NCERT Solutions for Class 11 Maths

NCERT Solutions for Class 11 Maths – Download Chapter wise PDF

Our subject specialists compiled the NCERT Solutions for Class 11 Maths available on this page. The solutions have primarily been designed to simplify the Class 11 Math problems found in the textbooks required by the CBSE syllabus (2021-2022). These NCERT Class 11 Math Solutions are structured methodically and cover all 16 chapters of the syllabus. As a result, the NCERT Class 11 Maths Solutions provide complete learning while also assisting students in developing stronger arithmetic skills as well as logical and reasoning abilities. To make learning easier, the challenging problems have been simplified and explained in these answers.

NCERT Maths Solutions is a must-have resource for students studying for the Class 11 Maths test. NCERT Solutions for Class 11 may help you clarify all of your concerns by providing resources such as example answered problems, shortcut techniques, summary, notes, and so on.

The questions in most competitive engineering examinations or common entrance tests for admittance to engineering colleges are created in accordance with textbook syllabuses. As a result, students are urged to practise these NCERT Class 11 Maths Solution exercises worksheets on a regular basis in order to achieve higher grades in exams. Students are also encouraged to tackle the sample problems and answers that are available on our website. These Class 11 Maths Solutions give clear instructions and a comprehensive learning experience. Students can review chapter-by-chapter solutions in the table below.

Class 11 Maths NCERT Solutions - Free PDF Download

Here you may access and download NCERT Class 11 sample problems per chapter.

Students who are experiencing difficulty answering NCERT Class 11 Maths questions can refer to the solutions provided below for greater advice and a fast refresher.

Term I NCERT Solutions for Class 11 Maths Chapter 1 Sets

This chapter explores the notion of Sets and how they are represented. Empty set, Finite and Infinite sets, Equal sets, Subsets, Power set, and Universal set are among the topics covered in this chapter. The chapter also teaches students how to make Venn diagrams and introduces them to the concepts of set union and set intersection. This chapter also discusses the difference between sets and the complement of a set, as well as its features. In the chapter, there are six exercises and one miscellaneous activity, giving students with a sufficient number of problems to solve and, as a result, comprehend the idea.

Chapter 1 of Class 11 Maths Topics Sets for the First Semester:

Sets and their graphical representations The set is empty. Sets can be finite or infinite. Sets of equals Subsets. Subsets of a real number set, particularly intervals (with notations). Set the power. Set with universal applications. Venn diagrams Set union and intersection

Class 11 Maths NCERT Solutions Chapter 2 Relations & Functions – Term I

Students were taught the concepts of ordered pairs, Cartesian product of sets, the number of elements in the cartesian product of two finite sets, relation definition, graphical diagrams, domain, co-domain, and range of a relation in this chapter. Along with the concept of relationships, students will also study about functions. Functions include topics such as 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 graphs. Students will learn to connect two sets of things and then introduce relationships between the two objects in the pair. They will then learn about exceptional relations that qualify to be functions. The chapter contains three exercises as well as a random exercise that address the themes indicated above.

Chapter 2 of Class 11 Maths Topics First Term Relationships and Functions:

Pairs that are ordered. Set Cartesian product The number of items included in the Cartesian product of two finite sets. Cartesian product of the real set and itself ( R x R only). A relation's definition, graphical diagrams, domain, co-domain, and range Function is a form of relationship. A function's domain, co-domain, and range are all represented graphically. Real valued functions, their domain and range, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic, and largest integer functions, with graphs.

Chapter 3 Trigonometric Functions – Term II NCERT Solutions for Class 11 Maths

The chapter explains positive and negative angles, how to measure angles in radians and degrees, and how to convert from one measure to another. The chapter also covers the definition of trigonometric functions using the unit circle, the general solution of trigonometric equations, the signs, domain, and range of trigonometric functions, and their graphs. The chapter teaches students how to describe sin (xy) and cos (xy) in terms of sinx, siny, cosx, and cosy, as well as their easy applications and identities for sin 2x, cos 2x, tan 2x, sin 3x, cos 3x, and tan 3x. The problems in the chapter's four exercises, as well as a miscellaneous exercise, cover all of the concepts stated above.

