1. Find the Cartesian product A × B, where A = {1, 2} and B = {3, 4}.
Solution: A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}
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- RD Sharma Solutions for Class 11 Maths Chapter 2 Relations PDF Includes:
- Benefits of Practicing with RD Sharma Solutions Relations PDF:
- Download RD Sharma Solutions for Class 11 Maths Chapter 2 Relations PDF Here
- RD Sharma Solutions Relations - Practice Questions with Solutions
- FAQs: RD Sharma Solutions for Class 11 Maths Chapter 2 Relations
RD Sharma Solutions for Class 11 Maths Chapter 2 Relations
By rohit.pandey1
|
Updated on 28 Apr 2025, 16:52 IST
The RD Sharma Solutions Relations PDF for Class 11 is an essential resource for mastering the fundamental topic of relations in mathematics. This chapter introduces students to important concepts such as relation between two sets, Cartesian product, ordered pairs, and various types of relations including reflexive relation, symmetric relation, transitive relation, equivalence relation, universal relation, void relation, identity relation, and inverse relation.
Understanding these concepts is crucial for building a strong base in Relations and Functions, a key part of the CBSE syllabus relations chapter, and is frequently tested in both board and competitive exams.
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Students will also learn about the representation of relations, the properties of relations, and the relation and function difference, helping them grasp the complete framework of relations in mathematics. These topics form the foundation for higher-level problem-solving and are vital for success in exams and future studies.
RD Sharma Solutions for Class 11 Maths Chapter 2 Relations PDF Includes:
- Comprehensive, step-by-step RD Sharma Relations solutions for all exercises, ensuring students clearly understand the approach and solution to each question.
- Detailed examples that clarify complex topics like relation as a subset of Cartesian product and the use of ordered pairs in relations.
- Extra questions and important problems, including MCQs and advanced-level HOTS questions, to deepen understanding and practice.
- Special focus on the types of relations in mathematics, providing real-world examples like examples of reflexive relation and guidance on how to identify symmetric relation.
By using these solutions, students can easily master how to solve relations in RD Sharma for both CBSE school exams and competitive entrance tests.
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Benefits of Practicing with RD Sharma Solutions Relations PDF:
By regularly practicing with the RD Sharma Solutions for Class 11 Maths Chapter 2 Relations PDF, students can:
- Strengthen their grasp of key concepts, ensuring clarity on topics like relation and function difference, properties of relations, and types of relations.
- Instantly resolve doubts using clear explanations verified by experts, in full alignment with the CBSE syllabus relations chapter.
- Improve speed and accuracy, vital for scoring high in both board exams and competitive tests.
- Prepare thoroughly using resources like CBSE board exam relations solutions, RD Sharma Relations MCQ solutions, and RD Sharma Relations HOTS questions solutions.
- Master critical topics such as equivalence relation criteria, relation between two sets, and the significance of ordered pairs in relations.
These solutions are student-friendly, detailed, and ideal for those preparing for school exams, competitive exams, and even students looking for RD Sharma solutions for competitive exams.
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Download RD Sharma Solutions for Class 11 Maths Chapter 2 Relations PDF Here
Download the RD Sharma Relations Solutions PDF now to access:
- Expertly explained step-by-step solutions for each problem.
- Worked examples demonstrating complex types of relations.
- Extra MCQs and HOTS questions for stronger exam readiness.
- Advanced-level questions aligned with CBSE and competition formats.
Whether you're searching for the best website for RD Sharma Relations solutions, step-by-step guides, or tips on how to solve relations in RD Sharma, this PDF is your one-stop resource.
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Also Check: RD Sharma Solutions Sets PDF for Class 11
RD Sharma Solutions Relations - Practice Questions with Solutions
2. If A = {a, b} and B = {1}, list all elements of A × B.
Solution: A × B = {(a,1), (b,1)}
3. Define a relation R from A = {1,2,3} to B = {1,4,9} such that R = {(x, y): y = x²}. Write R.
Solution: R = {(1,1), (2,4), (3,9)}
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4. Find the number of elements in A × A if A has 3 elements.
Solution: Number of elements = 3² = 9.
5. State whether the relation R = {(1,1), (2,2), (3,3)} on set {1,2,3} is reflexive.
Solution: Since (a,a) exists for each a ∈ {1,2,3}, R is reflexive.
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6. Define a universal relation on set A = {1,2}.
Solution: R = A × A = {(1,1), (1,2), (2,1), (2,2)}
7. Is the relation R = {(1,1), (2,2), (2,1)} on {1,2} symmetric?
Solution: (2,1) ∈ R but (1,2) ∉ R, hence R is not symmetric.
8. Is the relation R = {(a,a): a ∈ A} reflexive on A?
Solution: Yes, R is reflexive because each element maps to itself.
9. Find the domain and range of R = {(1,2), (3,4), (5,6)}.
Solution: Domain = {1,3,5}; Range = {2,4,6}.
10. Find whether the relation R = {(1,1), (2,2), (3,3), (2,3), (3,2)} is symmetric on A = {1,2,3}.
Solution: (2,3) and (3,2) are present, thus R is symmetric.
