case study questions from relations and functions class 12

CBSE Case Study Questions for Class 12 Maths Relations and Functions Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 12 Maths Relations and Functions  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 12 Maths Relations and Functions PDF

Mcq set 1 -, mcq set 2 -, checkout our case study questions for other chapters.

• Chapter 2 Inverse Trigonometric Functions Case Study Questions
• Chapter 3 Matrices Case Study Questions
• Chapter 4 Determinants Case Study Questions
• Chapter 5 Continuity and Differentiability Case Study Questions

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• Relations and Functions Class 12 Case Study Questions Maths Chapter 1

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.

Table of Contents

Case Study Questions on Relations and Functions

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

(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

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

(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

Ans. Option (b) is correct.

Matrices Class 12 Case Study Questions Maths Chapter 3

Inverse trigonometric functions class 12 case study questions maths chapter 2, 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
• 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.

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Class 12 Maths: Case Study of Chapter 1 Relations and Functions PDF Download

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In Class 12 Boards there will be Case studies and Passage Based Questions will be asked, So practice these types of questions. Study Rate is always there to help you. Free PDF Download of CBSE Class 12 Mathematics Chapter 1 Relations and Functions Case Study and Passage Based Questions with Answers were Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Relations and Functions  to know their preparation level.

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

In CBSE Class 12 Maths Paper, There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Relations and Functions Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 12 Mathematics  Chapter 1 Relations and Functions

Case Study/Passage-Based Questions

Case Study 1:

A general election of the Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever.

Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows: R = {(𝑉1, 𝑉2) ∶ 𝑉1, 𝑉2 ∈ 𝐼 and both use their voting right in the general election – 2019}

• Two neighbors X and Y∈ I. X exercised his voting right while Y did not cast her vote in general election – 2019. Which of the following is true? a. (X,Y) ∈R b. (Y,X) ∈R c. (X,X) ∉R d. (X,Y) ∉R
• Mr.’𝑋’ and his wife ‘𝑊’both exercised their voting right in general election -2019, Which of the following is true? a. both (X,W) and (W,X) ∈ R b. (X,W) ∈ R but (W,X) ∉ R c. both (X,W) and (W,X) ∉ R d. (W,X) ∈ R but (X,W) ∉ R
• Three friends F1, F2, and F3 exercised their voting right in the general election 2019, then which of the following is true? a. (F1,F2 ) ∈R, (F2,F3) ∈ R and (F1,F3) ∈ R b. (F1,F2 ) ∈ R, (F2,F3) ∈ R and (F1,F3) ∉ R c. (F1,F2 ) ∈ R, (F2,F2) ∈R but (F3,F3) ∉ R d. (F1,F2 ) ∉ R, (F2,F3) ∉ R and (F1,F3) ∉ R
• The above-defined relation R is __ a. Symmetric and transitive but not reflexive b. Universal relation c. Equivalence relation d. Reflexive but not symmetric and transitive
• Mr. Shyam exercised his voting right in General Election – 2019, then Mr. Shyam is related to which of the following? a. All those eligible voters who cast their votes b. Family members of Mr.Shyam c. All citizens of India d. Eligible voters of India

Answer: 1. (d) (X,Y) ∉R 2. (a) both (X,W) and (W,X) ∈ R 3. (a) (F1,F2 ) ∈R, (F2,F3) ∈ R and (F1,F3) ∈ R 4. (c) Equivalence relation 5. (a) All those eligible voters who cast their votes

Case Study 2:

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 belonging to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be the set of all possible outcomes. A = {S, D}, B = {1, 2, 3, 4, 5, 6}

(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

Answer: (a) Reflexive and transitive but not symmetric

(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

Answer: (a) 62

(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

Answer: (d) None of these three

(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

Answer: (d) 212

(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

Answer: (b) Reflexive and Transitive

Hope the information shed above regarding Case Study and Passage Based Questions for Class 12 Maths Chapter 1 Relations and Functions with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 12 Mathematics Relations and Functions Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible. By Team Study Rate

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Case Study on Relations And Functions Class 12 Maths PDF

The passage-based questions are commonly known as case study questions. Students looking for Case Study on Relations And Functions Class 12 Maths can use this page to download the PDF file. 

