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NCERT Solutions for Class 11 Maths 2024-25

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Last updated date: 19th Jul 2024
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NCERT Solutions for Class 11 Maths Chapter-Wise PDF Free Download

NCERT Solutions for Class 11 Maths created by Vedantu’s experts help you understand your textbook problems better. These solutions cover all the chapters in your CBSE syllabus for the 2024-25 academic year. They are organized neatly and explained step by step to make learning easier.

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Table of Content
1. NCERT Solutions for Class 11 Maths Chapter-Wise PDF Free Download
2. NCERT Solutions for Class 11 Maths
3. Class 11 Maths NCERT Solutions Chapter at a Glance
4. NCERT Solutions for Class 11 Maths Chapter Details, Formulas and Exercises PDF
    4.1Chapter 1 - Sets
    4.2Chapter 2 - Relations and Functions
    4.3Chapter 3 - Trigonometric Functions
    4.4Chapter 4 - Complex Numbers and Quadratic Equations
    4.5Chapter 5 - Linear Inequalities
    4.6Chapter 6 - Permutations and Combinations
    4.7Chapter 7 - Binomial Theorem
    4.8Chapter 8 - Sequences and Series
    4.9Chapter 9 - Straight Lines
    4.10Chapter 10 - Conic Sections
    4.11Chapter 11 - Introduction to Three Dimensional Geometry
    4.12Chapter 12 - Limits and Derivatives
    4.13Chapter 13 - Statistics
    4.14Chapter 14 - Probability
5. CBSE Class 11 Maths Weightage 2024-25
6. CBSE Class 11 Maths Exam Pattern for 2024-25
7. How NCERT Helps in Exam Preparation?
8. Key Benefits of NCERT Solutions Class 11 Maths
9. Vedantu Gives You Competitive Edge
10. Important Related Links for CBSE Class 11 Maths
FAQs


Using these solutions can enhance your math skills, including logic and reasoning. They simplify tough problems, making them easier to grasp. Whether you are preparing for exams or just want to strengthen your understanding of math concepts, these solutions are invaluable.


In competitive exams for engineering schools,  and common entrance tests questions often come from these textbooks. So, practicing with these solutions regularly can improve your scores. You can also find extra practice problems and solutions online. Use the table below to access solutions for each chapter, and make the most of your learning experience.


NCERT Solutions for Class 11 Maths

NCERT Solutions for Class 11 Maths have been provided for all the chapters. Download free PDFs of these chapter-wise NCERT solutions from the links below.



Note: The chapters on Principle of Mathematical Induction and Mathematical Reasoning have been excluded from the Class 10 Maths textbook for the 2024-25 academic year


Also check for: What are the important topics covered in the NCERT Solutions Class 11 Maths?


NCERT Solutions for Class 11 Maths - Chapter 1 to 16 with Exercises images


Class 11 Maths NCERT Solutions Chapter at a Glance

  • NCERT Solutions for Class 11 Maths for all the chapters and exercises from Chapters 1 to 14 are provided.

  • The article also provides details about the exam pattern, marks weightage, and question paper design for CBSE Class 10 Maths.

  • The chapters include topics like:

  • Sets and Functions: Introduces the concept of sets, functions, and relations.

  • Algebra: Covers topics like complex numbers, quadratic equations, and sequences and series.

  • Coordinate Geometry: Focuses on understanding the Cartesian plane, straight lines, and conic sections.

  • Calculus: Explores the fundamentals of differentiation and integration.

  • Statistics and Probability: Introduces statistical measures and probability theory.

  • It also provides resources such as class notes, important questions and formulas, exemplar solutions, RD Sharma and RS Aggarwal solutions for further reference.

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NCERT Solutions for Class 11 Maths Chapter Details, Formulas and Exercises PDF

Chapter 1 - Sets

A set is defined as the characterised accumulation of the various items. Sets are an integral part of modern-day Mathematics. The concepts in this chapter include different types of sets, various set operations and Venn diagrams. The concepts of relations and functions are characterised by using sets. Learning of sets also aids in the understanding of the concepts of sequences, probability, geometry and more. 


  1. Exercise 1.1 Introduces you to the fundamental concepts of sets, including their formation and basic operations like union, intersection, and difference.

  2. Exercise 1.2 Learn about roster form (listing the elements directly within curly braces), set-builder form (using a description to define the elements), and Venn diagrams (illustrating sets visually using circles).

  3. Exercise 1.3 Explores relationships between sets, concepts like subset, proper subset, equal sets, and disjoint sets, and how to determine these relationships between two sets.

  4. Exercise 1.4 This exercise ventures into more advanced set theory concepts. You'll be introduced to universal sets, complements of sets (elements that belong to the universal set but not the original set), and De Morgan's Laws, which are crucial properties that govern the relationships between complements of sets.


Topics Covered in Class 11 Maths Chapter 1 Sets

  • A set is called a well-defined collection of objects.

  • Representation of Sets:


We can represent a set in two methods:


  • Roster form: In the roster form, we list all the objects of the set within curly brackets { } and separate by commas.

  • Set-builder form: In this form, all the elements of the set should have a single property to be the member of that set.

  • Types of Sets

  • Empty Sets: A set which will not have any element is called an empty set. This is also called the void set or null set, and it is denoted by {} or Φ.

