to remain similar to previous years. Here's a breakdown of what to expect:

Type of Exam: Pen and paper based

Total Marks: 100 marks (divided into two parts)

• Internal Assessment: 20 marks (conducted by the school)

• External Exam: 80 marks (conducted by the CBSE board)

External Exam Paper Structure - The paper will be divided into three sections:

• Internal Choice: There will be internal choices within each section, allowing students to attempt the questions they are most comfortable with. (Typically, 33% internal choice)

• Syllabus Coverage: The entire NCERT syllabus for Class 11 Maths will be covered in the exam. (Though there might be a slight reduction as per some sources)

Internal Assessment for CBSE Class 11

How NCERT Helps in Exam Preparation?

These solutions for class 11 Maths are systematic. Moreover, it helps in time management for the final exam. The step-by-step explanations will allow students to grasp the concept behind each topic. Since each chapter contains questions, students can practice the same for the exam. The ultimate aim is to score high in the exam.

Key Benefits of NCERT Solutions Class 11 Maths

• Students can learn the NCERT solution class 11 Maths within their comfort zone. Once downloaded, they can prepare as per the timeline on desktop and mobile. Since it is available for free, students can further relax.

• Students can customise their learning experience by completing each topic at their own pace.

• Not just Maths, but students can opt for other subject solutions in PDF format and do the learning.

• Students can understand all the concepts from the 14 chapters of Class 11 Maths easily, with the help of Vedantu’s Class 11 Maths NCERT Solutions. The solutions are designed in a simple, straightforward language and all the solutions are given step by step, for the ease of students.

• The NCERT Solutions help students prepare for their Class 11 Maths exam quicker, as whenever they get stuck at any question, they can simply refer to the solutions, understand the answer and move to the next question.

All the chapters and their concepts are explained in detailed format, so students don't get confused. Since maths is a complex subject, students have the freedom to practice at their own pace and prepare for future exams.

You can also download the Class 11 Maths sample papers provided by Vedantu, as these papers can help them get an idea about the exam format. They can also learn to manage their time and identify their strong and weak areas and work on them accordingly.

Vedantu Gives You Competitive Edge

Vedantu’s NCERT Solutions for Class 11 Maths and other subjects’ experts familiarise the students with these topics so that the speed of learning is improved drastically. Thus, it helps in efficient time management skills for better results in the exams. You get to practise all the exercise questions and improve your mathematical skills. Register for our free webinar class with the best Mathematics tutor in India. Also, the Vedantu Learning App will benefit you by providing access to free live masterclasses and free conceptual videos. You will also have access to all the PDFs of study materials and solutions. Additionally, you will be provided absolutely FREE Online Tests. You will have all the required standard study materials handy and this will make the process of learning easier for you.

Important Related Links for CBSE Class 11 Maths

• CBSE Class 11 NCERT Books for Maths

• Important Questions for CBSE Class 11 Maths

• CBSE Syllabus for Class 11 Maths

• CBSE Class 11 NCERT RS Aggarwal

• CBSE Class 11 NCERT RD Sharma