Class 11 Mathematical Topics 3rd Chapter Second Term Trigonometric Functions:

Positive and negative perspectives. Angle measurement in radians and degrees, as well as conversion from one measure to another The unit circle is used to define trigonometric functions. For any x, the identity sin2x + cos2x = 1. Trigonometric function signs The domain and range of trigonometric functions, as well as their graphs Sin (xy) and cos (xy) expressed as sinx, siny, cosx, and cosy, with easy applications. Developing identities such as the following:

tan(x±y)=tanx±tany1∓tanxtany,cot(x±y)=cotxcoty∓1cotx±cotytan(x\pm y)=\frac{tanx\pm tany}{1\mptanxtany},cot(x\pm y)=\frac{cotxcoty\mp 1}{cotx\pm coty}tan(x±y)=1∓tanxtanytanx±tany​,cot(x±y)=cotx±cotycotxcoty∓1​

sinα±sinβ=2sin12(α±β)cos12(α∓β)sin\alpha \pm sin\beta =2sin\frac{1}{2}(\alpha \pm \beta )cos\frac{1}{2}(\alpha \mp \beta )sinα±sinβ=2sin21​(α±β)cos21​(α∓β)

cosα+cosβ=2cos12(α+β)cos12(α–β)cos\alpha + cos\beta =2cos\frac{1}{2}(\alpha + \beta )cos\frac{1}{2}(\alpha – \beta )cosα+cosβ=2cos21​(α+β)cos21​(α–β)

cosα–cosβ=−2sin12(α+β)sin12(α–β)cos\alpha – cos\beta =-2sin\frac{1}{2}(\alpha + \beta )sin\frac{1}{2}(\alpha – \beta )cosα–cosβ=−2sin21​(α+β)sin21​(α–β)

Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and tan3x.

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

The Principle of Mathematical Induction chapter covers a variety of subjects, including the procedure of demonstrating the induction and encouraging the application by considering natural numbers as the least inductive subset of real numbers. The chapter's exercise covers problems relating to the Principle of Mathematical Induction as well as its elementary applications.

Complex Numbers and Quadratic Equations – Term I NCERT Solutions for Class 11 Maths

The chapter goes into great length regarding the necessity for complex numbers, particularly 1, which is driven by the inability to solve some quadratic equations. Students can also learn about the algebraic characteristics of complex numbers, the argand plane, and the polar representation of complex numbers in this chapter. The chapter also covers the statement of the fundamental theorem of algebra, solutions of quadratic equations (with real coefficients) in the complex number system, and the square root of a complex number. This chapter has three exercises and one random exercise that cover these themes.

Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations for the First Term:

Inability to solve some quadratic equations motivates the need for complex numbers, particularly 1. Complex number algebraic characteristics The Argand plane. Algebraic statement, solution of quadratic equations (with real coefficients) in the complex number system

Chapter 6 Linear Inequalities - Term II NCERT Solutions for Class 11 Maths

The title of the chapter Linear Inequalities implies that it deals with the notion of Linear Inequalities. This chapter also covers the concepts of algebraic solutions of linear inequalities in one variable and their representation on the number line, graphical representation of linear inequalities in two variables, and the graphical method of solving a system of linear inequalities in two variables. This chapter has three exercises and one miscellaneous exercise that cover all of the subjects taught in the chapter.

Chapter 6 of Class 11 Maths Topics Second Term Linear Inequalities:

Inequalities that are linear. Linear inequalities in one variable with algebraic solutions and number line representation Linear inequalities in two variables are graphically solved. A graphical approach for solving a system of linear inequalities in two variables.

A permutation is an arrangement of a number of things in a certain order taken one at a time, whereas a combination is a collection of elements in which the order is irrelevant. The chapter covers the fundamental notion of counting, factorial n. (n! ), permutations, combinations, formula derivation and linkages, and basic applications. There are four exercises and one miscellaneous exercise with questions covering all of the subjects covered in the chapter.

Class 11 Maths Chapter 7 Permutations and Combinations for the Second Term:

Counting's fundamental premise. (n!) Factorial n. Permutations and combinations, nPr and nCr formulas, and simple applications

Exercise

Chapter 8 Binomial Theorem NCERT Solutions for Class 11 Math

Students learn about the Binomial Theorem for positive integers in this chapter. This theorem can be utilised to perform complicated computations that would otherwise be impossible to solve using repeated multiplication. The history, definition, and demonstration of the Binomial Theorem for positive integral indices are covered in this chapter. This chapter discusses in depth Pascal's triangle, general and intermediate terms in the binomial expansion, and their basic applications. The chapter includes two exercises as well as a miscellaneous exercise to assist students practise issues with the Binomial Theorem.

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

A sequence is a numerically ordered list. A series is the sum of all the terms in a sequence. The following concepts are covered in this chapter: Sequence and Series, Arithmetic Progression (A. P.), Arithmetic Mean (A.M.), Geometric 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, formulas for specific series sums, and more In the chapter, there are four exercises and one miscellaneous activity that assist students comprehend the topics presented by answering the questions.

Class 11 Maths Chapter 9 Sequences and Series for the First Term: Sequence and Series Progression in Arithmetic (A. P.). The Arithmetic Mean (A.M.) Geometric Progression (G.P. ), general term of a G.P., sum of n G.P. terms, infinite G.P. and its sum, geometric mean (G.M. ), relationship between A.M. and G.M.