  • Singleton Set: This is a set consisting of a single element.

  • Finite and infinite Set: If a set consists of a finite number of elements, then it is called a finite set, if nor the set will be an infinite set.

  • Equal Sets: Set A and Set B are said to be equal, only if all elements of A are also the elements of B i.e. two equal sets will have exactly the same element.

  • Equivalent Sets: Two finite sets are said to be equal if the number of elements are equal.

  • Every set will be a subset of itself.

  • The empty set will always be a subset of every set.

  • If a finite set contains n elements, then the total number of subsets is 2n.

  • Power Set: The power set is a set which has all of the subsets, and also the empty set & the original set. It's commonly denoted with the letter P.

  • Universal Set: The universal set is a set that contains all sets in a specific context.

  • Venn diagrams: Venn diagrams are diagrams that show the relationship between two sets.


Chapter 1 - Sets Exercises in PDF Format

Class 11 Maths Chapter 1 Exercise 1.1 - 6 Questions & Solutions

Class 11 Maths Chapter 1 Exercise 1.2 - 6 Questions & Solutions

Class 11 Maths Chapter 1 Exercise 1.3 - 9 Questions & Solutions

Class 11 Maths Chapter 1 Exercise 1.4 - 12 Questions & Solutions

Class 11 Maths Chapter 1 Exercise 1.5 - 7 Questions & Solutions

Class 11 Maths Chapter 1 Exercise 1.6 - 8 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 1 of CBSE Class 11 Maths Solutions



Chapter 2 - Relations and Functions

An upgrade on Sets, Relations and Functions explores the idea of linking pairs of objects from two different sets and then deriving relations between the said objects of the pair. Certain relations qualify as functions, a crucial concept in Mathematics for its capturing of the idea of two quantities corresponding with each other and the correspondence is mathematically precise.


  1. Exercise 2.1 deals with identifying whether a relation is a function or not. The key concept to remember here is that a function assigns a unique output (range element) to every input (domain element). You'll be given a relation and asked to determine if it follows this rule.

  2. Exercise 2.2 is about depicting a function using an arrow diagram. Arrow diagrams provide a visual representation of the connection between elements in a function's domain and range. Arrows point from the domain elements to their corresponding range elements.

  3. Exercise 2.3 practices representing a function as a set of ordered pairs. Ordered pairs define the function by listing the input (domain element) and the corresponding output (range element) together. Each ordered pair shows the relationship between an input and its unique output.


Topics Covered in Class 11 Maths Chapter 2 Relations and Functions

  • Ordered Pair: An ordered pair is formed by two objects or elements that are arranged in a specific order.

  • Equality of Two Ordered Pairs: If a = c and b = d, two ordered pairs (a, b) and (c, d) are equal.

  • Cartesian Product of Two Sets: The set of all ordered pairs (a, b) where a ∈ A and b ∈ B exist for any two non-empty sets A and B is termed the cartesian product of sets A and B and is denoted by A × B.

  • Relations: A relation R which is from a non-empty set A to a non-empty set B will be a subset of the cartesian product set A × B. The subset can be derived by describing a relationship between the first element & the second element of the ordered pairs in A × B.

  • Functions: A relation R from the sets A to B will be a function, if every element of set A has one and only image in set B. In simple words, a function f can be a relation if no two pairs in the relation has the first element.

  • Types of Functions

  • One One Function

  • Many One Function

  • Onto Function

  • One One and Onto Function

  • Into Function

  • Constant Function

  • Identity Function

 

Chapter 2 - Relations and Functions Exercises in PDF Format

Class 11 Maths Chapter 2 Exercise 2.1 - 10 Questions & Solutions

Class 11 Maths Chapter 2 Exercise 2.2 - 9 Questions & Solutions

Class 11 Maths Chapter 2 Exercise 2.3 - 5 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 2 of CBSE Class 11 Maths Solutions


 

Chapter 3 - Trigonometric Functions

This chapter generalises the concepts of trigonometric ratios to trigonometric functions, along with the study of their properties. Students get to explore the dynamic world of trigonometry as they attempt and solve the various numerical problems provided in this chapter.


  1. Exercise 3.1 focuses on understanding degrees and radians as units to measure angles. It involves converting between these units and solving problems related to angles and their corresponding measures.

  2. Exercise 3.2 explores the relationship between angles and arc lengths in a circle. You'll likely solve problems finding the angle measure based on a given arc length or vice versa.

  3. Exercise 3.3 dives into the concept of finding the values of trigonometric functions (sine, cosine, tangent) for a given angle. You might be provided with the angle in degrees or radians and asked to determine the trigonometric function's value.

  4. Exercise 3.4 introduces you to some basic trigonometric identities. You might encounter problems that require using these identities to simplify expressions or solve equations involving trigonometric functions.


