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NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions Exercise 1.2
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Chapter 1 – Relations and Functions Exercise 1.2
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Flashcard for Question 2
Quick Tip:
Check injectivity by seeing if different inputs can give the same output, and surjectivity by checking if every element in the codomain has a preimage in the domain.
Common Mistake:
Forgetting that in Z and R, negative and positive numbers can square to the same value, which breaks injectivity. Also, assuming all natural numbers are perfect squares or cubes without checking surjectivity.
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Flashcard for Question 3
Quick Tip:
Test injectivity by picking two different real numbers with the same integer part, and test surjectivity by checking if fractional real numbers can be in the range.
Common Mistake:
Assuming the greatest integer function outputs all real numbers—it only outputs integers, so it can’t be onto when codomain is R.
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Flashcard for Question 4
Quick Tip:
Check injectivity by testing a positive and its negative value, and check surjectivity by seeing if negative numbers appear in the range.
Common Mistake:
Assuming modulus covers all real numbers – it only produces non-negative values, so negative outputs are impossible.
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Flashcard for Question 8
Quick Tip:
Show injectivity by proving that swapping back gives the original pair, and show surjectivity by noting every element in B × A comes from exactly one element in A × B.
Common Mistake:
Forgetting to explicitly prove both injectivity and surjectivity – just stating “it’s bijective” without justification.
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Flashcard for Question 10
Quick Tip:
For injectivity, equate (x-2)/(x-3) = (y-2)/(y-3) and simplify to see if x = y. For surjectivity, solve (x-2)/(x-3) = b for x and check if it’s valid for all b in B.
Common Mistake:
Not checking the restrictions from A and B after solving – values making the denominator zero or mapping to excluded codomain elements are often missed.
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Download Exercise 1.2 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 |
| Miscellaneous | View Solutions |
Class 12 Relations and Functions – Exercise 1.2 Overview
Functions are a big element of Class 12 Math, and Exercise 1.2 is about them. This is where students learn how functions work, especially when it comes to the domain, codomain, and range. At this point, it’s vital to not just figure out if a relation is a function, but also to see how it works with other sets. So, this practice connects basic theory to solving real-world situations.
Our Relationships and Functions Exercise 1.2 in the Class 12 NCERT Solutions gives pupils a full, step-by-step tutorial on how to find the domain and range. It helps a lot to know how square roots and denominators modify the function’s valid inputs. Instead than just memorizing rules, students learn how to figure things out by looking at expressions, graphs, and mappings.
The new NCERT syllabus for 2025 focuses more stress on testing functions with real-world limits. Relations and Functions Class 12 NCERT Solutions Exercise 1.2 features questions about modulus, floor functions, and set-based mappings for that reason. Students also learn how to use other ways to exhibit items, like roster and set-builder form. These talents will come in handy all through the chapter.
These solutions help you understand the main ideas better, whether you’re studying for board exams or just trying to get better at the basics. The Relations and Functions Class 12 NCERT Solutions Exercise 1.2 is designed to help students understand ideas better and learn how to answer questions in a clear and orderly way. This makes it a lot easier to deal with harder problems later in the chapter.
FAQs – Relations and Functions Class 12 Exercise 1.2 NCERT
Verify for constraints such as square roots or division by zero. If any exist, eliminate the invalid values from the domain.
Range depends on outputs after applying the function. Unlike domain, which is based on input restrictions, range often requires deeper analysis.
Not always. However, a quick sketch often helps visualize tricky expressions, especially when modulus or square roots are involved.
Codomain is the expected output set, while range is the actual output values the function returns. So, they’re related but not identical.
They show you how to simplify logic and present answers step-by-step—so that you can avoid common mistakes and revise faster.