NCERT Solutions for Class 11 Maths (2024-25)

This chapter is an introduction to the concept of relation and functions. In class 11 NCERT maths, you are going to learn half of the relations and functions. In our life, there are well-defined relations like mother and father, brother and sister, etc. In a similar way, you can form relations in mathematics. A relation from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. Functions are very important in the case of data analysis. Most of the higher-level examination tests your knowledge over the chapter relations and functions. The chapter is very important for schools as well as exams like JEE and CAT.

Class 11 Maths Chapter 2, Relations and Functions, includes various topics such as Ordered pairs, Cartesian product of sets, the number of elements in the cartesian product of two finite sets, and the Cartesian product of the reals with itself (upto R× R× R). The chapter also covers the definition of relation, pictorial diagrams, domain, co-domain and range of a relation. It explains Function as a special kind of relation from one set to another, pictorial representation of a function, domain, co-domain and range of a function. Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. The chapter concludes with Sum, difference, product and quotients of functions.

Chapter 3 Trigonometric Functions

Trigonometry is the chapter that evolves around a right-angle triangle. The chapter was in class 10th where you have gone through the properties and usage of the properties. You have also done its application in daily life through chapter heights and distances. Here in class 11 NCERT maths, you will study a bit higher level of trigonometry. The study of various trigonometric functions and properties are introduced in class 11th maths solution. The identities studied will be used mainly in calculus and also in Physics.

This chapter includes a range of topics related to trigonometric functions, including measuring angles in both radians and degrees and converting between the two units. It also explores the definitions of trigonometric functions using the unit circle, as well as the truth of the identity sin²x + cos²x = 1 for all x. The course delves into the signs of trigonometric functions and how to graph them, as well as how to express sin(x + y) and cos(x + y) in terms of sin x, sin y, cos x, and cos y. The curriculum also covers identities pertaining to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x, and tan 3x. Additionally, the class examines the general solution of trigonometric equations, including those of the type sin θ = sin α, cos θ = cos α, and tan θ = tan α. Finally, the chapter provides proofs and simple applications of sine and cosine formulae.

Chapter 4 Principle of Mathematical Induction

This is a small but important chapter. The chapter Principle of Mathematical Induction contains one exercise with 24 questions in it. Induction is generalized by observing the patterns. The steps involved in solving the problems are the same. If you go through class 11 NCERT maths solutions for chapter 4 Principle of Mathematical Induction then it will help you in fetching good marks in the examinations.

Chapter 5 Complex Numbers and Quadratic Equations

In previous classes, we have learned the concepts of linear equations with one variable, linear equations with two variables and quadratic equations. We have studied that has no real roots or it has imaginary roots. This chapter is introduced to extend the concept of the real number system. This is one of the important chapters of mathematics which has a lot of applications in Mathematics and other subjects like Physics. The concept of Complex Numbers is used in vector algebra Mathematics and for solving problems related to alternating circuits in Physics.

Chapter 5 of Class 11 Mathematics covers the topics of complex numbers and quadratic equations. The curriculum discusses the necessity of introducing complex numbers, particularly the square root of -1, due to the limitation in solving every quadratic equation using real numbers alone. The class provides a brief overview of the algebraic properties of complex numbers and delves into the concepts of the Argand plane and polar representation of complex numbers. The chapter also introduces the Fundamental Theorem of Algebra and examines the solution of quadratic equations within the complex number system.

Chapter 6 Linear Inequalities

We have studied how to solve linear equations in our high school classes. For example, if three pen and two scales cost 40 rupees and if 5 pen and six scales cost 80 rupees, to find the cost of pen and scale we use linear equations. Now consider the situation that you have given 120 rupees and you are asked to buy the maximum number of books that cost 33 rupees. This type of problem is formulated using linear inequality. That is if you can bye x number of books then 33x = 120. This is how linear inequality problems are formulated.

Chapter 6 of Class 11 Mathematics covers the topic of linear inequalities. The course examines algebraic methods of solving linear inequalities in one variable and represents them on the number line. Additionally, the chapter delves into the graphical solution of linear inequalities in two variables. The class also explores the solution of systems of linear inequalities in two variables and solves them graphically.

