NCERT Solutions for Class 11 Maths

# NCERT Solutions for Class 11 Maths

Our experts have put together helpful NCERT Solutions for Class 11 Maths. These solutions are designed to make understanding Class 11 Math problems from your CBSE textbooks (for the years 2023-2024) easier. We’ve organized the solutions to match the 16 chapters you’re studying. Using these solutions, you’ll learn math in a way that boosts your logical and reasoning skills. We’ve made sure to explain the tough problems in a way that makes learning easier.

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If you’re getting ready for your Class 11 Maths exam, these NCERT Solutions for Class 11 are super useful. They have answers to sample questions, quick tips, summaries, and notes that can clear up any confusion you might have. When you’re preparing for exams that help you get into Engineering institutes, the questions often come from your textbook. So, practicing with our NCERT Solutions for Class 11 Maths exercises can really improve your exam scores. We also suggest trying out the tougher problems and using our online solutions. The Class 11 Maths Solutions guide you through a strong learning journey. You can explore the solutions for each chapter in the table we’ve provided to understand better.

## NCERT Solutions for Class 11 Maths

It may be difficult for pupils to understand what is taught in class. To deal with this issue, students should look up information online to clear their doubts. Regular practice of concepts in which they are weak will enhance their confidence in terms of the exam. Students should study the chapter from the NCERT textbook and answer the exercise problems to gain a sound conceptual understanding. Students’ problem-solving and analytical thinking skills will be improved if they use the NCERT Solutions available at Infinity Learn to react to the challenges.

### NCERT Solutions Class 11 Maths Chapter Details and Exercises

#### NCERT Solutions for Class 11 Maths Chapter 1: Sets

Sets, as well as their representation, are covered in this chapter. This chapter covers the empty set, finite and infinite sets, equal sets, subsets, power sets, and universal sets. Students are also taught how to draw Venn diagrams and are introduced to set union and intersect concepts in this chapter. The Difference between Sets and the Complements and features are also covered in this chapter. There are six exercises and a random exercise in this chapter, providing students with sufficient problems to solve and, as a result, comprehend the material.

The following topics were covered:

Sets and their representations, Empty sets, Finite and Infinite sets, Equal sets, Subsets, and Subsets of a set of real numbers, especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement.

 NCERT Class 11 Maths Solutions Chapter 1 Exercise Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.5 Exercise 1.6 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 1 Sets

#### NCERT Solutions for Class 11 Maths Chapter 2: Relations & Functions

This chapter taught students about ordered pairs, the Cartesian product of sets, the number of elements in the cartesian product of two finite sets, relation definition, graphical diagrams, the domain, co-domain, and the relation range. Kids will learn about functions in addition to learning about relationships. Functions as a special type of relation, pictorial representation of a function, domain, co-domain, and range of a function, real-valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic, and greatest integer functions with graphs are just some of the topics covered by the concept of Functions. Students will learn how to connect two groups of objects and then introduce relationships between the two things in the pair. After that, they’ll learn about special relationships that qualify them as functions.

The following topics were covered:

Ordered pairs. Cartesian product of sets. A number of elements in the Cartesian product of two finite sets. Cartesian product of the set of reals with itself (up to R x R x R). Definition of relation, pictorial diagrams, domain, co-domain, and range of a relation. Function as a special type of relation. Pictorial representation of a function, domain, co-domain, and range of a function. Real valued functions, domain, and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic, and greatest integer functions, with their graphs. Sum, difference, product, and quotients of functions.

 NCERT Class 11 Maths Solutions Chapter 2 Exercises Exercise 2.1 Exercise 2.2 Exercise 2.3 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 2 Relations and Functions

#### NCERT Solutions for Class 11 Maths Chapter 3: Trigonometric Functions

Positive and negative angles are discussed in this cha, and angles in radians and degrees and converted between the two. The use of a unit circle to define trigonometric functions, the general solution of trigonometric equations, the signs, domain, and range of trigonometric functions, and their graphs are all covered in this chapter. For sin 2x, cos 2x, tan 2x, sin 3x, cos 3x, and tan 3x, the chapter walks students through the process of expressing sin (X.Y.) and cos (X.Y.) in terms of sin x, sin y, cos x, and cos y, as well as their accessible applications and deducing identities. The issues in four exercises and a random exercise in this chapter address the topics mentioned above.

