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CBSE Class 11 Mathematics Chapter 2 Relations and Functions – NCERT Solutions 2025-26

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Download Free PDF of Relations and Functions Exercise 2.3 Solutions for Class 11 Maths

As you prepare for Class 11 Mathematics, mastering “Relations and Functions” from Chapter 2 becomes essential for building strong conceptual skills. This chapter’s Exercise 2.3 is especially important, offering deeper insight into the nature of functions, domain, and range through well-designed NCERT problems. Because “Sets and Functions” carries a significant 23-mark weightage in the CBSE exam, gaining full command of this exercise can directly strengthen your board results.


If you’ve searched for “class 11 maths ch 2 ex 2.3 solutions,” you’re likely looking for stepwise solutions that explain functions in mathematics and resolve confusion about domain and co-domain. On this page, every solution is broken down using clear logic and CBSE-approved steps, making concepts like mapping, one-one, and onto functions easier to understand.


Vedantu’s academic experts have crafted these explanations to match the latest board guidelines, ensuring you get reliable support for both school exams and fundamentals for higher topics. For more unit details, you may also refer to the Class 11 Maths syllabus as prescribed by CBSE.

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Access NCERT Solutions for Class 11 Maths Chapter 2 – Relations and Functions

NCERT Solutions for Chapter 2 Class 11 Exercise 2.3 Maths - What it covers

The best way to prepare for the examination is probably to look at the CBSE NCERT Solutions and practice accordingly. Let's have a look at the syllabus of Class 11 Maths for the Central Board of Secondary Education and how much the study materials are able to cover. The NCERT Solutions for Class 11 Maths Chapter 2 Exercise 2.3 should be looked up in this regard.

  •  The syllabus of the Class 11 Maths consists of 16 Chapters, where the first Chapter is Sets. In this chapter, you will get an     introduction to Sets. You will know about finite or infinite sets, null sets, subsets of the sets, disjoint sets and many other calculations related to set. The Class 11 Maths NCERT Solutions Chapter 2 Exercise 2.3 should be your guide in this regard.

  •  NCERT Solutions for Class 11 Maths Chapter 2 is Relations and Functions, the topics and subtopics are Cartesian Products of Sets, Relations, Functions, Some functions and their graphs, Algebra of real functions. Exercise 2.3 Class 11 maths will help you to clear your doubts. You can find Class 11 maths Chapter 2 Exercise 2.3 in the NCERT Solutions for Class 11 Maths. The Class 11 Maths Exercise 2.3 solution will help you revise core concepts in a really quick time indeed.

Other Chapters in Class 11 Maths

  • Chapter no 3 is Trigonometric Functions where the topics and subtopics are Angles, Degree measure, Radian measure, Relation between radian and real numbers, Relations between degree and radian, Trigonometric Functions, Sign of trigonometric functions, Domain and range of trigonometric functions, Trigonometric Functions of Sum and Difference of Two Angles, Trigonometric Equations.

  • The 4th Chapter Principle of Mathematical Induction will let you know how to solve equations with the help of mathematical induction. The topics are Introduction, Motivation, Illustration and The Principle of Mathematical Induction.

  • The fifth Chapter Complex Numbers and Quadratic Equations comes with topics like Complex Numbers, Algebra of Complex Numbers, Addition of two complex numbers, Difference of two complex numbers, Multiplication of two complex numbers, Division of two complex numbers, Power of i, The square root of a negative real number, Identities, The Modulus and the Conjugate of a Complex Number, Argand Plane and Polar Representation, Polar representation of a complex number, Quadratic Equations. 

  • Linear Inequalities comes with topics and subtopics like Inequalities, Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation, Graphical Solution of Linear Inequalities in Two Variables, Solution of System of Linear Inequalities in Two Variables in the sixth Chapter.

  • The topics and subtopics in the seventh Chapter Permutation and Combination are Fundamental Principle of Counting, Permutations, Permutations when all the objects are distinct, Factorial notation, Derivation of the formula, Permutations when all the objects are not distinct objects, Combinations.

  • Eight Chapter Binomial Theorem has the topics like Binomial Theorem for Positive Integral Indices, Binomial theorem for any positive integer n, Some special cases, General and Middle Terms.

  • The 9th Chapter Sequences and Series is the Chapter where you get to know about the topics like Sequences, Series, Arithmetic Progression(A.P), Arithmetic mean, Geometric Progression (G.P), General term of a G.P, Sum to n terms of a G.P, Geometric Mean, Relationship Between A.M and G.M, Sum to n Terms of Special Series.