Topics Covered in Class 11 Maths Chapter 3 Trigonometric Functions:

  • Introduction to Trigonometric Functions

  • Angles and Their Measurements

  • Trigonometric Ratios

  • Trigonometric Functions

  • Trigonometric Identities

  • Heights and Distances


Chapter 3 - Trigonometric Functions Exercises in PDF Format

Class 11 Maths Chapter 3 Exercise 3.1 - 7 Questions & Solutions

Class 11 Maths Chapter 3 Exercise 3.2 - 10 Questions & Solutions

Class 11 Maths Chapter 3 Exercise 3.3 - 25 Questions & Solutions

Class 11 Maths Chapter 3 Exercise 3.4 - 9 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 3 of CBSE Class 11 Maths Solutions–



Chapter 4 - Complex Numbers and Quadratic Equations

This chapter introduces students to the concept of complex numbers and their relation to quadratic equations. It explores the properties of complex numbers, including algebraic operations and graphical representation. Additionally, it covers the solutions of quadratic equations involving complex roots, along with the fundamental theorem of algebra. 


  1. Exercise 4.1 focuses on basic operations and properties of complex numbers. This might involve simplifying expressions, finding conjugates, and performing arithmetic operations like addition, subtraction, multiplication, and division.

  2. Exercise 4.2 delve into concepts like modulus and argument of complex numbers. You might find problems calculating distances, angles, or converting complex numbers to polar forms.

  3. Exercise 4.3 explores applications of complex numbers in solving quadratic equations. This involves finding complex roots of quadratic equations and understanding their relationship with the discriminant.


Topics Covered in Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations:


  • Introduction to Complex Numbers

  • Algebra of Complex Numbers

  • Quadratic Equations in One Variable

  • Solutions of Quadratic Equations

  • Graphical Representation of Complex Numbers


Chapter 4 - Complex Numbers and Quadratic Equations Exercises in PDF Format

Class 11 Maths Chapter 4 Exercise 4.1 - 14 Questions & Solutions

Class 11 Maths Chapter 4 Exercise 4.2 - 8 Questions & Solutions

Class 11 Maths Chapter 4 Exercise 4.3 - 10 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 4 of CBSE Class 11 Maths Solutions



Chapter 5 - Linear Inequalities

Chapter 5 delves into the concept of linear inequalities, a fundamental topic in algebra. Linear inequalities are expressions involving linear functions that express a relationship between two variables, stating that one is less than, greater than, or equal to the other. These inequalities are widely used to represent constraints or conditions in various real-life situations. 


  1. Exercise 5.1 focuses on recognizing how inequalities are represented. It helps you understand how mathematical expressions translate into comparisons on a number line (greater than, less than, etc.).

  2. Exercise 5.2 you will practice solving linear inequalities algebraically. This involves isolating the variable and manipulating the inequality to find the values of the variable that satisfy the given condition.

  3. Exercise 5.3 introduces you to solving linear inequalities graphically. You'll learn how to represent inequalities on a number line and identify the solution set based on the graphical representation.


Topics Covered in Class 11 Maths Chapter 5 Linear Inequalities:


  • Introduction to Inequalities

  • Algebraic Solutions of Inequalities

  • Graphical Solutions of Linear Inequalities in One Variable

  • Graphical Solutions of Linear Inequalities in Two Variables


Chapter 5 - Linear Inequalities Exercises in PDF Format

Class 11 Maths Chapter 5 Exercise 5.1 - 26 Questions & Solutions

Class 11 Maths Chapter 5 Exercise 5.2 - 10 Questions & Solutions

Class 11 Maths Chapter 5 Exercise 5.3 - 15 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 5 of CBSE Class 11 Maths Solutions



Chapter 6 - Permutations and Combinations

Chapter 6, "Permutations and Combinations," introduces students to advanced mathematical concepts with applications in various fields. This chapter consists of 4 exercises with 31 questions covering permutations and combinations. It includes fundamental principles of counting, basic arrangements and selections, permutations under certain conditions, division of objects, permutations of alike objects, distribution of alike objects, circular permutations, selection of objects, number of divisors, sum of divisors, and rearrangements.


  1. Exercise 6.1 deals with finding the number of ways to arrange distinct objects in a row. This is a fundamental concept of permutations.

  2. Exercise 6.2 introduces selection of objects. You'll need to find the number of ways to choose a specific number of objects from a larger collection. This is related to combinations.

  3. Exercise 6.3 applies the concept of combinations to selecting a group of members from a set of people.

  4. Exercise 6.4 introduces a constraint into arrangements. You'll need to find the number of arrangements considering two objects that must always be together. This requires applying permutation formulas with some modifications.


Topics Covered in Class 11 Maths Chapter 6 Permutations and Combinations:


  • Fundamental Principle of Counting

  • Factorial Notation

  • Permutations

  • Linear Arrangement

  • Circular Arrangement

  • Permutations when Objects are Repeated

  • Combinations

  • Selections of Objects

  • Combinations with Repetition

  • Mathematical Induction


Chapter 6 - Permutations and Combinations Exercises in PDF Format

Class 11 Maths Chapter 6 Exercise 6.1 - 6 Questions & Solutions

Class 11 Maths Chapter 6 Exercise 6.2 - 5 Questions & Solutions

Class 11 Maths Chapter 6 Exercise 6.3 - 11 Questions & Solutions

Class 11 Maths Chapter 6 Exercise 6.4 - 9 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 6 of CBSE Class 11 Maths Solutions



Chapter 7 - Binomial Theorem

Persian Mathematician Omar Khayyam, in the 11th century, provided the general formula for (a + b)n, where n is a positive whole number. This equation or its expansion has been provided in this chapter Binomial hypothesis. Chapter 7 of Class 11 Maths NCERT Solutions is “Binomial Theorem”. 