The following topics were covered:

Positive and negative angles. Measuring angles in radians and degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circles. The truth of the identity, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing and in terms of their simple applications. Deducing identities like the following:

Identities related to and. The general solution of trigonometric equations of the type and tan.

 NCERT Class 11 Maths Solutions Chapter 3 Exercises Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 3 Trigonometric Functions

#### NCERT Solutions for Class 11 Maths Chapter 4: Principle of Mathematical Induction

The chapter Principle of Mathematical Induction covers various topics, taking natural numbers as the least inductive subset of real numbers, including constructing the induction and inspiring the application. The exercise in this chapter presents issues with the Principle of Mathematical Induction and its basic applications.

The following subjects were discussed:

The approach is motivated by looking at natural numbers as the least inductive subset of real numbers, which is the process of proof by induction. Simple uses of the mathematical induction principle.

 NCERT Class 11 Maths Solutions Chapter4 Exercises Exercise 4.1

Also, access the following resources for Class 12 Maths Chapter 4 Principle of Mathematical Induction

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

In this chapter, the need for complex numbers is discussed in-depth, inspired by the inability to solve quadratic equations. This chapter covers the algebraic properties of complex numbers and the argand plane and polar representation of complex numbers. This chapter covers the fundamental theorem of algebra, solutions to quadratic equations in the complex number system (with real coefficients), and the square root of a complex integer. Three exercises and various exercises cover these topics in this chapter.

The following topics were covered:

Need for complex numbers, especially, to be motivated by the inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system. The square root of a complex number.

 NCERT Class 11 Maths Solutions Chapter 5 Exercises Exercise 5.1 Exercise 5.2 Exercise 5.3 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 5 Complex Numbers and Quadratic Equations

#### NCERT Solutions for Class 11 Maths Chapter 6: Linear Inequalities

The concept of linear inequalities is covered in the chapter titled Linear Inequalities. The concepts of algebraic solutions of Linear Inequalities in one variable and their representation on the number line, the graphical representation of Linear Inequalities in two variables, and the graphical method of solving a system of Linear Inequalities in two variables are also covered in this chapter. Three exercises and a random activity in this chapter cover all of the topics covered in the chapter.

The following subjects were discussed:

Linear inequalities. The number line representation of algebraic solutions of linear inequalities in one variable. Linear inequalities in two variables are graphically solved—a graphical approach for solving a system of two-variable linear inequalities.

 NCERT Class 11 Maths Solutions Chapter 6 Exercises Exercise 6.1 Exercise 6.2 Exercise 6.3 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 6 Linear Inequalities

#### NCERT Solutions for Class 11 Maths Chapter 7: Permutations and Combinations

A permutation is an arrangement of several things in a specific order taken simultaneously. In contrast, a combination is a collection of elements in which the order is irrelevant—the fundamental principle of counting, factorial n. (n! ), permutations, combinations, formulas derivation and connections, and elementary applications are all covered in this chapter. There are four exercises, plus various exercises with questions spanning all the themes covered in the chapter.

The following topics were covered:

The fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of formulae for and their connections, simple applications.

 NCERT Class 11 Maths Solutions Chapter 7 Exercises Exercise 7.1 Exercise 7.2 Exercise 7.3 Exercise 7.4 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 7 Permutations and Combinations

#### NCERT Solutions for Class 11 Maths Chapter 8: Binomial Theorem

In this chapter, students learn about the Binomial Theorem for positive integers. This theorem can solve multiplication issues that are difficult to solve. This chapter covers the history, definition, and demonstration of the Binomial Theorem for positive integral indices. Some of the topics this chapter covers include the general and middle terms in the binomial ex-pat and applications. This chapter consists of two exercises and spontaneous activity to help students practice problems with the Binomial Theorem.

