NCERT Solutions for Class 11 Maths

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NCERT Solutions for Class 11 Maths provided here has been put together by our subject experts. The solutions have been mainly crafted to simplify all Class 11 Math problems, which are given in the textbooks prescribed in the CBSE syllabus (2023-2024). These NCERT Solutions of Class 11 Maths is organized systematically and covers all 16 chapters included in the syllabus. Therefore, the NCERT Class 11 Maths Solutions offers comprehensive learning and also helps students to develop better math skills along with logical and reasoning skills. The difficult problems have been simplified and explained here in these solutions to make learning much more comfortable.

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NCERT Solutions of Maths is an essential resource for students preparing for the Class 11 Maths exam. NCERT Solutions for Class 11 can clear all your doubts with the help of materials like sample-solved questions, shortcut tips, summaries, notes, etc.

In most of the competitive engineering exams or common entrance tests conducted for admissions to Engineering institutes, the questions are designed as per the syllabus of textbooks. Therefore, the students are advised to practice these NCERT Solutions for Class 11 Maths exercises worksheets on a regular basis to score better marks in exams. Also, students are advised to solve the exemplar problems and solutions available with us online. The Class 11 Maths Solutions provides proper guidance and a thorough learning experience. The students can go through chapter-wise solutions from the table provided below.

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NCERT Solutions for Class 11 Maths Chapter 1 Sets

This chapter discusses the concept of Sets along with their representation. The topics included in the chapter are Empty set, Finite and Infinite sets, Equal sets, Subsets, Power set and Universal set. The chapter also helps students learn to draw Venn diagrams as well as to get familiar with the concepts of Union and Intersection of sets. The Difference of sets and Complement of a set, along with its properties are also covered in this chapter. There are 6 exercises along with a miscellaneous exercise in the chapter, providing a sufficient number of questions to the students to solve and in turn, understand the concept.

Topics Covered in Class 11 Maths Chapter 1 Sets:

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of the 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.

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NCERT Solutions for Class 11 Maths Chapter 2 Relations & Functions

In this chapter, students are taught about the concepts of Ordered pairs, Cartesian product of sets, the number of elements in the cartesian product of two finite sets, the definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Along with the topic of relation, students get to learn about the topic of functions as well. 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 are the topics that come under the concept of Functions. Students will learn to link pairs of objects from two sets and then introduce relations between the two objects in the pair. And then, they will learn about special relations which will qualify to be functions. There are 3 exercises along with a miscellaneous exercise present in the chapter which covers the topics mentioned above.

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Topics Covered in Class 11 Maths Chapter 2 Relations and Functions :

Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the reals with itself (upto R× R× R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. 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. Sum, difference, product and quotients of functions.

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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

The chapter discusses positive and negative angles, method of measuring angles in radians as well as in degrees and conversion from one measure to the other. The chapter also deals with the definition of Trigonometric Functions with the help of unit circle, general solution of trigonometric equations, signs, domain and range of Trigonometric Functions and their graphs. The chapter helps the students in learning the process of expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy along with their simple applications and deducing the identities, related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x. The problems in 4 exercises, along with a miscellaneous exercise, present in the chapter cover all the topics mentioned above.

Topics Covered in Class 11 Maths Chapter 3 Trigonometric Functions :

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of
the identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing
the identities like following:

tan(x±y)=tanx±tany1∓tanxtany,cot(x±y)=cotxcoty∓1cotx±coty

 

sinx±siny=2sin12(x±y)cos12(x∓y)

 

cosx+cosy=2cos12(x+y)cos12(x–y)

 

cosx–cosy=−2sin12(x+y)sin12(x–y)

Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x. General solution of trigonometric equations of the type sin θ = sin α, cos θ = cos α and tan θ = tan α. Proofs and simple applications of sine and cosine formulae.

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

The chapter, Principle of Mathematical Induction, covers a number of topics that includes the process of proving the induction and motivating the application by looking at natural numbers as the least inductive subset of real numbers. Problems related to the Principle of Mathematical Induction, along with its simple applications are covered in the exercise given in the chapter.

Class 11 Maths NCERT Solutions PDF Chapter 4 Exercises

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

The chapter discusses in detail, the need for complex numbers, especially √−1, to be motivated by the inability to solve some of the quadratic equations. The chapter also enables the students to learn about the algebraic properties of complex numbers, argand plane and polar representation of complex numbers. 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 are also among the topics discussed in the chapter. There are 3 exercises and a miscellaneous exercise in this chapter that covers these topics.