  1. Exercise 7.1 focuses on using the Binomial Theorem to expand expressions raised to a power. You'll probably apply the formula and simplify the terms.

  2. Exercise 7.2 concentrates on the properties of the expansion based on the Binomial Theorem. This might involve finding the number of terms, analysing the powers of 'a' and 'b' in each term, or understanding the relationship between their exponents.


Topics Covered in Class 11 Maths Chapter 7 Binomial Theorem:


  • Binomial Theorem for Positive Integral Indices

  • Binomial Coefficients

  • General and Middle Term in Binomial Expansion

  • Properties of Binomial Coefficients

  • Binomial Theorem for any Index

  • Applications of Binomial Theorem


Chapter 7 - Binomial Theorem Exercises in PDF Format

Class 11 Maths Chapter 7 Exercise 7.1 - 14 Questions & Solutions

Class 11 Maths Chapter 7 Exercise 7.2 - 2 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 7 of CBSE Class 11 Maths Solutions:



Chapter 8 - Sequences and Series

Chapter 8, "Sequence and Series," covers topics like Geometric Progression, Arithmetic Progression, General Term of a G.P, and Sum to n terms of a G.P. This chapter is important in exams, so practice all exercises. It starts with definitions of sequence, series, and progression, then covers arithmetic and geometric progressions, means, sigma notations, and special sequences. Formulas need to be memorized for easy problem-solving in Class 11 Maths.


  1. Exercise 8.1 asks you to write the first 15 terms of an Arithmetic Progression (AP) given the first few terms. An Arithmetic Progression is a sequence of numbers where the difference between consecutive terms (common difference) is constant.

  2. Exercise 8.2 involves finding the sum of the first 10 terms of an Arithmetic Progression. You're given the formula for the nth term of the AP and likely need to use the concept of arithmetic series summation to solve it.

  3. Exercise 8.3, for the given values of the second term and the eleventh term of an Arithmetic Progression. Based on this information, you're expected to find the general formula for the nth term of the AP.

  4. Exercise 8.4 is about finding the common difference of an Arithmetic Progression. You're given a formula for the sum of n terms in the AP and likely need to use concepts related to arithmetic series and possibly solve for the common difference.


Topics Covered in Class 11 Maths Chapter 8 Sequences and Series:


  • Introduction to Sequences

  • Arithmetic Progression (AP)

    • Definition and properties

    • General term of an AP

    • Sum of first n terms of an AP

    • Arithmetic Mean (AM) and Geometric Mean (GM)

  • Geometric Progression (GP)

    • Definition and properties

    • General term of a GP

    • Sum of first n terms of a GP

    • Infinite Geometric Series

  • Relation between Arithmetic Mean, Geometric Mean, and Harmonic Mean

  • Special Series


Chapter 8 - Sequences and Series Exercises in PDF Format

Class 11 Maths Chapter 8 Exercise 8.1 - 14 Questions & Solutions

Class 11 Maths Chapter 8 Exercise 8.2 - 8 Questions & Solutions

Class 11 Maths Chapter 8 Exercise 8.3 - 32 Questions & Solutions

Class 11 Maths Chapter 8 Exercise 8.4 - 10 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 8 of CBSE Class 11 Maths Solutions–



Chapter 9 - Straight Lines

In Chapter 9, you will learn about topics like Slope of a line, angle between two lines, Collinearity, and more. Practice all three exercises. It covers the distance formula, section formula, centroid, incentre, excentre, area of triangle, and equation of a straight line. It also includes concepts like position of a point relative to a line, angle between two lines, parallel and perpendicular lines, and bisectors of angles between lines.


  1. Exercise 9.1 likely focuses on finding the equation of a line under various conditions. It might ask you to find the equation when given: Slope and y-intercept (point-slope form), Two points on the line (two-point form) and Slope and a point on the line (point-slope form again)

  2. Exercise 9.2 deals with properties of lines related to their slopes. It could involve questions about: Parallel lines (equal slopes), Perpendicular lines (slopes are negative reciprocals of each other) and Angle between lines using slopes

  3. Exercise 9.3 is about applications of straight lines or explore some additional concepts. It could involve: Distance formula to find the distance between two points. Finding the equation of the line passing through the midpoint of two other lines


Topics Covered in Class 11 Maths Chapter 9 Straight Lines:


  • Introduction

  • Slope of a Line

  • Various Forms of the Equation of a Line

    • Slope-intercept form, Point-slope form, Two-point form, Intercept form, Normal form, General form

  • General Equation of a Line

  • Distance of a Point from a Line

  • Foot of a Perpendicular

  • Equation of Family of Lines Passing through the Point of Intersection of Two Lines

  • Miscellaneous Examples


Chapter 9 - Straight Lines Exercises in PDF Format

Class 11 Maths Chapter 9 Exercise 9.1 - 14 Questions & Solutions

Class 11 Maths Chapter 9 Exercise 9.2 - 20 Questions & Solutions

Class 11 Maths Chapter 9 Exercise 9.3 - 18 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 10 of CBSE Class 11 Maths Solutions–



Chapter 10 - Conic Sections

Chapter 10 of Class 11 Maths NCERT Solutions covers conics, including circles, ovals, parabolas, and hyperbolas. It delves into their significance and applications on the x, y, and z axes. Topics include the definition and properties of conic sections, distinguishing various conics, terminology of parabolas, ellipses, and hyperbolas, parametric representations, positions of points relative to these curves, tangents, normals, and more.