The following subjects were discussed:

The binomial theorem for positive integral indices is stated and proved from a historical perspective—the triangle of Pascal; Simple uses binomial expansion in the general and middle terms.

 NCERT Class 11 Maths Solutions Chapter 8 Exercises Exercise 8.1 Exercise 8.2 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 8 Binomial Theorem

#### NCERT Solutions for Class 11 Maths Chapter 9: Sequence and Series

A sequence is a set of integers arranged in a particular order. The total of all the terms in a sequence is called a series. This chapter discusses the following topics: The terms sequence and series are used interchangeably. Sequence and Series, Sequence and Series, Sequence and Series, Sequence and Series, Sequence and Series, Sequence and Series, Sequence and Series, Sequence and Series, Sequence and Series, Sequence Sequ Arithmetic Progression (A.P.), Arithmetic Mean (A.M. ), Arithmetic Progression (G.P.), general term of a G.P., sum of first n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relationship between A.M. and G.M., formulae for specific series sums, and more.

The chapter offers four exercises and a random activity that ask students to answer questions to help them understand the concepts taught in the chapter.

The following topics were covered:

Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M. Formulae for the following special sums.

 NCERT Class 11 Maths Solutions Chapter 9 Exercises Exercise 9.1 Exercise 9.2 Exercise 9.3 Exercise 9.4 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 9 Sequences and Series

#### NCERT Solutions for Class 11 Maths Chapter 10: Straight Lines

Students can revisit two-dimensional geometry from previous classes in this chapter. Shifting the origin, line slope, and angle, several forms of line equations, including those parallel to the axis, point-slope form, slope-intercept form, two-point form, intercept form, and normal form, are just a few of the topics covered in this chapter. The chapter covers the general equation, the equation of a family of lines passing through the point of the Intersection of two lines, the distance between two points, and other topics. Three exercises and spontaneous activities are included in this chapter to help students solve and practice questions related to the topic.

The following subjects were discussed:

Recalling some two-dimensional geometry from previous classes. Origins are shifts in two lines from two lines to form a line’s slope and angle. Different types of line equations: axis parallel, axis-parallel, axis-parallel, axis-parallel, axis-parallel, axis-parallel, axis parallel

 NCERT Class 11 Maths Solutions Chapter 10 Exercises Exercise 10.1 Exercise 10.2 Exercise 10.3 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 10 Straight Lines

#### NCERT Solutions for Class 11 Maths Chapter 11: Conic Sections

This chapter digs further into the subject of Conic SectioAs; a conic section is a curve created by the Intersection of a cone’s surface with a p in mathematics lane. The topics discussed are the circle, ellipse, parabola, hyperbola, point, straight line, and a pair of intersecting lines as a degenerate instance of a conic section. Standard equations and basic properties of the circle, parabola, ellipse, and hyperbola are also covered in this chapter. Students learn the above principles by completing this chapter’s four exercises and a miscellaneous activity.

The following subjects were discussed:

Conic sections include circles, ellipses, parabolas, hyperbolas, a point, a straight line, and a pair of intersecting lines as a degraded case—Parabola, ellipse, hyperbola standard equations, and basic characteristics A circle’s standard equation.

 NCERT Class 11 Maths Solutions Chapter 11 Exercises Exercise 11.1 Exercise 11.2 Exercise 11.3 Exercise 11.4 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 11 Conic Sections

#### NCERT Solutions for Class 11 Maths Chapter 12: Introduction to Three–Dimensional Geometry

For a point in space, there are three coordinates. This chapter will teach students in Class 11 the principles of three-dimensional geometry. This chapter delves into three-dimensional coordinate axes, coordinate planes, point coordinates, and the distance between two points. The section from this chapter includes three activities for students to overcome obstacles and better understand the concept. At the end of the chapter, there is a random exercise with additional questions covering all of the topics covered in the chapter.