Chapter 7 Permutations and Combinations

Before starting the concepts of Permutations and Combinations, it is mandatory to be familiar with the concepts of the fundamental principle of counting. So the chapter starts with the fundamental principle of counting. The combination means selection of the things and permutation means selection + arrangement. This is a chapter based on all new concepts. It is not linked with any of the chapters studied in the previous classes. Apart from NCERT 11 maths , the chapter is also important for JEE Main, CAT and many other competitive examinations.

• Permutation and Combination Class 11 exercise 7.1
• Permutation and Combination Class 11 exercise 7.2
• Permutation and Combination Class 11 exercise 7.3
• Permutation and Combination Class 11 exercise 7.4
• Permutation and Combination Class 11 miscellaneous exercise

Chapter 8 Binomial Theorem

We have studied the expansions like (a+b)² and (a+b)³ in previous classes. The binomial theorem is part of algebra which describes the algebraic expansion of powers and binomials. In this particular chapter Binomial Theorem, we will study how to expand (a+b)ⁿ in an easy way. We will study the binomial theorem for positive integral indices only and It can be used only with positive integral values of n.

• Binomial Theorem class 11 exercise 8.1
• Binomial Theorem class 11 exercise 8.2
• Binomial Theorem class 11 exercise miscellaneous exercise

Chapter 9 Sequences and Series

In class 10 maths, you have studied a chapter arithmetic progression. The chapter 9 sequence and series of class 11 maths is the extended version of the class 10 chapter. In class 10 maths, we have studied only arithmetic progression but in class 11 you will study arithmetic progression, geometric progression, and harmonic progression. The chapter is a part of arithmetic and the question on the chapter will be on finding nth term, sum, and combination of two series.

• Sequence and Series class 11 exercise 9.1
• Sequence and Series class 11 exercise 9.2
• Sequence and Series class 11 exercise 9.3
• Sequence and Series class 11 exercise 9.4
• Sequence and Series class 11 miscellaneous exercise

Chapter 10 Straight Lines

In previous classes, we have gone through the two-dimensional coordinate geometry. In class 11 we will learn three-dimensional coordinate geometry. This is a very important chapter of co-ordinate geometry. We will use the concepts of this chapter in the coming chapters of coordinate geometry as well as physics. Mainly the concepts of slope and tangents will be used further in Maths, Physics, and Chemistry too.

• Straight Lines Class 11 exercises 10.1
• Straight Lines Class 11 exercises 10.2
  
• Straight Lines Class 11 exercises 10.3
  
• Straight Lines Class 11 miscellaneous exercises

Chapter 11 Conic Sections

The chapter is the extension of the equation of lines class 10 maths. In this particular chapter, we will study the concept of the equation of circles and its applications, the equation of ellipse and hyperbolas and its applications. Terms parabola and hyperbola has been introduced by a mathematician Apollonius. The curves introduced in the chapter are known as conic sections or conics. The concept studied in this chapter will be used in the NCERT class 12 chapter applications of integrals.

• Conic Section Class 11 NCERT Exercise 11.1
• Conic Section Class 11 NCERT Exercise 11.2
• Conic Section Class 11 NCERT Exercise 11.3
• Conic Section Class 11 NCERT Exercise 11.4
• Conic Section Class 11 NCERT Miscellaneous Exercise

Chapter 12 Introduction to Three-dimensional Geometry

In previous classes you have learned , to locate the position of a point in a plane, we need two intersecting lines in the plane. Both the lines are called coordinate axes and the two numbers are called coordinates of that point. In the previous classes, we have studied about points lying on a plane. Here in this chapter, we will learn about the points on a multidimensional figure. The Class 11 NCERT Maths Solutions for Chapter 12 is very important in the analysis of motion in space. In this chapter, we will study how to represent a point in space, the distance between two points in three dimensions and section formulae.