  • Straight Line is the Chapter no 10 where the topics and subtopics are Slope of a Line, the Slope of a line when coordinates of any two points on the line are given, Conditions for parallelism and perpendicularity of lines in terms of their slopes, Angle between two lines, Collinearity of three points, Various Forms of the Equation of a Line, Horizontal and vertical lines, Point-slope form, Two-point form, Slope-intercept form, Intercept - form, Normal form, General Equation of a Line, Different forms of Ax + By + C = 0, Distance of a Point From a Line, Distance between two parallel lines.

  • Conic Sections is the 11 the Chapter where the topics and subtopics are Sections of a Cone, Circle, ellipse, parabola, and hyperbola, Degenerated conic sections, Circle, Parabola, Standard equations of parabola, Latus rectum, Ellipse, Relationship between semi-major axis, semi-minor axis and the distance of the focus from the center of the ellipse, Special cases of an ellipse, Eccentricity, Standard equations of an ellipse, Latus rectum, Hyperbola, Eccentricity, Standard equation of Hyperbola, Latus rectum.

  • The topics and subtopics in Chapter 12 Introduction to Three Dimensional Geometry are Coordinate Axes and Coordinate Planes in Three Dimensional Space, Coordinates of a Point in Space, Distance between Two Points, Section Formula.

  • Limits and Derivatives is the Chapter no. 13 where you will learn about topics and subtopics like Intuitive Idea of Derivatives, Limits, Algebra of limits, Limits of polynomials and rational functions, Limits of Trigonometric Functions, Derivatives, Algebra of derivative of functions, Derivative of polynomials and trigonometric functions.

  • Chapter no 14 is Mathematical Reasoning and the topics are Statements, New Statements from Old, Negation of a statement, Compound statements, Special Words/Phrases, The word "And", The word "Or", Quantifiers, Implications, Contrapositive and Converse, Validating Statements, By Contradiction.

  • The topics and subtopics in chapter 15, like Measures of Dispersion, Range, Mean Deviation, Mean deviation for ungrouped data, Mean deviation for grouped data, Limitations of mean deviation, Variance, and Standard Deviation, Standard Deviation, Standard deviation of a discrete frequency distribution, Standard deviation of a continuous frequency distribution, Shortcut method to find variance and standard deviation, Analysis of Frequency Distributions, Comparison of two frequency distributions with the same mean are there in the fifteenth Chapter Statistics.

  • To solve the problems of Chapter no. 16 Probability, you will have to know about topics and subtopics like Random Experiments, Outcomes And Sample Spaces Events, Occurrences of Events, Types of Events, Mutually Exclusive Events, Axiomatic Approach to Probability, Probability of an event, Probabilities of equally likely outcomes, Probability of event or B', Probability of event 'not A'.

NCERT Solutions for Class 11 Maths Chapter 2 PDF and others 

From the website of Vedantu, you will be able to download all the latest series of study materials as per the syllabus. You will just have to register on the website of Vedantu and you will get step by step links of the syllabus for free PDFs downloads which you can access from anywhere and anytime. Not only many students but teachers are also using the study materials which Vedantu offers. You will get the standard study materials for all subjects which will help you stay updated and it also teaches you shortcut techniques to solve problems. The Class 11 maths NCERT solutions ex 2.3 will be invaluable in this regard. You should download the NCERT maths Class 11 Exercise 2.3 solutions right away. The NCERT Class 11 Maths Exercise 2.3 solution will prove really useful indeed.

NCERT Solution Class 11 Maths of Chapter 1 All Exercises

Exercise

Number of Questions

Exercise 2.1

10 Questions & Solutions

Exercise 2.2

9 Questions & Solutions

Miscellaneous Exercise

12 Questions & Solutions


CBSE Class 11 Maths Chapter 2 Other Study Materials


NCERT Class 11 Maths Solutions Chapter-wise Links - Download the FREE PDF


Important Related Links for CBSE Class 11 Maths


Exam Preparation Tips For CBSE Class 11 Maths

Mathematics is the subject for which you will have to practice always to be an expert. The more you practice the more you become confident. Use a little diary to note down every important formulas and theory in short. Get proper sleep at night to wake up early in the morning and start your studies. Eat healthy foods and drink plenty of water. Don't try to clear your doubts in the last minute preparation, if you have any doubts then clear it earlier from Vedantu with reference from Exercise 2.3 Class 11 maths NCERT solutions.