  1. Exercise 10.1 focuses on deriving the standard equation of a parabola when given its focus (F1, 0) and the directrix, which is a line represented by the equation y = -d.

  2. Exercise 10.2 deals with formulating the standard equation of an ellipse. The exercise provides you with one focus (F1, 0) and the eccentricity (e) of the ellipse.

  3. Exercise 10.3 similar to exercise 10.2, this one involves deriving the standard equation of a hyperbola. Here, you're given one focus (F1, 0) and the eccentricity (e) of the hyperbola.

  4. Exercise 10.4 introduces the concept of the director circle associated with a parabola. The task is to find the equation of the director circle for a given parabola, represented by the equation y2 = 4ax.


Topics Covered in Class 11 Maths Chapter 10 Conic Sections:


  • Circle: The set of all points in a plane that are at a fixed length from a fixed point in a plane is called a circle. The circle's fixed point is known as the centre, and the distance between the centre and any point on the circle is known as the radius.

  • Parabola: A parabola is a set of points P whose distances from a fixed point F in the plane are equal to their distances from a fixed line l in the plane. The fixed point F is known as the focus, and the fixed line l is known as the parabola's directrix.

  • Ellipse: It is a set of points in a plane whose distances from two fixed points add up to a constant sum.

  • Hyperbola: A hyperbola is a two-branched open curve formed by the intersection of a plane and both halves of a double cone. The plane does not have to be parallel to the cone's axis. The fixed point is known as the focus, the fixed line is known as the directrix, and the constant ratio, indicated by, is known as the eccentricity of the hyperbola.


Chapter 10 - Conic Sections Exercises in PDF Format

Class 11 Maths Chapter 10 Exercise 10.1 - 15 Questions & Solutions

Class 11 Maths Chapter 10 Exercise 10.2 - 12 Questions & Solutions

Class 11 Maths Chapter 10 Exercise 10.3 - 20 Questions & Solutions

Class 11 Maths Chapter 10 Exercise 10.4 - 15 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 10 of CBSE Class 11 Maths Solutions:



Chapter 11 - Introduction to Three Dimensional Geometry

Conic sections pave the way for 3D geometry as we learn about the applications of the conical segments here as well.  Coordinate geometry has been extensively dealt with in this chapter, and students also get to practise from the three exercises. This chapter talks about coordinate axes, coordinate planes, coordinates of a point in space, distance between two points, and section formula.


  1. Exercise 11.1 Distinguishes between scalars and vectors. Scalars are quantities that only have magnitude (size or amount), like distance, mass, or temperature. Vectors, on the other hand, possess both magnitude and direction. Examples of vectors include displacement, force, velocity, and acceleration.

  2. Exercise 11.2 Performs operations on vectors. This exercise deals with adding and subtracting vectors using graphical methods like the parallelogram law and the tail-to-head method.

  3. Exercise 11.3 helps in Understanding and applying direction cosines of vectors. Direction cosines are the cosines of the angles that a vector makes with the positive x, y, and z axes in a three-dimensional space.


Topics Covered in Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry:


  • Coordinate system in 3D space

  • Distance between two points in 3D

  • Direction ratios and cosines

  • Equations of lines and planes in 3D

  • Angles between lines


Chapter 11 - Introduction to Three Dimensional Geometry Exercises in PDF Format

Class 11 Maths Chapter 11 Exercise 11.1 - 4 Questions & Solutions

Class 11 Maths Chapter 11 Exercise 11.2 - 5 Questions & Solutions

Class 11 Maths Chapter 11 Exercise 11.3 - 5 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 11 of CBSE Class 11 Maths Solutions


Chapter 12 - Limits and Derivatives

Calculus, a very important concept of Mathematics, associated with the study of change in the value of a function with the change of points in the domain is explained in this chapter. Students, through this chapter, are introduced to the vast world of calculus, which finds a host of applications across various fields. 


  1. Exercise 12.1 likely focuses on the concept of derivatives, which are fundamental tools in calculus for understanding how a function's output changes with respect to its input. It might involve finding the derivatives of simple algebraic expressions using the basic differentiation rules.

  2. Exercise 12.2 introduce the differentiation of exponential functions, specifically the derivative of the function e^x (where e is the mathematical constant approximately equal to 2.71828).


Topics Covered in Class 11 Maths Chapter 12 - Limits and Derivatives


  • Finding limits by direct substitution (when possible)

  • Techniques for finding limits of indeterminate forms

  • Finding one-sided limits (left-hand limit and right-hand limit)

  • Introduction to the concept of derivatives and their applications (rate of change)

  • Finding the derivative of a function using the first principle

  • Differentiation formulas for basic functions (like sin(x), cos(x), etc.)