The following subjects were discussed:

Axes and planes of coordinates in three dimensions. A point’s coordinates. Section formula and distance between two places

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

Also, access the following resources for Class 12 Maths Chapter 12 Introduction to Three-Dimensional Geometry

#### NCERT Solutions for Class 11 Maths Chapter 13: Limits and Derivatives

The first chapter in the Calculus series is Limits and Derivatives. Calculus is a branch of mathematics that investigates how a function’s value changes when the domain’s points change. This chapter provides students with an intuitive understanding of derivatives (without defining them). The chapter closes with some limit algebra and a fundamental idea of a limit. The chapter concludes with a review of the derivative and some derivative algebra. Two exercises and various exercises cover all of the topics in the chapter.

The following subjects were discussed:

As a distance function and geometrically, the derivative is introduced as a rate of change. The limitation is an intuitive concept: polynomial and rational function li and metric, exponential, and logarithmic functions. The scope of the curve’s tangent, a derivative of the sum, difference, product, and quotient of operations are all included in the definition of the derivative—polynomial and trigonometric derivatives.

 NCERT Class 11 Maths Solutions Chapter 13 Exercises Exercise 13.1 Exercise 13.2 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 13 Limits and Derivatives

#### NCERT Solutions for Class 11 Maths Chapter 14: Mathematical Reasoning

This chapter focuses on mathematics and introduces some basic notions in mathematical reasoning. Students should have learned inductive reasoning in the context of Mathematical Induction by this time. This chapter covers the fundamentals of deductive reasoning. This chapter covers mathematically admissible statements, connecting words/phrases, etc. It covers “if and only if (necessary and sufficient) condition,” “implies,” “and,” “implied by,” “and,” “our,” and “there exists,” validating assertions involving the connecting words, and more. To help students thoroughly grasp the concept of Mathematical Reasoning, the chapter offers five tasks and a miscellaneous activity.

The following subjects were discussed:

Mathematically sound statements. Connecting words/phrases – consolidating comprehension of “if and only if (necessary and sufficient) condition,” “implies,” “and,” “implied by,” “and,” “our,” “there exists,” and their applications through a variety of real-world and mathematical situations. They validate the statements that involve the linking, difference among contradiction, converse, and contrapositive.

 NCERT Class 11 Maths Solutions Chapter 14 Exercises Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4 Exercise 14.5 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 14 Mathematical Reasoning

#### NCERT Solutions for Class 11 Maths Chapter 15: Statistics

TerAs, as we all know, is concerned with collecting data for specific purposes. In this chapter, we’ll look at some of the most important dispersion metrics and how to compute them for ungrouped and grouped data. This chapter covers dispersion, range, mean deviation, variance, and standard deviation of ungrouped/grouped and landmines frequency distributions with identical means but different variances. Students can learn more about the topic by completing the three assignments and an additional exercise contained in the chapter.

The following subjects were discussed:

Range, mean deviation, variance, and standard deviation of ungrouped/grouped data are all measures of dispersion. Frequency distributions with equal means but different variances are analyzed.

 NCERT Class 11 Maths Solutions Chapter 15 Exercises Exercise 15.1 Exercise 15.2 Exercise 15.3 Miscellaneous Exercise

Also, access the following resources for Class 12 Maths Chapter 15 Statistics

#### NCERT Solutions for Class 11 Maths Chapter 16: Probability

In this chapter, probability is defined as a measure of uncertainty in various phenomena or the chances of an event occurring. This chapter covers random experiments, outcomes, sample spaces (set representation), and events, including ‘not,’ ‘and,’ and ‘or’ events, specific events, mutually exclusive events, axiomatic (set theoretic) probability, and linkages with other theories studied in preceding classes. The likelihood of an e and of ‘not,’ ‘and,’ and ‘or’ events are all covered in this chapter. To thoroughly grasp the concept of probability, students can complete the three exercises and the miscellaneous activity.