• NCERT Solutions Class 11 Maths Chapter 12 Exercise 12.1
• NCERT Solutions Class 11 Maths Chapter 12 Exercise 12.2
• NCERT Solutions Class 11 Maths Chapter 12 Exercise 12.3
• NCERT Solutions Class 11 Maths Chapter 12 Miscellaneous Exercise

Chapter 13 Limits and Derivatives

The chapter limits and derivatives in an introduction to the introductory chapter of calculus and the concept studied here will be further used in class 12 mathematics also. Calculus is the branch of mathematics in which we learn to deal with the study of change in the function's value as the points in the domain change. Through this chapter, you will learn the idea of derivative, then the definition of a limit and some algebra of limits. The chapter creates as strong foundations for calculus and plays a vital role in higher mathematics.

• Limits And Derivatives NCERT Exercise 13.1 Solutions
• Limits And Derivatives NCERT Exercise 13.2 Solutions
• Limits And Derivatives Miscellaneous Solutions

Chapter 14 Mathematical Reasoning

The chapter is structured in a manner that if you go through it in the given manner then this will definitely work well for you all in terms of an increase in logical ability. Logical ability is an important thing that one should have. Logic is important to make a decision or conclude some using some data points. In this chapter, we will discuss some fundamentals of deductive reasoning. In deductive reasoning we will be given some set of facts and using this fact we will deduct another fact.

• Mathematical Reasoning Class 11 NCERT Chapter-Exercise 14.1 Solutions
• Mathematical Reasoning Class 11 NCERT Chapter-Exercise 14.2 Solutions
• Mathematical Reasoning Class 11 NCERT Chapter-Exercise 14.3 Solutions
• Mathematical Reasoning Class 11 NCERT Chapter-Exercise 14.4 Solutions
• Mathematical Reasoning Class 11 NCERT Chapter-Exercise 14.5 Solutions
• Mathematical Reasoning Class 11 NCERT Chapter-Miscellaneous Exercise Solutions

Chapter 15 Statistics

In previous classes, we have studied statistics. Here it is introduced with a bit higher level of concepts. Statistics on its own is an individual subject apart from mathematics. This is one of the most important chapters of class 11 NCERT solutions. We keep statistics on many things in our daily life. The concept that we will study in this chapter is widely used in data analysis. The statistics obtained using data will be helpful for prediction. This chapter is very important in daily life and for the exam also.

• NCERT Solutions For Class 11 Maths Chapter 15 Statistics Exercise 15.1
• NCERT Solutions For Class 11 Maths Chapter 15 Statistics Exercise 15.2
• NCERT Solutions For Class 11 Maths Chapter 15 Statistics Exercise 15.3
• NCERT Solutions For Class 11 Maths Chapter 15 Statistics Miscellaneous Exercise

Chapter 16 Probability

Before coming to the concept of probability, you must go through the concepts related to chapter permutation and combination. We are already aware of the basic concepts related to probability. In class 11 maths, the probability is of a bit higher level as compared to previous classes. It is a very important chapter for the board examination and many other competitive exams. The concept of random variable and probability will be used for prediction and estimation. We will find the probability on the basis of observations and collected data. The concept of sets, functions, statistics, and probability are used in the modern theory of machine learning and artificial intelligence.

Probability Class 11 NCERT Exercise 16.1

Probability Class 11 NCERT Exercise 16.2

Probability Class 11 NCERT Exercise 16.3

Probability Class 11 NCERT Miscellaneous Exercise

CBSE Class 11 Maths - Unit Wise Weightage

The CBSE Class 11 Maths syllabus for 2024-25 is an essential guide for students preparing for their board exams. The syllabus outlines the unit-wise weightage for various topics, which is crucial for students to plan and prioritize their studies effectively.

Key Benefits of Maths NCERT Solutions Class 11

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• Students can comfortably learn NCERT or CBSE-based Class 11 Maths from the convenience of their homes, using their personal computers or tablets, provided they have internet access, or they can download from Careers360 website.
• The Class 11 Maths NCERT Solutions PDF can be downloaded for free, enabling students to prepare for their exams efficiently.
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• Careers360 has a team of highly skilled subject experts who can guide students to grasp the subject and its concepts in an engaging and simplified manner.

NCERT Solutions (Subject-wise )

NCERT Books and NCERT Syllabus

• NCERT Books Class 11 Maths
• NCERT Syllabus Class 11 Maths
• NCERT Books Class 11
• NCERT Syllabus Class 11