  • Product rule and quotient rule for differentiation


Chapter 12 - Limits and Derivatives Exercises in PDF Format

Class 11 Maths Chapter 12 Exercise 12.1 - 32 Questions & Solutions

Class 11 Maths Chapter 12 Exercise 12.2 - 11 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 12 of CBSE Class 11 Maths Solutions:



Chapter 13 - Statistics

Statistics is an important part of higher mathematics, covering topics like range, mean deviation, measures of dispersion, standard deviation, and mean deviation for ungrouped data. This chapter introduces key terms such as statistics, class limit, class interval, primary and secondary data, variable, frequency, and types of frequency distributions. It also explains graphical representation methods like histograms, bar diagrams, pie charts, frequency polygons, and cumulative frequency curves.


  1. Exercise 13.1 revisits the idea of organizing data into a frequency table. It emphasizes how to group data points into classes (intervals) and record the frequency (number of occurrences) for each class.

  2. Exercise 13.2 builds on frequency tables by introducing histograms. It guides you through the process of constructing a histogram, which visually represents the distribution of data using bars. You'll learn how to divide data into classes, calculate the width of each class, and determine the frequency density (number of observations per unit width) for each class.

  3. Exercise 13.3 dives into cumulative frequency distribution. It explains how to calculate the cumulative frequency for each class. The cumulative frequency refers to the total number of observations less than or equal to a specific class. You'll also learn how to represent the cumulative frequency distribution graphically using a cumulative frequency curve.


Topics Covered in Class 11 Maths Chapter 13 - Statistics

  • Measures of Central Tendency: Mean (average), Median, Mode

  • Measures of Dispersion: Range, Quartile deviation, Variance, Standard deviation

  • Frequency Distribution

  • Additional Concepts (depending on your specific textbook):

  • Correlation: Studying the relationship between two variables

  • Regression analysis: Modelling the relationship between variables


Chapter 13 - Statistics Exercises in PDF Format

Class 11 Maths Chapter 13 Exercise 13.1 - 12 Questions & Solutions

Class 11 Maths Chapter 13 Exercise 13.2 - 10 Questions & Solutions

Class 11 Maths Chapter 13 Exercise 13.3 - 5 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 13 of CBSE Class 11 Maths Solutions



Chapter 14 - Probability

Probability is computing the level of the conviction of occasions under perfect conditions. A much-used concept in various spheres of life, students should make sure they understand the underlying core concerts and the applications in order to attempt a maximum number of questions from this chapter.


  1. Exercise 14.1 deals with theoretical probability. It presents problems involving one or more events and helps you solve them using the concept of probability itself. Theoretical probability refers to the likelihood of an event happening, calculated based on assumptions and without involving any experiments.

  2. Exercise 14.2 focuses on Conditional probability. It introduces you to scenarios where the probability of an event depends on another event that has already occurred. The problems challenge you to apply the concept of conditional probability to find solutions.

  3. Exercise 14.3 covers independent events. Independent events are those where the occurrence of one event doesn't affect the probability of the other event happening. You'll practice solving problems that involve determining whether events are independent, and then calculate probabilities based on that.


Topics Covered in Class 11 Maths Chapter 14 - Probability


  • Basic Concepts

  • Axiomatic Approach to Probability

  • Conditional Probability


Chapter 14 - Probability Exercises in PDF Format

Class 11 Maths Chapter 14 Exercise 14.1 - 16 Questions & Solutions

Class 11 Maths Chapter 14 Exercise 14.2 - 7 Questions & Solutions

Class 11 Maths Chapter 14 Exercise 14.3 - 21 Questions & Solutions


Along with this, students can also download additional study materials provided by Vedantu, for Chapter 14 of CBSE Class 11 Maths Solutions



CBSE Class 11 Maths Weightage 2024-25

Units

Unit Name

Marks

I

Sets and Functions

23

II

Algebra

25

III

Coordinate Geometry

12

IV

Calculus

08

V

Statistics & Probability

11


Total

80


CBSE Class 11 Maths Exam Pattern for 2024-25

The CBSE Class 11 Maths exam pattern for 2024-25 is likely to remain similar to previous years. Here's a breakdown of what to expect:


Type of Exam: Pen and paper based

Total Marks: 100 marks (divided into two parts)

  • Internal Assessment: 20 marks (conducted by the school)

  • External Exam: 80 marks (conducted by the CBSE board)

External Exam Paper Structure - The paper will be divided into three sections:


Section

Type of Questions

Marks

A

Objective-type (MCQ or one-word answers)

15 marks

B

Short answer type (2-3 marks each)

30 marks

C

Long answer type (4-6 marks each)

35 marks


  • Internal Choice: There will be internal choices within each section, allowing students to attempt the questions they are most comfortable with. (Typically, 33% internal choice)

  • Syllabus Coverage: The entire NCERT syllabus for Class 11 Maths will be covered in the exam. (Though there might be a slight reduction as per some sources)


Internal Assessment for CBSE Class 11


Internal Assessment

Marks

Periodic Tests (Best 2 out of 3 tests conducted)

10 Marks

Mathematics Activities

10 Marks

Total Marks

20 Marks


How NCERT Helps in Exam Preparation?

These solutions for class 11 Maths are systematic. Moreover, it helps in time management for the final exam. The step-by-step explanations will allow students to grasp the concept behind each topic. Since each chapter contains questions, students can practice the same for the exam. The ultimate aim is to score high in the exam.


