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NCERT Solutions for Class 11 Maths (2024-25)

NCERT Solutions for Class 11 Maths (2024-25)

Edited By Irshad Anwar | Updated on May 10, 2024 07:19 PM IST

NCERT Solutions for Class 11 Maths (2024-2025) has been curated for students who are preparing for board exams as well as competitive exams such as JEE. All the important concepts of the Class 11 Maths NCERT textbook are covered in these NCERT solutions by the expert team at Careers360, These solutions are in accordance with the latest CBSE syllabus and pattern, comprehensively covering all the steps. So you should clear all your doubts and prepare for exams. In NCERT 11 maths solution, there are 16 chapters that cover important theorems and formulas from the NCERT textbook. These Class 11 Math NCERT solutions are organised logically. You will find the chapter-wise NCERT solutions for Class 11 Maths that will help you perform well in the board exams. These NCERT solutions are 100% accurate according to the Class 11 Maths syllabus.

NCERT Solutions for Class 11 Maths (2024-25)
NCERT Solutions for Class 11 Maths (2024-25)

Chapter-wise NCERT Solutions for Class 11 Maths

NCERT Maths Class 11 solutions are listed below for all chapters. Select chapter number to view Class 11 Maths NCERT chapter wise solutions.

Interested students can also Access and download NCERT Class 11 exemplar problems chapter-wise here.

CBSE Class 11 Maths Solutions will be helpful in the majority of competitive engineering examinations or common entrance exams for admission to engineering colleges. The main goal of the solutions is to make all of the Class 11 Math problems easier to understand than they are in the textbooks recommended by the CBSE syllabus (2024-2025). and cover all 16 chapters on the syllabus. Therefore, the NCERT Class 11 Maths Solutions provides thorough learning and aids in the improvement of students' arithmetic abilities as well as their logical and reasoning abilities. Students studying for the Class 11 Math exam should consult the NCERT Solutions of Math. With the use of resources like sample-solved problems, time-saving tricks, summaries, notes, etc., NCERT solutions for class 11 can allow you to understand all of your questions.

NCERT Class 11 Maths Chapters and exercises Detail

Class 11 maths chapters are very important for building a foundation for class 12 board exam. Upcoming articles concepts form each are discussed in detail in class 11 maths NCERT book solutions.

Chapter 1 Sets

The theory of sets is introduced by a German mathematician Georg Cantor. A well-defined collection of objects is called sets. In your daily life, you can use the concept of sets in different situations mainly to arrange things in order. For example, in the kitchen, we arrange masalas in one set, plates as another set, teacup as a different set, etc. This chapter will test your logical strength along with mathematical skills. The concept of sets is an important part of modern mathematics. Study of sequence, geometry, and probability, etc. use the knowledge of sets. also for ease you can study NCERT solutions for class 11 maths pdf.

Topics covered in this chapter are Empty set, Finite and Infinite sets, Equal sets, Subsets, and subsets of the set of real numbers (with notations), such as intervals. The chapter also explores Power set, Universal set, Venn diagrams, Union and Intersection of sets, Difference of sets, and Complement of a set.

Chapter 2 Relations & Functions

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 x^{2}+1 = 0 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

No.
Units
Marks
I
Sets and Functions
23
II
Algebra
25
III
Coordinate Geometry
12
IV
Calculus
08
V
Statistics and Probability
12

Total
80

Internal Assessment
20

Internal Marks Assessment

Internal Assessment
Marks
Periodic Tests (Best 2 out of 3 tests conducted)
10 Marks
Mathematics Activities
10 Marks
Total Marks
20 Marks


Key Benefits of Maths NCERT Solutions Class 11

The mathematics class 11 NCERT solutions offered by Careers360 provide several advantages to students.

  • 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.
  • Students have the flexibility to tailor their learning experience by studying each topic at their own pace without worrying about time restrictions.
  • 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

Frequently Asked Question (FAQs)

1. List the important concepts discussed in Chapter 11 of NCERT Solutions for Class 11 Maths.

In Chapter 11 of NCERT Solutions for Class 11 Maths PDF, the focus is on various aspects of a cone, including parabola, ellipse, circle, degenerate conic sections, and hyperbola. The chapter of NCERT 11 maths solutions also covers significant topics such as the correlation between semi-minor axis, semi-major axis, the distance of focus from the center of the ellipse, and standard equations of parabola and ellipse. This chapter holds great importance in class 11 maths solutions  as it lays the foundation for understanding essential concepts related to conic sections that would be further explored in higher classes.

2. What will I study in Chapter 4 Mathematical Induction of NCERT Solutions for Class 11 Maths?

In mathematics class 11, The method of Mathematical Induction is utilized to verify the correctness of a given statement. It is necessary that the theorem holds true for every natural number. By studying this chapter, students will become familiar with the following aspects:

  1. The main objective is to establish the validity of a statement or an example.
  2. The proof must hold true for all natural numbers.
  3. The statement should be true for the initial value.
  4. The statement should hold true for values up to the nth iteration.
  5. All steps involved in the proof must be valid and justified.
3. What are the important topics covered in relations and functions of NCERT Solutions for Class 11 Maths?

In 11th standard maths guide , The focus of this chapter is to familiarize students with the fundamentals of relations and their traits. One of the crucial concepts covered in this chapter is the relations between sets through their Cartesian product. The chapter also provides real-life examples of Cartesian products in a simple and comprehensible manner to aid students in their learning. By emphasizing the fundamental concepts, Class 11 maths chapters  aid in strengthening students' foundational knowledge, which is critical from an examination perspective.

4. How Careers360 NCERT Solutions for Class 11 Maths help us to score good marks in the exam?

The NCERT Solutions for Class 11 provided by Careers360 have been designed by subject matter experts in line with the CBSE board's syllabus. The solutions offer in NCERT maths textbook have comprehensive explanation of important concepts to facilitate easy learning for students. The solutions are available both chapter-wise and exercise-wise, with the objective of assisting students in acing their exams without fear. Primarily, the solutions aid in enhancing students' problem-solving skills, which are crucial for the exam. For ease students can study NCERT maths book class 11 solutions pdf both online and offline.

5. Which are the most difficult chapters in the CBSE class 11 maths ?

Permutations and combinations, trigonometric functions are considered to be most difficult chapters but the rigorous practice you will get command on them also.

6. Which is the best book for CBSE class 11 maths ?

There are several good books available for CBSE Class 11 Maths, but the best book may vary from student to student depending on their individual needs and preferences. However, some of the popular books recommended by experts are:

  1. NCERT Mathematics for Class 11
  2. RD Sharma Mathematics for Class 11
  3. Mathematics for Class 11 by RS Aggarwal
  4. New Simplified Physics: A Reference Book for Class 11
  5. Arihant Mathematics for Class 11 by Amit M Agarwal.

It's essential to choose a book that provides clear explanations, sufficient practice problems, and covers the entire CBSE syllabus. Students should also refer to the NCERT textbook, as it is the primary source of the curriculum and exam preparation.

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Upcoming School Exams

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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