11. If R = {(a,b): a and b are integers, and a-b is divisible by 5}, show that R is an equivalence relation.
Solution: R is reflexive, symmetric, and transitive. Hence, R is an equivalence relation.
12. Is the relation R = {(x,y): x ≤ y} reflexive on set {1,2,3}?
Solution: Since x ≤ x for all x, R is reflexive.
13. Find the inverse of relation R = {(1,2), (3,4), (5,6)}.
Solution: Inverse relation R⁻¹ = {(2,1), (4,3), (6,5)}
14. Let A = {1,2,3}. Define the identity relation on A.
Solution: Identity relation = {(1,1), (2,2), (3,3)}
15. Let R be the relation on N given by R = {(a,b): a divides b}. Is R reflexive?
Solution: Yes, a divides itself. Thus, R is reflexive.
16. If A = {1,2}, how many binary relations are possible on A?
Solution: Number of binary relations = 2^(n²) = 2⁴ = 16.
17. Find whether the relation R = {(a,b): |a-b| ≤ 2} is symmetric.
Solution: Since |a-b| = |b-a|, R is symmetric.
18. Find the set of all ordered pairs representing R if A = {1,2,3} and R = {(x,y): x < y}.
Solution: R = {(1,2), (1,3), (2,3)}
19. If R = {(1,1), (2,2), (3,3), (1,2)} on {1,2,3}, is R transitive?
Solution: No extra pairs needed; thus, R is transitive.
20. Let R be a relation on set A = {a,b,c} such that R = {(a,a), (b,b), (c,c), (a,b), (b,c), (a,c)}. Check reflexivity and symmetry.
Solution: R is reflexive but not symmetric (e.g., (a,b) exists but (b,a) doesn't).
FAQs: RD Sharma Solutions for Class 11 Maths Chapter 2 Relations
Where can I find reliable RD Sharma Solutions for the Relations chapter?
You can access expert-verified RD Sharma Solutions for the Relations chapter exclusively at Infinity Learn.
We provide free downloadable PDFs, step-by-step solutions, and comprehensive study materials for both Class 11 and Class 12 students, following the latest CBSE guidelines.
Thousands of students across India trust Infinity Learn for accurate and exam-focused resources.
What topics are covered in the Relations chapter of RD Sharma?
At Infinity Learn, the Relations chapter solutions cover:
- Types of relations: Void, universal, identity, reflexive, symmetric, transitive, antisymmetric, equivalence
- Important theorems on relations
- Composition and inverse of relations
- Binary operations and Cartesian products
- A wide range of MCQs, theory-based, and application-based problems.
Every concept is explained clearly to help CBSE Class 11 and 12 students across India master the chapter easily.
Why should I solve all the questions in RD Sharma’s Relations chapter?
Practicing all problems from RD Sharma Relations with Infinity Learn's solutions will:
- Strengthen your conceptual foundation
- Sharpen your problem-solving abilities for exams like CBSE Boards and competitive exams (e.g., JEE, CUET)
- Ensure you gain full clarity and confidence before attempting school or national-level exams.
How do RD Sharma Solutions help in exam preparation for Relations?
Infinity Learn's RD Sharma Solutions make exam preparation easy by:
- Providing step-by-step detailed explanations for every question
- Offering important formulas and summaries for fast revision
- Including MCQs, HOTS, and previous year questions aligned to CBSE and competitive exam standards.
- Perfect for students aiming to excel in Class 11, Class 12 board exams, and national-level tests across India.
Are the RD Sharma Solutions for Relations sufficient for board and competitive exams?
Yes, Infinity Learn’s RD Sharma Solutions for Relations are:
- Fully aligned with the latest CBSE syllabus
- Structured to strengthen conceptual clarity
- Designed to help students score high in CBSE boards and crack exams like JEE Main, CUET, and state-level engineering entrances.
- Trusted by students nationwide, from Delhi to Mumbai to Hyderabad.
How can I improve my understanding of Relations using RD Sharma Solutions?
To boost your understanding with Infinity Learn’s RD Sharma Relations Solutions:
- Study the textbook concepts first
- Practice exercises independently before checking the solutions
- Review mistakes and revisit difficult concepts
- Use solved examples for revision
Attempt mock tests and sample papers available on Infinity Learn for self-assessment.
What are some tips for studying the Relations chapter effectively?
Follow these tips for mastering Relations:
- Revise basic set theory and Cartesian products before starting
- Focus on understanding each type of relation (reflexive, symmetric, transitive, etc.)
- Practice regularly using Infinity Learn’s step-by-step solutions
- Join peer study groups and participate in online doubt-clearing sessions if available.
- Create a consistent study plan leading up to your school and entrance exams.
What is the importance of practicing different types of relation questions?
Practicing a variety of questions through Infinity Learn’s RD Sharma Relations Solutions helps you:
- Strengthen your conceptual grip on all types of relations
- Get ready for all kinds of exam questions, whether short, long, or MCQs
- Identify weak areas early and work on improving them
- Boost your confidence and speed for CBSE boards, JEE, CUET, and other exams.
- Students from metro cities and smaller towns across India have benefited immensely from consistent practice.