Key Benefits of NCERT Solutions Class 11 Maths

  • Students can learn the NCERT solution class 11 Maths within their comfort zone. Once downloaded, they can prepare as per the timeline on desktop and mobile. Since it is available for free, students can further relax.

  • Students can customise their learning experience by completing each topic at their own pace.

  • Not just Maths, but students can opt for other subject solutions in PDF format and do the learning.

  • Students can understand all the concepts from the 14 chapters of Class 11 Maths easily, with the help of Vedantu’s Class 11 Maths NCERT Solutions. The solutions are designed in a simple, straightforward language and all the solutions are given step by step, for the ease of students.

  • The NCERT Solutions help students prepare for their Class 11 Maths exam quicker, as whenever they get stuck at any question, they can simply refer to the solutions, understand the answer and move to the next question.


All the chapters and their concepts are explained in detailed format, so students don't get confused. Since maths is a complex subject, students have the freedom to practice at their own pace and prepare for future exams.


You can also download the Class 11 Maths sample papers provided by Vedantu, as these papers can help them get an idea about the exam format. They can also learn to manage their time and identify their strong and weak areas and work on them accordingly.


Vedantu Gives You Competitive Edge

Vedantu’s NCERT Solutions for Class 11 Maths and other subjects’ experts familiarise the students with these topics so that the speed of learning is improved drastically. Thus, it helps in efficient time management skills for better results in the exams. You get to practise all the exercise questions and improve your mathematical skills. Register for our free webinar class with the best Mathematics tutor in India. Also, the Vedantu Learning App will benefit you by providing access to free live masterclasses and free conceptual videos. You will also have access to all the PDFs of study materials and solutions. Additionally, you will be provided absolutely FREE Online Tests. You will have all the required standard study materials handy and this will make the process of learning easier for you.


Important Related Links for CBSE Class 11 Maths

FAQs on NCERT Solutions for Class 11 Maths 2024-25

1. How Many Chapters are There in Class 11 Maths NCERT Textbook?

There are a total of 16 chapters in NCERT Class 11 Maths textbook. The chapters are Sets (Chapter 1), Relations and Functions (Chapter 2), Trigonometric Functions (Chapter 3), Principle of Mathematical Induction (Chapter 4), Complex Numbers and Quadratic Equations (Chapter 5), Linear Inequalities (Chapter 6), Permutations and Combinations (Chapter 7), Binomial Theorem (Chapter 8), Sequences and Series (Chapter 9), Straight Lines (Chapter 10), Conic Sections (Chapter 11), Introduction to Three Dimensional Geometry (Chapter 12), Limits and Derivatives (Chapter 13), Statistics (Chapter 15) and Probability (Chapter 16). You can find NCERT Solutions for Maths Class 11 on Vedantu’s website.

2. How Vedantu's NCERT Solutions for Class 11 Maths helps in scoring good marks?

The class 11 maths solution is framed by subject experts as per the CBSE guidelines. Each chapter comes with a proper explanation and all major points are covered to ensure the concept is understandable. The solution will help students in improving problem-solving skills.

3. Why Do Most of the Students Find Class 11 Maths CBSE Syllabus Difficult to Study?

Students often have difficulty in coping with the Class 11 Maths syllabus as they find it to be widely varying from what they had learned in Class 10. Students are also often overwhelmed with a vast range of new concepts that they are introduced to in the syllabus of Maths in Class 11 and often feel that they are not able to comprehend all the topics. Class 11 Maths NCERT textbook is thoughtfully designed to explain every concept in a simple manner. Hence, students need not panic in advance. If they have any doubts regarding any topic, they can register on Vedantu’s site and join LIVE Classes taken by experts.

4. Does the solution cover all chapters?

Yes, the NCERT Solutions for Class 11 Maths cover all 16 chapters. Each chapter comes with a solution and questionnaire according to the board.

5. Where Can I Get NCERT Solutions for Class 11 Maths in Free to Download PDF Format?

Vedantu provides the Class 11 NCERT Solutions for Maths in a PDF format. This PDF can be downloaded for absolutely no cost. The solutions in this PDF have been provided in a stepwise manner and this allows students to familiarise themselves with all the concepts included in the syllabus of Class 11 Maths. To download the PDF, students are simply required to log in to the official website. Moreover, the solutions have been prepared by subject experts and academicians. Hence, students can rely on them without any second thoughts. So grab your copy of the PDF today.

6. Which are the best books for preparing Class 11 Maths?

There are a lot of books available in the market that claim to be the best to prepare for the Class 11 Maths exam. This can be overwhelming for the students. However, the most important book that students need to focus on is the NCERT textbooks. These books cover the curriculum well. Most of the questions in the exam will be directly or indirectly from NCERT textbooks. In order to prepare well, you can use Vedantu's NCERT Solutions for Class 11 Maths.