Vedantu – Your Digital Study-Mate

At Vedantu, we believe in offering our readers the convenience to read at their leisure. It ensures that their study schedule isn’t an imposition, instead, it is an enjoyable time, what with the availability of the study material across the online platform. In this endeavor, our expert teachers support us to the fullest with their proficiency. Our study materials are crafted, taking into account your understanding of the subject. With step by step answers providing an in-depth knowledge of the exercises, we uphold the quality of solutions in our free to download study materials.

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FAQs on CBSE Class 11 Mathematics Chapter 2 Relations and Functions – NCERT Solutions 2025-26

1. How do stepwise NCERT solutions help clarify the concept of functions in Class 11 Maths Chapter 2?

Stepwise NCERT solutions guide you through each problem by breaking down the process into logical steps. This approach reinforces the concept of functions by showing:

  • How to identify the domain and range accurately
  • The method of checking whether a given relation is a function
  • Best practices for correct mapping and notation, as required by the CBSE 2025-26 pattern
This structure helps prevent confusion and strengthens your ability to solve similar questions in exams.

2. What is the correct method to determine if a given mapping is a function in Class 11 Maths NCERT Solutions Chapter 2?

To determine if a mapping is a function:

  • List all elements in the domain.
  • Check that each element is paired with exactly one element in the co-domain.
  • If any domain element is mapped to more than one value, it is not a function.
Following these steps aligns with the methodology outlined in NCERT Solutions for Class 11 Maths Chapter 2.

3. Why is it important to consistently state the domain and range in your NCERT solutions for relations and functions?

Stating the domain and range in solutions ensures your answers address all CBSE marking criteria.

  • It clearly identifies allowed inputs and possible outputs.
  • Full marks are often awarded only when both are correct and well presented.
  • It helps avoid common mistakes related to mismatched pairs in functions.
By always noting these, you align your answers with board expectations for full scoring.

4. How can you use step-by-step NCERT Solutions to master high-weightage exercises like 2.3 in Relations and Functions?

Using step-by-step NCERT Solutions lets you:

  • Follow the correct process for each type of question as per CBSE norms
  • Understand reasoning for each step, especially with new terms like mapping and function
  • Quickly clear conceptual doubts by comparing your method with the provided solution
  • Revise and reinforce important formulas before exams
This method boosts speed and accuracy, crucial for scoring well in chapter-wise assessments.

5. What is a common misconception students face while identifying functions in Class 11 Maths Chapter 2?

A common misconception is thinking a relation is a function even if a domain element maps to multiple range elements. In NCERT Solutions for Relations and Functions, only relations where each domain element is mapped to exactly one range element qualify as functions. Careful mapping and regular practice of solved examples help avoid such errors.

6. How does the CBSE syllabus structure for Class 11 Maths support mastering relations and functions through NCERT Solutions?

The CBSE syllabus for 2025-26 introduces foundational topics like sets and mapping before advancing to relations and functions. By following NCERT Solutions in sequence:

  • You build stepwise understanding from basic to complex problems
  • Learn standardized solution techniques adopted in board exams
  • Connect theory to application, as all examples are syllabus-aligned
This progression ensures syllabus coverage and clear conceptual growth.

7. What steps should you take if your answer in Exercise 2.3 solutions does not match the NCERT key?

If your solution differs from the NCERT answer key:

  • Re-examine your steps, especially mapping and set definitions
  • Check calculations of domain and range
  • Review definitions for relations and functions
  • Consult stepwise NCERT Solutions for logical errors
This process hones your accuracy and strengthens your maths problem-solving skills as per the latest NCERT methodologies.

8. How do NCERT Solutions for Class 11 Maths Chapter 2 benefit last-minute exam revision?

They provide summarized, stepwise methods and highlight key points such as function identification, domain, and range. This format:

  • Makes revision quick and effective
  • Ensures exposure to all question types covered in board exams
  • Helps clarify any remaining doubts before the exam
Reviewing solutions just before exams maximizes retention and confidence.

9. In what ways do graphical representations in NCERT Solutions help understand functions better?

Graphical representations like mapping diagrams visually show how each element in the domain connects to the range. This helps you:

  • Quickly identify whether a relation meets the function criteria
  • Spot errors in mapping with ease
  • Develop deeper conceptual clarity for function-based questions
NCERT Solutions often incorporate such diagrams to enhance comprehension.

10. What strategies from NCERT Solutions can improve your ability to answer application-based function problems in board exams?

Following NCERT-suggested strategies such as showing all working steps, justifying function or relation status, and using proper notation helps in answering application-based problems.

  • Break down problems and highlight reasoning at each step
  • Always state assumptions, domains, and conclusions clearly
  • Use solved examples to understand format and logical flow expected by CBSE
This systematic approach is essential for high scores in Class 11 Maths Chapter 2.