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Chapter 1 – Relations and Functions Miscellaneous Exercise
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Flashcard for Question 2
Quick Tip:
For injectivity, set x³ = y³ and use cube root property to show x = y.
Common Mistake:
Overcomplicating the proof – forgetting that cube root is defined for all real numbers, so no separate positive/negative cases are needed.
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Download Miscellaneous Exercise NCERT Solutions PDF
You can download the PDF from the link below for offline study.
Class 12 Maths Chapter 1 – Relations and Functions: All Exercises
| Exercise | Link |
|---|---|
| Exercise 1.1 | View Solutions |
| Exercise 1.2 | View Solutions |
Class 12 Relations and Functions – Miscellaneous Exercise Overview
The Miscellaneous Exercise in the chapter Relations and Functions acts as a comprehensive wrap-up of all key concepts introduced so far. It includes a wide range of problems that test your understanding of reflexive, symmetric, and transitive relations, as well as function mapping, domain, codomain, and inverse relations. Because it combines everything, this exercise is a great checkpoint for identifying any gaps in your preparation.
Our Relations and Functions Class 12 NCERT Solutions Miscellaneous Exercise are crafted to make complex logic approachable. Whether you’re asked to determine if a relation is an equivalence relation or analyze a set mapping, these solutions walk you through each step. In addition, they help you shift comfortably between roster form, arrow diagrams, and set-builder notation—all essential for solving advanced-level problems with confidence.
As per the 2025 NCERT syllabus, there’s more emphasis on logical reasoning and visual interpretation in this chapter. Therefore, this exercise includes a mix of representation formats and conceptually tricky questions. But with clear guidance, even abstract topics like function inverses or function testing become simpler. These solutions are designed to offer clarity, not just final answers.
Ultimately, mastering this exercise prepares you for application-based questions in both board exams and entrance tests. The Relations and Functions Class 12 NCERT Solutions Miscellaneous Exercise are structured to boost both accuracy and speed. By practicing regularly, you’ll improve your problem-solving logic, which will benefit you throughout the maths syllabus.
FAQs – Relations and Functions Class 12 Miscellaneous Exercise NCERT
It combines all types of relation and function questions. That’s why it feels tougher—it’s meant to challenge your overall understanding.
Use examples or tables to check each condition separately. This way, you won’t confuse one with the other while analyzing ordered pairs.
Both matter. However, applying logic step-by-step is more useful in this exercise. Definitions only help if you can apply them properly.
Inverse functions test your understanding of one-to-one mappings. Since they appear in exams, learning to test invertibility is important here.
They simplify complex logic into clear steps. So, you can revise difficult concepts faster without going back to lengthy theory.