Straight Lines - Term I NCERT Solutions for Class 11 Maths

The chapter assists students in recalling two-dimensional geometry from previous classes. The chapter discusses issues such as shifting the origin, the slope of a line and the angle between two lines, several forms of equations of a line including those parallel to the axis, point-slope form, slope-intercept form, two-point form, intercept form, and normal form. The chapter also discusses the general equation of a line, the equation of the family of lines passing through the point of intersection of two lines, the distance of a point from a line, and other topics. The chapter includes three exercises and one miscellaneous activity to assist students in solving and practising chapter-related questions.

Chapter 10 of Class 11 Maths Topics First Term Straight Lines:

Recalling two-dimensional geometry from previous classes. Line slope and angle between two lines

There are several types of line equations: parallel to the axis, point-slope form, slope-intercept form, two-point form, intercept form, and normal form. A line's general equation. The distance between two points on a line.

Chapter 11 Conic Sections - Term II NCERT Solutions for Class 11 Maths

This chapter delves further into the notion of Conic Sections. A conic section is a curve formed by the intersection of the surface of a cone with a plane in mathematics. The sections of a cone discussed include the circle, ellipse, parabola, hyperbola, a point, a straight line, and a pair of intersecting lines as a degenerate instance of a conic section. The chapter also includes standard equations and basic characteristics of the circle, parabola, ellipse, and hyperbola. This chapter contains four exercises and one miscellaneous activity, through which students study the aforementioned subjects.

Chapter 11 Topics Covered in Class 11 Math Second Term Conic Sections:

Cone sections include circles, ellipses, parabolas, and hyperbolas. Standard equations and basic parabola, ellipse, and hyperbola characteristics A circle's standard equation.

Chapter 12 Introduction to Three-dimensional Geometry – Term II NCERT Solutions for Class 11 Maths

There are three coordinates for a point in space. Students in Class 11 will master the fundamentals of geometry in three dimensions in this chapter. The chapter delves deeply into the concepts of three-dimensional coordinate axes and planes, coordinates of a point, distance between two points, and section formula. The chapter includes three activities to assist students better solve and comprehend the idea. A random exercise is also included at the end of the chapter, which comprises extra questions covering all of the themes covered in the chapter.

Class 11 Maths Chapter 12 Topics Covered Second Term Introduction to Three-dimensional Geometry:

In three dimensions, coordinate axes and planes. A point's coordinates. Section formula and distance between two places

Limits and Derivatives NCERT Solutions for Class 11 Math

Derivatives – Term II and Limits – Term I

Limits and Derivatives is a chapter that introduces Calculus. Calculus is a field of mathematics that studies how the value of a function changes when the points in its domain change. Initially, students get an intuitive understanding of derivatives in this chapter (without actually defining it). Later in the course, the chapter presents a simple definition of a limit as well as some limit algebra. Finally, the chapter returns to a discussion of derivatives and some derivative algebra. There are two exercises and one miscellaneous exercise that cover all of the chapter's subjects.

Class 11 Maths Chapter 13 Limits for First Term:

Intuitive concept of limit. Polynomial and rational function bounds functions trigonometric, exponential and logarithmic.

Chapter 13 of Class 11 Maths Topics Second-Term Derivatives:

The derivative was presented as a rate of change in both the distance function and geometrically. Derivative definition, tangent of the curve, derivative of sum, difference, product, and quotient of functions Polynomial and trigonometric function derivatives.

NCERT Solutions for Class 11 Mathematical Reasoning, Chapter 14

This chapter explores several fundamental concepts of Mathematical Reasoning, particularly in the context of Mathematics. Students should have learned inductive thinking in the framework of Mathematical Induction by now. Some principles of deductive reasoning are taught in this chapter. The chapter covers topics such as mathematically acceptable statements, connecting words/phrases – consolidating understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists", validating statements involving the connecting words, and more. The chapter includes 5 exercises and a miscellaneous activity to assist students in properly learning the idea of Mathematical Reasoning.

Class 11 NCERT Solutions for Maths Chapter 15 Statistics - Term I

Statistics, as we all know, deals with data collected for certain goals. In this chapter, we will learn about some of the most significant measures of dispersion and how to calculate them for ungrouped and grouped data. Measures of dispersion, range, mean deviation, variance, and standard deviation of ungrouped/grouped data, as well as analysis of frequency distributions with identical means but distinct variances, are among the topics covered in this chapter. Students can learn more about the topic by completing the three tasks and an additional exercise in the chapter.