The case study questions on Relations And Functions are based on the CBSE Class 12 Maths Syllabus, and therefore, referring to the Relations And Functions case study questions enable students to gain the appropriate knowledge and prepare better for the Class 12 Maths board examination. Continue reading to know how should students answer it and why it is essential to solve it, etc.

Case Study on Relations And Functions Class 12 Maths with Solutions in PDF

Our experts have also kept in mind the challenges students may face while solving the case study on Relations And Functions, therefore, they prepared a set of solutions along with the case study questions on Relations And Functions.

The case study on Relations And Functions Class 12 Maths with solutions in PDF helps students tackle questions that appear confusing or difficult to answer. The answers to the Relations And Functions case study questions are very easy to grasp from the PDF - download links are given on this page.

Why Solve Relations And Functions Case Study Questions on Class 12 Maths?

There are three major reasons why one should solve Relations And Functions case study questions on Class 12 Maths - all those major reasons are discussed below:

• To Prepare for the Board Examination: For many years CBSE board is asking case-based questions to the Class 12 Maths students, therefore, it is important to solve Relations And Functions Case study questions as it will help better prepare for the Class 12 board exam preparation.
• Develop Problem-Solving Skills: Class 12 Maths Relations And Functions case study questions require students to analyze a given situation, identify the key issues, and apply relevant concepts to find out a solution. This can help CBSE Class 12 students develop their problem-solving skills, which are essential for success in any profession rather than Class 12 board exam preparation.
• Understand Real-Life Applications: Several Relations And Functions Class 12 Maths Case Study questions are linked with real-life applications, therefore, solving them enables students to gain the theoretical knowledge of Relations And Functions as well as real-life implications of those learnings too.

How to Answer Case Study Questions on Relations And Functions?

Students can choose their own way to answer Case Study on Relations And Functions Class 12 Maths, however, we believe following these three steps would help a lot in answering Class 12 Maths Relations And Functions Case Study questions.

• Read Question Properly: Many make mistakes in the first step which is not reading the questions properly, therefore, it is important to read the question properly and answer questions accordingly.
• Highlight Important Points Discussed in the Clause: While reading the paragraph, highlight the important points discussed as it will help you save your time and answer Relations And Functions questions quickly.
• Go Through Each Question One-By-One: Ideally, going through each question gradually is advised so, that a sync between each question and the answer can be maintained. When you are solving Relations And Functions Class 12 Maths case study questions make sure you are approaching each question in a step-wise manner.

What to Know to Solve Case Study Questions on Class 12 Relations And Functions?

 A few essential things to know to solve Case Study Questions on Class 12 Relations And Functions are -

• Basic Formulas of Relations And Functions: One of the most important things to know to solve Case Study Questions on Class 12 Relations And Functions is to learn about the basic formulas or revise them before solving the case-based questions on Relations And Functions.
• To Think Analytically: Analytical thinkers have the ability to detect patterns and that is why it is an essential skill to learn to solve the CBSE Class 12 Maths Relations And Functions case study questions.
• Strong Command of Calculations: Another important thing to do is to build a strong command of calculations especially, mental Maths calculations.

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Case Study Questions for Class 12 Maths Chapter 1 Relations and Functions

• Last modified on: 2 years ago
• Reading Time: 4 Minutes

Question 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

(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

(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

(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

(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

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Case study relation and function 1 chapter 1 class 12

Case study Chapter 1(Relation and Function)

Case study 1:- Read the following and answer the question:(Case study relation and function 1)

A general election of Lock sabha is a gigantic exercise. About 311 million people were eligible to vote and voter turnout  was about 67%, the highest ever

Let I be the set of all citizens of India who were eligible to exercise their voting right in general electio held in 2019. A relation ‘R’ is defined on I as follows:

(i) Two neighbours X and Y ∈ I. X exercised his voting right while Y did not cast her vote in general election – 2019, while of the following is true ?

