Class 12th Math Chapter 1, “Relations and Functions,” is an important algebraic topic included in the CBSE syllabus for 2023-24. The NCERT Solutions for this chapter provide step-by-step answers to all exercise questions, helping students understand the concepts clearly and effectively. These solutions are designed to sharpen problem-solving skills and ensure students grasp both fundamental and advanced concepts.
The chapter introduces various types of relations, such as symmetric, transitive, universal, and empty relations (also called void relations, where no relationship exists between elements). It also explores functions, their compositions, invertible functions, and binary operations. By regularly practicing these solutions, students can strengthen their command over the chapter, making even the challenging questions seem manageable during exams.
Understanding this chapter thoroughly is essential for success in mathematics. Solving questions from the NCERT textbook ensures students build a solid foundation while gaining confidence in advanced topics. For additional practice, students can download the NCERT Solutions PDF from the links provided below and enhance their preparation further.
In Hindi
Class 12th Math Chapter 1, “Relations and Functions,” CBSE syllabus 2024-25 का एक महत्वपूर्ण अध्याय है। इस अध्याय के NCERT Solutions में सभी प्रश्नों के हल एक स्टेप-बाय-स्टेप तरीके से दिए गए हैं, जिससे छात्रों को हर कॉन्सेप्ट को अच्छे से समझने में मदद मिलती है। इन सॉल्यूशन्स को हल करने से गणित की स्किल्स बेहतर होती हैं और छात्रों का आत्मविश्वास बढ़ता है।
यह अध्याय विभिन्न प्रकार के रिलेशन्स जैसे, symmetric relation, transitive relation, universal relation और empty relation (जिसे void relation भी कहते हैं) के बारे में सिखाता है। इसके अलावा, यह functions, उनके composition, invertible functions, और binary operations पर भी गहराई से चर्चा करता है। अगर छात्र इन NCERT Solutions का नियमित अभ्यास करें, तो वे मुश्किल सवालों को भी आसानी से हल कर पाएंगे और परीक्षा की तैयारी में मजबूत बनेंगे।
इस अध्याय को समझना न सिर्फ आसान है, बल्कि परीक्षा के लिए बहुत जरूरी भी है। NCERT किताब के सवालों को हल करने से छात्र बुनियादी और एडवांस्ड टॉपिक्स में अच्छी पकड़ बना सकते हैं। अभ्यास के लिए आप नीचे दिए गए लिंक से इस अध्याय का NCERT Solutions PDF डाउनलोड कर सकते हैं।
- NCERT Solutions Class 12 Maths Chapter 1 Ex 1.1
- NCERT Solutions Class 12 Maths Chapter 1 Ex 1.2
- NCERT Solutions Class 12 Maths Chapter 1 Ex 1.3
- NCERT Solutions Class 12 Maths Chapter 1 Ex 1.4
- NCERT Solutions Class 12 Maths Chapter 1 Miscellaneous Exercise
List of key formulas and concepts from NCERT Solutions Class 12th Math Chapter 1: Relations and Functions:
1. Relation and Cartesian Product
2. Types of Relations
3. Functions
4. Types of Functions
5. Composition of Functions
6. Invertible Function
7. Binary Operations
These are the most important formulas and concepts from Class 12th Math Chapter 1, which are essential for solving related problems.
Here are some FAQs on Class 12th Math Chapter 1: Relations and Functions – NCERT Solutions:
1. What are the main topics covered in Chapter 1: Relations and Functions?
The chapter includes:
- Definition of relations and functions
- Types of relations (reflexive, symmetric, transitive, and equivalence relations)
- Types of functions (one-to-one, onto, many-to-one)
- Composition of functions and inverse of functions
- Binary operations
2. What is the importance of Relations and Functions in Class 12 Mathematics?
Relations and Functions form the foundation for understanding advanced concepts in mathematics like calculus, algebra, and set theory. This chapter is also crucial for competitive exams like JEE and other entrance tests.
3. What are the types of functions discussed in this chapter?
The main types of functions covered are:
- One-to-One (Injective)
- Onto (Surjective)
- Bijective (One-to-One and Onto)
- Constant functions and identity functions
4. How is the inverse of a function determined?
To find the inverse of a function:
- Check if the function is bijective (one-to-one and onto).
- Swap the input and output values (x ↔ y) in the function and solve for y.
- The result is the inverse of the function.
5. What are binary operations, and where are they used?
A binary operation is a rule that combines two elements of a set to produce another element of the same set. Examples include addition, subtraction, multiplication, and division. Binary operations are widely used in algebra and computer science.
6. Where can I find NCERT Solutions for Relations and Functions?
You can access step-by-step NCERT solutions for Relations and Functions in textbooks, online learning platforms, or websites like WINS Technologies that offer detailed explanations, exercises, and downloadable PDFs.
7. How can I prepare for board exams using this chapter?
- Understand the key definitions and properties of relations and functions.
- Solve all examples and exercises from the NCERT book.
- Refer to NCERT Solutions for clarification and practice.
- Practice additional questions from sample papers and previous years’ board exams.
