## NCERT for Class 12 Maths Chapter 1 Miscellaneous Exercise Solutions - Free PDF Download

## FAQs on NCERT Solutions for Class 12 Maths Miscellaneous Exercise Chapter 1 - Relation and Functions

1. What topics are covered in the Miscellaneous Exercise of Chapter 1?

The Miscellaneous Exercise in Chapter 1 covers a variety of problems related to relations and functions, including types of relations, types of functions, composition of functions, and inverse functions.

2. How do I identify different types of relations?

Different types of relations include reflexive, symmetric, transitive, and equivalence relations. You can identify them by checking the properties they satisfy.

3. What are the main types of functions discussed?

The main types of functions discussed are one-one (injective), onto (surjective), and bijective functions. Understanding their definitions and properties is crucial.

4. How is the composition of functions performed?

The composition of functions involves applying one function to the result of another function. If ff and gg are functions, then the composition (g∘f)(x)is g(f(x)).

5. What is an inverse function?

An inverse function reverses the effect of the original function. If ff is a function, then its inverse $f^{-1}$ satisfies $(f^{-1}(x))$=x for all x in the domain of $f^{-1}$.

6. Are there any specific formulas I need to remember?

Yes, remember the definitions and properties of different types of relations and functions, the formulas for the composition of functions, and how to find the inverse of a function.

7. How can I solve the problems in the Relations and Functions Miscellaneous Exercise Class 12?

To solve the problems, carefully read each question, understand the concepts involved, and apply the appropriate formulas and methods learned in the chapter.

8. Why are relations and functions important in math?

Relations and functions are fundamental concepts in mathematics that are used in various fields such as algebra, calculus, and computer science. They help in understanding and modelling real-world situations.

9. How can the NCERT solutions help me with miscellaneous exercise?

NCERT solutions provide step-by-step explanations for each problem, helping you understand the methods and concepts required to solve them. They are a valuable resource for exam preparation.

10. Are there any tricky questions in the Miscellaneous Exercise Class 12 Chapter 1?

Yes, the Miscellaneous Exercise includes some challenging questions designed to test your understanding of the entire chapter. Practice them thoroughly to improve your problem-solving skills.