(a) (X, Y) ∈ R                        (b) (Y, X) ∈ R

(c) (X, X) ∉ R                         (d) (X, Y) ∉ R

(ii) Mr. ‘X’ and his wife ‘W’ both exercised their voting right in general election – 2019, which of the following is true ?

(a) Both (X, W) and (W, X) ∈ R                   (b) (X, W) ∈ R but (W, X) ∉ R

(c) Both (X, W) and (W, X) ∉ R                    (d) (W, X) ∈ R but (X, W) ∉ R

(iv) The above defined relation R is

(a) Symmetric and transitive but not reflexive

(b) Universal relation

(c) Equivalence relation

(d) Reflexive but not symmetric and transitive

(v) Mr. Shyam exercised his voting right in General Election – 2019, then Mr. Shyam is related to which of the following ?

(a) All those eligible voters who cast their votes

(b) Family members of Mr. Shyam

(c) All citizens of India

(d) Eligible voters of India

Solution: We have a relation ‘R’ is defined on I as follows:

(i) Answer (d)

Two neighbours  X and Y ∈ I. Simce X exercised his voting right while Y did not cast her vote in general election – 2019

Therefore, (X, Y) ∉ R

(ii) Answer (a)

Since Mr. ‘X’ and his wife ‘W’ both exercised their voting right in general election -2019.

∴  Both (X, W) and (W, X) ∈ R

(iii) Answer (a)

(iv) Answer (c)

This relation is an equivalence relation.

(v) Answer(a)

Mr. Shyam exercised his voting right in General election – 2019, then Mr. Shyam is related to all tose eligible votes who cast their votes.

Some other Case study problem

Case study 2:- Sherlin and Danju are playing Ludo at home during COVID- 19. While rolling the dice, Sherlin’s sister Raji cbserved 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 the set of all possible outcomes.(Case study relation and function 2)

 A = {S, D}, B = {1, 2, 3, 4, 5, 6}

Based on the above information answer the question.

Solution: For solution click here

Case Study 3:- Read the following and answer the question:(Case study relation and function 3)

 An organization conducted bike race under 2 different categories- boys and girls. In all, there were 250 participants. Among all of them finally three from category 1 and two from category 2 were selected for the final race. Ravi from two sets B and G with these participants for his college project.

Ravi decides to explore these sets for various types of relations and functions

Solution : For solution click here

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CBSE 12th Standard Maths Subject Relations and Functions Case Study Questions With Solution 2021

By QB365 on 21 May, 2021

QB365 Provides the updated CASE Study Questions for Class 12 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

QB365 - Question Bank Software

12th Standard CBSE

Final Semester - June 2015

Case Study Questions

A relation R on a set A is said to be an equivalence relation on A iff it is (a) Reflexive i.e..,  \((a, a) \in R \ \forall \ a \in A\) (b) Symmetric i.e.,  \((a, b) \in R \Rightarrow(b, a) \in R \ \forall \ a, b \in A\)   (c) Transitive i.e.,  \((a, b) \in R\)  and  \((b, c) \in R \Rightarrow(a, c) \in R\ \forall\ a, b, c \in A\)   Based on the above information, answer the following questions. (i) If the relation R = {(1, 1), (1, 2), (1, 3), (2,2), (2, 3), (3,1), (3, 2), (3, 3)} defined on the set A = {1, 2, 3}, then R is

(ii) If the relation R = {(1, 2), (2,1), (1, 3), (3, I)} defined on the setA = {1, 2, 3}, then R is

 (iii) If the relation R on the set N of all natural numbers defined as R = {(x, y) : y = x + 5 and x < 4}, then R is

(iv) If the relation R on the set A = {1, 2, 3, , 13, 14}defined as R = {(x, y) : 3x - y = 0}, then R is

Consider the mapping  \(f: A \rightarrow B\)  is defined by  \(f(x)=\frac{x-1}{x-2}\)  such that f is a bijection.  Based on the above information, answer the following questions. (i) Domain of f is

(ii) Range of f is

(iii) If g:  \(R-\{2\} \rightarrow R-\{1\}\)  is defined by g(x) = 2f(x) - I, then g(x) in terms of x is

(iv) The function g defined above, is

(v) A function J(x) is said to be one-one iff

*****************************************

Cbse 12th standard maths subject relations and functions case study questions with solution 2021 answer keys.

