Last Updated on July 29, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 12 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 12 maths. In this article, you will find case study questions for CBSE Class 12 Maths Chapter 1 Relations and Functions. It is a part of Case Study Questions for CBSE Class 12 Maths Series.

Chapter | Relations and Functions |

Type of Questions | Case Study Questions |

Nature of Questions | Competency Based Questions |

Board | CBSE |

Class | 12 |

Subject | Maths |

Useful for | Class 12 Studying Students |

Answers provided | Yes |

Difficulty level | Mentioned |

Important Link | Class 12 Maths Chapterwise Case Study |

### Case Study Questions on Relations and Functions

**Questions**

Passage 1: Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be set of all possible outcomes. A = {S, D}, B = {1, 2, 3, 4, 5, 6}

*Based on the above information answer the following:*

(i) Let R : B –> B be defined by R = {(x, y) : y is divisible by x} is

(a) Reflexive and transitive but not symmetric

(b) Reflexive and symmetric but not transitive

(c) Not reflexive but symmetric and transitive

(d) Equivalence

**Difficulty Level: **Medium

Ans. Option (a) is correct.

(ii) Raji wants to know the number of functions from A to B. How many number of functions are possible?

(a) 6^{2}

(b) 2^{6}

(c) 6!

(d) 2^{12}

**Difficulty Level: **Medium

Ans. Option (a) is correct.

(iii) Let R be a relation on B defined by R = {(1, 2), (2, 2), (1, 3), (3, 4), (3, 1), (4, 3), (5, 5)}. Then R is

(a) Symmetric

(b) Reflexive

(c) Transitive

(d) None of these three

**Difficulty Level: **Medium

Ans. Option (d) is correct.

(iv) Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible?

(a) 6^{2}

(b) 2^{6}

(c) 6!

(d) 2^{12}

**Difficulty Level: **Medium

Ans. Option (d) is correct.

(v) Let R : B –> B be defined by R = {(1, 1), (1, 2), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}, then R is

(a) Symmetric

(b) Reflexive and Transitive

(c) Transitive and symmetric

(d) Equivalence

**Difficulty Level: **Medium

Ans. Option (b) is correct.

### Also check

- Matrices Class 12 Case Study Questions Maths Chapter 3
- Inverse Trigonometric Functions Class 12 Case Study Questions Maths Chapter 2
- Relations and Functions Class 12 Case Study Questions Maths Chapter 1

### Topics from which case study questions may be asked

- Definition of Relation
- Domain & Range of a Relation
- Types of Relations from One Set to Another Set
- Types of Intervals
- Function
- Types of Functions
- Algorithm to Check for Surjectivity of a Function

A relation R, from a non-empty set A to another non-empty set B is mathematically as a subset of A × B. Equivalently, any subset of A × B is a relation from A to B.

A relation from A to B is also called a relation from A into B.

Case study questions from the above given topic may be asked.

### Frequently Asked Questions (FAQs) on Relations and Functions Case Study

#### Q1: What is a case study question in mathematics?

A1: A case study question in mathematics is a problem or set of problems based on a real-life scenario or application. It requires students to apply their understanding of mathematical concepts to analyze, interpret, and solve the given situation.

#### Q2: How should students tackle case study questions in exams?

A2: To tackle case study questions effectively, students should:**Read the problem carefully:** Understand the scenario and identify the mathematical concepts involved.**Break down the problem:** Divide the case study into smaller parts to manage the information better.**Apply relevant formulas and theorems:** Use the appropriate mathematical tools to solve each part of the problem.

#### Q3: Why are case study questions included in the Class 12 Maths curriculum?

A3: Case study questions are included to bridge the gap between theoretical knowledge and practical application. They help students see the relevance of what they are learning and prepare them for real-life situations where they may need to use these mathematical concepts.

#### Q4: What is a relation in mathematics?

A4: In mathematics, a relation is a set of ordered pairs, typically defined between two sets. If set A has elements a1, a2, and a3, and set B has elements b1, b2, and b3, a relation R from set A to set B is a subset of the Cartesian product A × B, consisting of ordered pairs (a, b) where ‘a’ belongs to A and ‘b’ belongs to B.

#### Q5: What is a function? How is it different from a relation?

A5: A function is a special type of relation where every element in the domain (set A) is associated with exactly one element in the codomain (set B). In other words, for every ‘a’ in A, there is only one ‘b’ in B such that (a, b) is in the relation. While all functions are relations, not all relations are functions.

#### Q6: **What are the types of functions?**

A6: Functions can be categorized into several types, including:**One-to-one function (Injective):** Each element of the domain is mapped to a unique element of the codomain.**Onto function (Surjective):** Every element of the codomain is mapped by at least one element of the domain.**One-to-one and onto function (Bijective):** A function that is both injective and surjective.**Constant function:** Every element of the domain is mapped to the same single element of the codomain.

#### Q7: **What is the domain and range of a function?**

A7: The domain of a function is the set of all possible input values (x-values) for which the function is defined. The range is the set of all possible output values (y-values) produced by the function.

#### Q8: What is the vertical line test?

A8: The vertical line test is a graphical method to determine if a relation is a function. If a vertical line intersects the graph of a relation at more than one point, then the relation is not a function. This is because a function can only have one output value for each input value.

#### Q9: How do you determine if a function is one-to-one?

A9: To determine if a function is one-to-one, check that each element in the domain maps to a unique element in the codomain. Mathematically, a function f(x) is one-to-one if f(a) = f(b) implies a = b for all elements a and b in the domain.

#### Q10: What is the composition of functions?

A10: The composition of functions is the process of applying one function to the results of another. If you have two functions, f and g, the composition (f ∘ g)(x) is defined as f(g(x)). This means you first apply g to x, then apply f to the result of g(x).

#### Q11: What are inverse functions?

A11: An inverse function reverses the operation of the original function. If f is a function, its inverse f^(-1) satisfies the condition that f(f^(-1)(x)) = x and f^(-1)(f(x)) = x for all x in the domain of f^(-1) and f, respectively. Inverse functions exist only for bijective functions.

#### Q12: **Are there any online resources or tools available for practicing **relations and functions** case study questions?**

A12: We provide case study questions for CBSE Class 12 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.