The following subjects were discussed:

Experiments at random; results, sample spaces (set representation). Events; their occurrence, ‘not,’ ‘and,’ and ‘or’ events, comprehensive, mutually exclusive, etc. Axiomatic (set-theoretic) probably and our classes’ ideas. Probability of an event, probability of ‘not,’ probability of ‘not,’ probability of ‘not,’ probability of ‘not’ ‘and’ and ‘or’ events.

 NCERT Class 11 Maths Solutions Chapter 16 Exercises Exercise 16.1 Exercise 16.2 Exercise 16.3 Miscellaneous Exercise

Because Infinity Learn is a learning organization, we understand the significance of study materials and how they influence academic performance. Each chapter of the NCERT Class 11 textbook has many concepts that may stress students. As a result, it’s critical to first master the tricks and techniques for remembering everything. NCERT Class 11 Books can be downloaded from this page. As a result, we developed Class 11 NCERT Solutions, a learning resource aimed at helping students study and achieve their objectives.

Also, access the following resources for Class 12 Maths Chapter 16 Probability

### Key Benefits of NCERT Solutions for Class 11 Maths of Infinity learn

1. Comprehensive Coverage: Infinity Learn’s NCERT Solutions for Class 11 Maths provide in-depth coverage of all chapters, ensuring a thorough understanding of concepts.
2. Step-by-Step Guidance: Clear and concise step-by-step solutions make complex problems easy to comprehend and solve.
3. Enhanced Learning: Our solutions foster logical thinking, problem-solving, and analytical skills, preparing students for exams and beyond.
4. Exam Confidence: Practicing with our solutions boosts confidence, helping students excel in their Class 11 Maths exams.
5. Interactive Platform: Enjoy an engaging online platform, making learning enjoyable and effective.
6. Accessible Anytime: Access solutions anytime, anywhere, ensuring flexibility in your learning journey.
7. Expert Guidance: Benefit from expertly curated content and guidance from experienced educators.
8. Extra Practice: Supplementary exercises and exemplar problems enrich your practice and understanding.
9. Scoring Edge: Gain an edge in competitive exams with thorough understanding of NCERT concepts.
10. Success Path: Start building a strong foundation for higher classes and future academic success.

## Frequently Asked Questions on NCERT Solutions for Class 11 Maths

### How often should I practice NCERT Solutions for Class 11 Maths?

Regular practice is essential. You can practice these solutions alongside your regular studies to reinforce your understanding of concepts. Consistent practice can improve your problem-solving skills and boost your confidence in math.

### Can I use NCERT Solutions for Class 11 Maths for competitive exams?

While NCERT Solutions provide a strong foundation, competitive exams might require additional preparation. However, practicing these solutions can help you build a solid understanding of concepts that might be useful in competitive exams as well.

### Do NCERT Solutions for Class 11 Maths cover the entire syllabus?

Yes, NCERT Solutions cover the entire syllabus outlined in the NCERT Class 11 Maths textbook. They provide solutions for all the exercises and problems given in the textbook, ensuring comprehensive coverage.

### How can NCERT Solutions for Class 11 Maths help me learn better?

NCERT Solutions provide clear explanations and solutions to each problem, helping you grasp the concepts in a structured manner. They offer step-by-step guidance, making it easier to understand and solve complex math problems.

### Can you list the key ideas covered in Chapter 11 of NCERT Solutions for Class 11 Maths?

Chapter 11 of NCERT Solutions Class 11 Maths PDF revolves around significant concepts like parts of a cone, which covers topics such as parabola, ellipse, circle, degenerate conic sections, and hyperbola. Additionally, it delves into crucial subjects like the interplay between semi-minor axis, semi-major axis, the distance of the focus from the center of the ellipse, and standard equations of parabola and ellipse. This chapter holds particular importance in Class 11 as it explores fundamental conic section concepts that will continue to be relevant in higher classes.

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