This mathematics worksheet on Relations and Functions, prepared for Class 11 CBSE students, is mainly meant for board exam preparation and for building strong fundamentals for higher mathematics. It contains 75 multiple-choice questions, covering relations, types of relations, functions, domain and range, inverse relations, and application-based problems involving logarithmic, trigonometric, and modulus functions. The questions are framed directly from NCERT concepts and closely reflect the style of questions asked in school examinations Relations and Functions WS 1.
I am writing about this worksheet because Relations and Functions is often the chapter where students feel they understand everything, but still lose marks due to small conceptual mistakes. Confusion between relations and functions, errors in domain and range, and misinterpretation of properties like symmetry or transitivity are very common. A worksheet like this helps students convert NCERT theory into exam-oriented thinking. By analysing the questions carefully, one can clearly see which concepts are repeatedly tested and how definitions are turned into scoring MCQs.
Structure of the Relations and Functions Worksheet
The worksheet consists of 75 MCQs, with each question carrying one mark. The questions are arranged in a progressive manner, starting from basic definitions and moving towards application-based and reasoning-oriented problems. While many questions look direct, the answer options are closely framed, which tests accuracy and conceptual clarity rather than guesswork.
The overall difficulty level ranges from moderate to slightly challenging, making it suitable for both revision and self-assessment.
Relations and Their Mathematical Properties
A significant number of questions focus on relations and their properties. Students are tested on identifying whether a relation is:
- Reflexive
- Symmetric
- Transitive
- An equivalence relation
Examples involving sets of numbers, geometric objects, and real-life-style relations are used to check whether students truly understand these properties instead of memorising definitions Relations and Functions WS 1.
Cartesian Products and Set-Based Relations
The worksheet includes several questions based on Cartesian products. These questions test whether students can:
- Identify valid ordered pairs
- Determine the domain and range of a relation
- Count the number of possible relations between two finite sets
Such questions reinforce the idea that every relation is a subset of a Cartesian product, which is a core concept in this chapter.
Functions and Their Classification
Functions form the backbone of this worksheet. Many questions require students to decide whether a given relation is a function and further classify it as:
- One-one
- Onto
- Both one-one and onto
- Neither one-one nor onto
There are also numerical questions asking for the total number of functions possible between two sets, which are frequently asked in CBSE exams.
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Domain and Range-Based Questions
Domain and range are among the most heavily tested topics in this worksheet. Questions involve functions containing:
- Logarithmic expressions
- Square roots
- Rational functions
- Modulus functions
- Trigonometric and inverse trigonometric functions
Students must carefully apply conditions like non-zero denominators, positive arguments for logarithms, and valid ranges for inverse trigonometric functions. These questions highlight common error areas where students tend to lose easy marks.
Modulus and Greatest Integer Function Applications
Several MCQs are based on modulus and greatest integer functions. These problems require interval-wise analysis and careful logical thinking rather than direct substitution. Such questions are important because they strengthen analytical skills needed for later chapters in calculus.
Composite and Inverse Functions
The worksheet also includes questions on composite functions and inverse relations. These questions test whether students understand function operations clearly and can apply them step by step. This area is particularly important for students aiming to build a solid foundation for Class 12 mathematics.
Trigonometric and Logarithmic Reasoning Questions
Some questions combine trigonometric identities with logarithmic expressions. These are slightly tricky and demand proper step-by-step reasoning. They test attention to detail and conceptual clarity, making them useful for higher-level problem-solving.
What Students Can Learn from This Worksheet
From analysing this worksheet, a few clear points emerge:
- NCERT concepts form the base of most questions
- Domain and range need careful handling
- Properties of relations must be logically understood
- Options are closely framed, so careless reading leads to mistakes
- Regular practice improves confidence and speed
Overall, this Relations and Functions worksheet is a strong practice resource for Class 11 students. It closely matches CBSE exam expectations and helps build a solid conceptual foundation that will be crucial for advanced topics in mathematics.