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

Here are some important concepts in Chapter 11 of NCERT Solutions for Class 11 Maths; all of which you can find on Vedantu (vedantu.com):

  • Concept of Subset, Superset, and Power Set

  • Cartesian Product of Sets

  • Concept of Relations

  • Real-Valued Functions

  • Signs of Trigonometric Functions

  • Trigonometric Functions and Their Graphs

  • Trigonometric Identities and equations

  • Modulus and Conjugate of a Complex Number

  • Polar Representation of Complex Numbers

  • General and Middle Term of a Binomial Expansion

  • Concept of Permutations when All Objects are Distinct

  • Concept of Permutations when All Objects are Not Distinct

  • Concept of Combinations

  • Solving Linear Inequalities in One Variable

  • Solving a System of Linear Inequalities in Two Variables

  • Sum of n Terms of an Arithmetic Progression

  • Properties of Arithmetic Progressions and the Concept of Arithmetic Mean

  • nth term and Sum of n Terms of a Geometric Progression

  • Concept of Geometric Mean and Its Relation with Arithmetic Mean

  • Sum of n Terms of Special Series

  • Angle between Two Lines

  • Point-slope and Two-point Form of Straight Lines

  • Slope-Intercept Form of Straight Lines

  • Intercept Form of Straight Lines

  • Normal form of Straight Lines

  • Distance of a Point from a Line and Distance between Two Parallel Lines

  • Circle

  • Parabola

  • Ellipse

  • Hyperbola

  • Distance between Two Points in Three Dimensional Space

  • Section Formula

  • Limit of a Polynomial and a Rational Function

  • Limit of a Trigonometric Function

  • Derivative of a Function

  • Derivative of Trigonometric and Polynomial Functions

  • Negation of a Statement.

  • Implications.

  • Validity of “If-then” and “If and only if” Statements.

  • Validation of a Statement by Method of Contradiction and by Giving a Counterexample.

  • Mean Deviation for Continuous Frequency Distribution.

  • Variance and Standard Deviation of Continuous Frequency Distribution.

  • Coefficient of Variation.

  • Finding Probability Using Complement of a Known Event.

  • Algebra of Events and Mutually Exclusive and Exhaustive Events.

  • Probability of an Event.

8. What are the main topics covered in Relations and Functions of NCERT Solutions for Class 11 Maths?

Here are some main topics covered in Relations and Functions of Vedantu’s NCERT Solutions for Class 11 Maths:

  • Cartesian product of sets.

  • Cartesian product of the reals with itself (up to R × R × R).

  • Co-domain and range of a function.

  • Constant, identity, polynomial, rational, modulus, signum, and greatest integer

  • Definition of relation.

  • Domain, co-domain, and range of a relation.

  • Finite sets

  • Functions

  • Functions with their graphs.

  • Number of elements in the Cartesian product of two.

  • Ordered pairs

  • Pictorial diagrams

  • Pictorial representation of a function, domain,

  • The real-valued function of the real variable, 

  • Sum, difference, product, and quotients of functions.

9. How many exercises are there in Class 11 Maths?

There are 16 chapters in Class 11 NCERT Maths books and a total number of 53 exercises. You can find the solutions for all the exercises on Vedantu's website (vedantu.com). These solutions have been created by top subject matter experts. They have ensured that all the solutions are correct and the concepts are explained in an easy way. With these solutions in your hand, you will be able to finish your NCERT syllabus in no time and be prepared for the exam.

10. Is NCERT enough for Class 11 Maths?

Yes, NCERT textbooks are enough for your Class 11 Maths exam. NCERT textbooks are created by experts and contain all the concepts explained in detail and easy language. Also, most of the questions that will be in your exam will be directly or inspired by the NCERT textbooks. So, in order to prepare well for your Class 11 Maths exam, you have to finish the NCERT books. You can get the solutions for Class 11 Maths in PDF format on Vedantu’s website (vedantu.com) free of cost. You can download these from Vedantu mobile app as well.

11. What is the toughest maths chapter in class 11?

The toughest maths chapter in class 11 can vary depending on individual preferences and strengths, but some commonly perceived challenging chapters include Chapter 4 - Principle of Mathematical Induction, Chapter 10 - Straight Lines, and Chapter 13 - Limits and Derivatives.

12. Which chapter of class 11 maths is most important?

Every chapter in class 11 maths is important as they build the foundation for higher-level concepts. However, some chapters like Chapter 3 - Trigonometric Functions, Chapter 8 - Binomial Theorem, and Chapter 14 - Probability are frequently considered essential due to their application in various fields.

13. Is maths in class 11 tough?

Whether maths in class 11 is tough or not depends on an individual's aptitude, interest, and dedication. With proper understanding, practice, and guidance, maths in class 11 can be manageable.

14. Which is the easiest lesson in maths class 11?

Easiest lessons in maths class 11 can vary based on personal strengths and interests. However, chapters like Chapter 1 - Sets, Chapter 6 - Sequences and Series, and Chapter 7 - Permutations and Combinations are often perceived as relatively easier compared to others.

15. Which is the best channel to study class 11 maths?

Several YouTube channels Like Vedantu provide excellent resources for studying class 11 maths. Also at Vedantu you get completely solved class 11 maths ncert solutions.

16. How to pass class 11 math?

To pass class 11 math, you can follow these steps:

  • Understand the concepts thoroughly by attending classes regularly.

  • Practice regularly using NCERT textbooks and reference books.

  • Solve previous years' question papers and sample papers to understand exam patterns.

  • Seek help from teachers or tutors if you encounter difficulties.

  • Utilize online resources such as educational websites and YouTube tutorials for additional help.

  • Stay organized, manage your time effectively, and revise regularly before exams.