(i) (a) :  Clearly (1, 1), (2, 2), (3, 3),  \(\in\)  R. So, R is reflexive on A. Since,  \((1,2) \in R \text { but }(2,1) \notin R\)  So, R is not symmetric on A. Since,  \((2,3), \in R\)  and  \((3,1) \in R\)  but  \((2,1) \notin R\)  .So, R is not transitive on A. (ii) (b) : Since, (1,1), (2, 2) and (3, 3) are not in R. So, R is not reflexive on A. Now,  \((1,2) \in R \Rightarrow(2,1) \in R\)   and  \((1,3) \in R \Rightarrow(3,1) \in R\)   So, R is symmetric Clearly, \((1,2) \in R \text { and }(2,1) \in R \text { but }(1,1) \notin R\)   So, R is not transitive on A. (iii) (c) :  We have,  \(R=\{(x, y): y=x+5 \text { and } x<4\}\)  ,where  \(x, y \in N\)  . \(\therefore R=\{(1,6),(2,7),(3,8)\}\)   Clearly, (1, 1), (2, 2) etc. are not in R. So, R is not reflexive. Since,  \((1,6) \in R\)  but  \((6,1) \notin R\)  So, R is not symmetric.  Since,  \((1,6) \in R\)  R and there is no order pair in R which has 6 as the first element. Same is the case for (2, 7) and (3, 8). So, R is transitive. (iv) (d) : We have,R = {(x, y) : 3x - y = 0}, where  \(x, y \in A=\{1,2, \ldots \ldots, 14\}\)  . \(\therefore\)  R = {(I, 3), (2, 6), (3, 9), (4, 12)} Clearly, \((1,1) \notin R\)  So, R is not reflexive on A. Since,  \((1,3) \in R\)  but  \((3,1) \notin R\)  .So, R is not symmetric on A. Since,  \((1,3) \in R\)  and  \((3,9) \in R\)   but   \((1,9) \notin R\)  So, R is not transitive on A. (v) (d) : Clearly, (1, 1), (2, 2), (3, 3) ∈  R. So, R is reflexive on A. We find that the ordered pairs obtained by interchanging the components of ordered pairs in R are also in R. So, R is symmetric on A. For  \(1,2,3 \in A\)   such that (1, 2) and (2, 3) are in Rimplies that (1, 3) is also, in R. So, R is transitive on A. Thus, R is an equivalence relation.

(i) (a) : For f(x) to be defined  \(x-2 \neq 0\)  i.e., \(x \neq 2\)   \(\therefore\)  Domain of f = R - {2} (ii) (b) : Let y =J(x), then  \(y=\frac{x-1}{x-2}\)   \(\Rightarrow x y-2 y=x-1 \Rightarrow x y-x=2 y-1 \Rightarrow x=\frac{2 y-1}{y-1}\)   Since,   \(x \in R-\{2\}\) ,therefore  \(y \neq 1\) Hence, range of f = R-{1}  (iii) (d):  We have,g(x) = 2f(x) - 1 \(=2\left(\frac{x-1}{x-2}\right)-1=\frac{2 x-2-x+2}{x-2}=\frac{x}{x-2}\) (iv) (a) : We have,  \(g(x)=\frac{x}{x-2}\)  , Let   \(g\left(x_{1}\right)=g\left(x_{2}\right) \Rightarrow \frac{x_{1}}{x_{1}-2}=\frac{x_{2}}{x_{2}-2}\)     \(\Rightarrow x_{1} x_{2}-2 x_{1}=x_{1} x_{2}-2 x_{2} \Rightarrow 2 x_{1}=2 x_{2} \Rightarrow x_{1}=x_{2}\)   Thus,  \(g\left(x_{1}\right)=g\left(x_{2}\right) \Rightarrow x_{1}=x_{2}\)   Hence, g(x) is one-one. (v) (c) 

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