Topics Covered in Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations:

Need for complex numbers, especially √−1, to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane and polar
representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system.

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NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities

The chapter Linear Inequalities, as the name suggests, deals with the concept of Linear Inequalities. 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 as well as the graphical method of finding a solution of the system of Linear Inequalities in two variables are also covered in this chapter. A total of 3 exercises and a miscellaneous exercise is present in this chapter.

Topics Covered in Class 11 Maths Chapter 6 Linear Inequalities :

Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of system of linear inequalities in two variables – graphically.

Class 11 Maths NCERT Solutions PDF Chapter 6 Exercises

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NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations

A permutation is an arrangement of a number of objects in a definite order taken at a time whereas Combination is a collection of the objects where the order doesn’t matter. The chapter discusses everything about the Fundamental principle of counting, factorial n. (n!), permutations, combinations, derivation of formulae and their connections along with simple applications. A total of 4 exercises and a miscellaneous exercise that includes questions covering all the topics present in the chapter.

Topics Covered in Class 11 Maths Chapter 7 Permutations and Combinations :

Fundamental principle of counting. Factorial n. Permutations and combinations, derivation of formulae and their connections, simple applications.

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NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem

In this chapter, students study about Binomial Theorem for positive integers. This theorem can be used to solve complex calculations that are difficult to solve using repeated multiplication. The chapter discusses the history, statement and proof of the Binomial Theorem for positive integral indices. Pascal’s triangle, general and middle term in the binomial expansion and their simple applications are some topics that are explained, in detail, in this chapter. Two exercises, along with a miscellaneous exercise, are present in the chapter to help students practise problems related to Binomial Theorem.

Topics Covered in Class 11 Maths Chapter 8 Binomial Theorem:

History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, general and middle term in binomial expansion, simple applications.

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NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series

A sequence is an ordered list of numbers. The sum of all the terms of a sequence is a series. The chapter discusses the following topics which include Sequence and Series, Arithmetic Progression (A. P.), Arithmetic Mean (A.M.), Geometric Progression (G.P.), general term of a G.P., the sum of first n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), the relation between A.M. and G.M, formulae for the special series sums, and more. There are 4 exercises and a miscellaneous exercise present in the chapter that help the students in understanding the concepts given in the chapter.

Topics Covered in Class 11 Maths Chapter 9 Sequences and Series :

Sequence and Series. Arithmetic progression (A. P.), Arithmetic Mean (A.M.). Geometric progression
(G.P.), general term of a G. P., sum of n terms of a G.P., geometric mean (G.M.), relation between A.M. and G.M. Sum to n terms of the special series: ∑ n, ∑ n2 and ∑ n3.

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NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines

The chapter helps students recall two-dimensional geometry from earlier classes. Shifting of origin, the slope of a line and angle between two lines, various forms of equations of a line including the ones parallel to the axis, point-slope form, slope-intercept form, two-point form, intercept form, and normal form are some of the topics that are being discussed in the chapter. Other concepts that the chapter covers are the general equation of a line, equation of the family of lines passing through the point of intersection of two lines, the distance of a point from a line and more. There are 3 exercises and a miscellaneous exercise provided in the chapter to help the students solve and practise questions related to the chapter.

Topics Covered in Class 11 Maths Chapter 10 Straight Lines:

Brief recall of 2D from earlier classes. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept form, two-point form, intercepts form and normal form. General equation of a line. Distance of a point from a line.

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NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections

This chapter discusses the concept of Conic Sections in detail. In Maths, a conic section is a curve obtained as the intersection of the surface of a cone with a plane. The topics covered include the sections of a cone, namely, circle, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerate case of a conic section. Standard equations and simple properties of circle, parabola, ellipse and hyperbola are also present in the chapter. There are 4 exercises in the 11 Maths NCERT Solutions PDF and a miscellaneous exercise in this chapter, solving which helps the students learn the topics mentioned above.

Topics Covered in Class 11 Maths Chapter 11 Conic Sections:

Sections of a cone: Circles, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

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

A point in space has three coordinates. In this chapter, students of Class 11 shall learn the basic concepts of geometry in three-dimensional space. The chapter discusses the concept of coordinate axes and coordinate planes in three dimensions, coordinates of a point, distance between two points and section formula, in detail. There are 3 exercises in the chapter to help students solve and understand the concept in a better way. A miscellaneous exercise is also present at the end of the chapter that contains additional questions which cover all the topics in the chapter.