Class 11 Maths Chapter 15 Statistics Topics for First Term:

Dispersion measures include range, mean deviation, variance, and standard deviation for ungrouped and grouped data.

Class 11 Maths NCERT Solutions Chapter 16 Probability - Term II

The chapter covers the notion of probability as a measure of uncertainty in diverse phenomena, or simply, the likelihood of an event occurring. Students will learn about random experiments, outcomes, sample spaces (set representation), and events, as well as the occurrence of events, 'not,' 'and,' and 'or' events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, and connections with other theories studied in previous classes. The chapter also discusses the likelihood of an occurrence, as well as the probability of 'not,' 'and,' and 'or' events. Students can answer the three tasks as well as the miscellaneous exercise to fully grasp the idea of probability.

Class 11 Maths Chapter 16 Probability for the Second Term:

Random experiments, results, and sample spaces (set representation). Events; event occurrence, 'not,' 'and,' and 'or' events, comprehensive events, mutually exclusive events The likelihood of an occurrence, as well as the probability of 'not', 'and', and 'or' events.

ALGEBRIANS assists students in discovering better approaches to solve math problems by utilising their logical talents. Using these NCERT Solutions will help you improve your Math proficiency and achieve higher success. Students can use these study materials as a reference and effectively prepare for tests. Finally, by answering NCERT Maths sample papers, students will be able to perform well in the examinations since they will have a better understanding of the different sorts of questions offered, as well as their difficulty level and marking system.

The Advantages of Maths NCERT Solutions Class 11

·         ALGEBRIANS NCERT Solutions provide several advantages to students.

·         To begin, students can learn NCERT or CBSE-based Class 11 Math in the comfort of their own home. They may do it from home using their PCs and tablets if they have internet access, or they can download and utilise our free app.

·         Students may personalise their learning experience by studying each topic at their own speed without regard for time limits.

·         ALGEBRIANS also has the top subject specialists that can help students study the subject and its principles in a pleasant and plain manner.

CBSE Class 11 Maths Weightage by Unit for First Term

Internal Assessment Class 11 Term I

CBSE Class 11 Maths Unit wise weightage for Second Term

Internal Assessment Class 11 Term II

Students can also come in any questions they have about other courses, such as physics, chemistry, and biology. ALGEBRIANS, on the other hand, maintains track of all the progress that students make. Periodic assessments give feedback and counselling. ALGEBRIANS provides CBSE exam preparation tips and tactics, as well as Class 11 Maths revision notes and class-wise NCERT example question papers, to assist students prepare for board examinations, state-level exams, entrance tests, and other competitive exams. Students may learn Math and other topics by using our solutions at any time and from any location. If students have any difficulties while using the NCERT Class 11 Maths book or solutions, they can always contact the ALGEBRIANS support staff for assistance.

Frequently Asked Questions on NCERT Solutions for Class 11 Maths

How will ALGEBRIANS NCERT Solutions for Class 11 Maths help us achieve high test results?

ALGEBRIANS subject matter experts developed the NCERT Solutions in conformity with the CBSE board's syllabus. The important explanation is offered for major aspects to make understanding ideas easy for pupils. Both chapter-by-chapter and exercise-by-exercise solutions are intended to assist pupils in acing the exam without anxiety. The solutions primarily assist students in improving their problem-solving abilities, which are essential for the test.

Name the key ideas covered in Chapter 11 of the NCERT Solutions for Class 11 Maths.

Parts of a cone, which explains parabola, ellipse, circle, degenerate conic sections, and hyperbola, is covered in Chapter 11 of NCERT Solutions for Class 11 Maths. Other essential subjects include the connection between the semi-minor and semi-major axes, the distance of focus from the centre of the ellipse, and typical parabola and ellipse equations. This is a crucial chapter in Class 11 since it explores fundamental topics of conic sections that will be studied in higher courses.

What are the primary subjects covered in NCERT Solutions for Class 11 Maths relations and functions?

This chapter exposes students to the many types of relationships and their features. One of the key ideas discussed here is the Cartesian product of sets and its relations. To make learning easy for pupils, the real-life model of cartesian products is given in simple words. This chapter assists students in establishing a solid foundation of fundamental ideas that are critical for test success.

What will I learn in NCERT Solutions for Class 11 Maths Chapter 4 Mathematical Induction?

Mathematical induction is a strategy for determining if a given assertion is correct or incorrect. The crucial thing to remember is that the theorem should be true for every given natural number. By studying this chapter, students will be familiar with the following points.

1.       The basic goal is to prove a proposition or provide an illustration.

2.       The proof should hold true for all natural number values.

3.       The assertion should be true for the original value.

4.       The assertion should be true for values up to the nth iteration.

5.       Every stage of the proof must be genuine and justified.