Relations and Functions Chapter 2 Class 11 Maths Online Practice Worksheet

Relations and Functions Class 11 Mathematics — Complete Worksheet Practice Guide

This DigiSadhan Class 11 Mathematics Chapter 2 practice tool is designed for systematic revision of Relations and Functions. It focuses on the mathematical ideas normally needed when students study ordered pairs, Cartesian products, relations, domain and range, functions, types of functions, algebraic operations on functions, composition and graphical interpretation. Use this interactive resource alongside your prescribed NCERT textbook, teacher's notes and classroom exercises. The requested NCERT page is the official textbook-access page for the Class 11 Mathematics material. citeturn0view0

1. Ordered Pairs

An ordered pair records two objects in a particular order and is written as (a,b). The order matters: in general, (a,b) and (b,a) are different. Two ordered pairs are equal precisely when their corresponding first and second components are equal.

(a,b) = (c,d) ⇔ a = c and b = d.

2. Cartesian Product

The Cartesian product of sets A and B is the set of all ordered pairs whose first component belongs to A and second component belongs to B. It is written A × B. Students should be able to list Cartesian products and count their elements for finite sets.

A × B = {(a,b) : a ∈ A and b ∈ B}. If n(A)=m and n(B)=n, then n(A×B)=mn.

3. Relations

A relation from A to B is a subset of A × B. Thus, a relation selects some ordered pairs from the Cartesian product. Practice questions may ask you to identify a relation, list its ordered pairs, or determine which pairs belong to it.

4. Domain and Range

For a relation, the domain consists of first components of its ordered pairs, while the range consists of second components. Repeated values are listed only once when describing the set of domain or range.

Domain(R) = set of first coordinates; Range(R) = set of second coordinates.

5. Number of Relations

If A and B are finite with n(A)=m and n(B)=n, then A×B contains mn ordered pairs. Since a relation is any subset of A×B, the total number of possible relations from A to B is determined by the number of subsets of A×B.

Number of relations from A to B = 2^mn.

6. Functions

A function from A to B assigns exactly one element of B to every element of A. It is commonly written f : A → B. A function is therefore a special kind of relation: every input has one and only one output. A single input cannot have two different outputs in the same function.

f : A → B means every a ∈ A is assigned exactly one f(a) ∈ B.

7. Domain, Codomain and Range of a Function

The set A in f:A→B is the domain, B is the codomain, and the actual values produced by the function form the range. The range is always a subset of the codomain. A frequent error is to call the entire codomain the range without checking which values are actually attained.

8. Types of Functions

Important types include one-one (injective), many-one, into and onto functions. A one-one function sends distinct domain elements to distinct outputs. An onto function has every element of the codomain as an output of at least one domain element. A function can be both one-one and onto; such a function is called bijective.

One-one: f(a₁)=f(a₂) ⇒ a₁=a₂. Onto: Range(f)=Codomain(f).

9. Into and Onto

If at least one codomain element is not used, the function is into. If every codomain element is used, it is onto. For finite sets with equal numbers of elements, a one-one function is also onto, and an onto function is also one-one.

10. Real Functions

A real-valued function has real numbers as outputs. Students should read formulas carefully, identify the domain for which the expression is defined, and calculate values such as f(2), f(−1), or f(a+h). Expressions involving denominators, square roots or other restrictions require special attention to the allowed inputs.

11. Algebra of Functions

If f and g are functions with suitable domains, their sum, difference, product and quotient can be formed. The quotient requires the denominator to be non-zero. These operations are useful in simplifying expressions and evaluating combined functions.

(f+g)(x)=f(x)+g(x); (f−g)(x)=f(x)−g(x); (fg)(x)=f(x)g(x); (f/g)(x)=f(x)/g(x), where g(x)≠0.

12. Composition of Functions

Composition means applying one function after another. In (g∘f)(x), first apply f to x and then apply g to the resulting value. The order matters: g∘f is generally different from f∘g.

(g∘f)(x)=g(f(x)).

13. Seven-plus Question Types in This Tool

1 Ordered Pairs2 Cartesian Product3 Relations4 Domain & Range5 Function Identification6 Types of Functions7 Algebra of Functions8 Composition9 Counting Relations

14. Difficulty Levels

Easy questions focus on notation, direct definitions and simple calculations. Medium questions combine two ideas, such as a Cartesian product followed by a domain/range calculation. Hard questions involve multiple steps, function classification, composition or relation-counting formulas. Mixed mode gives balanced revision.

15. Randomized Practice

Every time the worksheet is generated, the question order is randomized. The whole-sheet Shuffle button also rearranges questions and independently randomizes multiple-choice choices. This helps students avoid memorizing positions and makes repeated practice more meaningful.

16. Answer Checking and Feedback

Students must attempt a question before the answer is revealed. After clicking Check Answer, the tool marks the response green when correct and red when incorrect. A short animation and optional sound provide immediate feedback. The Show Answer button remains hidden until the question has been checked.

17. Timer, Progress and Final Score

Select no timer or a 5, 10, 15 or 30-minute session. The progress bar tracks checked questions. When every question is checked, the final score and percentage are displayed. If the timer reaches zero, the session is finalized automatically.

18. PDF and Print

Save as PDF is separate from Print. The PDF button downloads a generated practice sheet, while Print uses the browser's print facility. This makes it easy to keep a digital worksheet or create a paper copy.

19. Mobile-Friendly Student Design

The worksheet is optimized for phones first, with touch-friendly controls, responsive cards and one-column answer choices on smaller screens. The colorful animated mathematical symbols add a kid-and-student-friendly visual layer without making the learning content difficult to read.

20. Quick Revision Strategy

First revise definitions and notation. Then practise Cartesian products and relations. Next identify domains, codomains and ranges. After that, classify functions as one-one, many-one, into or onto. Finally practise algebra and composition, paying close attention to domains and the order of composition. Use the shuffle feature for a fresh test after reviewing mistakes.

Looking for a free Class 11 Relations and Functions online practice worksheet? DigiSadhan's Chapter 2 Mathematics worksheet gives students an engaging way to practise ordered pairs, Cartesian products, relations, domain and range, functions, one-one and onto functions, algebra of functions and composition. With up to 2,000 questions, randomized worksheets, difficulty selection, instant answer checking, progress tracking, optional timer, sound effects, animations, PDF download and print support, it is built for fast revision on mobile, tablet and desktop.