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

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

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NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives

The chapter, Limits and Derivatives, provides an introduction to Calculus. Calculus is a branch of Maths dealing with the study of change in the value of a function as the points in the domain change. In this chapter, initially, students gain an intuitive idea of derivative (without actually defining it). Later, the chapter provides a simple definition of a limit and some algebra of limits. Finally, the chapter returns to a description of derivative and some algebra of derivatives. There are 2 exercises and a miscellaneous exercise that covers all the topics in the chapter.

Topics Covered in Class 11 Maths Chapter 13 Limits and Derivatives:

Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

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NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning

This chapter in the NCERT Solutions discusses some basic ideas of Mathematical Reasoning, especially in the context of Mathematics. Students, by now, must have already learnt inductive reasoning in the context of Mathematical Induction. In this chapter, some fundamentals of deductive reasoning are covered. The topics present in the chapter include mathematically acceptable statements, connecting words/ phrases – consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists”, validating the statements involving the connecting words, and more. 5 exercises and a miscellaneous exercise are present in the chapter to help the students in understanding the concept of Mathematical Reasoning thoroughly.

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NCERT Solutions for Class 11 Maths Chapter 15 Statistics

We know that statistics deals with data collected for specific purposes. In this chapter, we shall learn some of the important measures of dispersion and their methods of calculation for ungrouped and grouped data. The topics that students learn in the chapter include measures of dispersion, range, mean deviation, variance and standard deviation of ungrouped/grouped data and analysis of frequency distributions with equal means but different variances. Students can learn more about the chapter by solving the problems given in 3 exercises along with an additional exercise in the chapter.

Topics Covered in Class 11 Maths Chapter 15 Statistics :

Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.

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NCERT Solutions for Class 11 Maths Chapter 16 Probability

The chapter discusses the concept of probability as a measure of uncertainty of various phenomena or simply, chances of occurrence of an event. In this chapter, students will learn the concepts such as random experiments; outcomes, sample spaces (set representation) and Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories studied in earlier classes. Probability of an event, the probability of ‘not’, ‘and’ and ‘or’ events are also covered in the chapter. To understand the concept of probability properly, students can solve the 3 exercises along with the miscellaneous exercise.

Topics Covered in Class 11 Maths Chapter 16 Probability :

Random experiments: Outcomes, sample spaces (set representation). Events: Occurrence of events,
‘not’, ‘and’ & ‘or’ events, exhaustive events, mutually exclusive events. Axiomatic (set theoretic) probability, connections with the theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ & ‘or’ events.

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CBSE Class 11 Maths 2023-24 Unit wise weightage

No.UnitsMarks

ISets and Functions23

IIAlgebra25

IIICoordinate Geometry12

IVCalculus08

VStatistics and Probability12

Total80

Internal Assessment20

Internal Assessment Class 11

Internal AssessmentMarks

Periodic Tests (Best 2 out of 3 tests conducted)10 Marks

Mathematics Activities10 Marks

Total Marks20 Marks

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Frequently Asked Questions on NCERT Solutions for Class 11 Maths

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

Chapter 11 of NCERT Solutions PDF Class 11 Maths deals with concepts like parts of a cone which explains about parabola, ellipse, circle, degenerate conic sections and hyperbola. Other important topics like the relationship between semi-minor axis, semi-major axis, the distance of focus from the centre of the ellipse, standard equations of parabola and ellipse. This is one of the important chapters in Class 11 as it discusses the important concepts of conic sections which would be continued in higher classes as well.

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What are the main topics covered in relations and functions of NCERT Solutions for Class 11 Maths?

This chapter introduces students to relations and their characteristics. The Cartesian product of sets and its relations are one of the important concepts explained here. The real-life model of cartesian products is explained in an understandable language to make it easier for students while studying. This chapter helps students to build a strong foundation of basic concepts which are important from the exam point of view.

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

Mathematical Induction is a technique which is used to prove whether a given statement is right or wrong. The important fact is that the theorem should be true for every given natural number. Students will be familiar with the following points by studying this chapter.
1. Proving a statement or illustration is the main motive.
2. The proof should be true for all the values of natural numbers.
3. For initial value, the statement should be true.
4. For values till nth iteration, the statement should be true.
5. All the steps in the proof should be true and justified.