Q9(iii):

Let $R$ be a relation from $\mathbb{N}$ to $\mathbb{N}$ defined by $R = \{(a, b) : a, b \in \mathbb{N} \text{ and } a = b^2\}$. Are the following true? (iii) $(a,b) \in R, (b,c) \in R$ implies $(a,c) \in R$. Justify your answer in each case.

I have been actively involved in teaching Class 11 students, especially in Chemistry, with a strong focus on building conceptual clarity, exam preparation, and confidence in the subject. My teaching experience includes guiding students from CBSE and state boards through both online and offline classes. I specialize in simplifying difficult topics such as Organic Chemistry, Thermodynamics, Chemical Bonding, Equilibrium, Redox Reactions, and Structure of Atom by using practical examples and easy language so that students can understand concepts without fear. While teaching Class 11 students, I follow a student-friendly and interactive approach. I begin every chapter from basic concepts and gradually move toward advanced numerical and application-based questions. This helps average as well as high-performing students learn comfortably at their own pace. I regularly conduct doubt-clearing sessions, short tests, and revision classes to ensure that students remain confident and prepared for school examinations as well as competitive exams like NEET and JEE Foundation level. My teaching method focuses on conceptual understanding rather than rote learning. I encourage students to ask questions freely and participate actively during the class. To make learning more effective, I use diagrams, flowcharts, reaction mechanisms, and real-life examples. In Organic Chemistry, I explain reaction mechanisms step-by-step, while in Physical Chemistry I train students to solve numericals with proper formulas and shortcuts. This balanced approach helps students improve both theoretical understanding and problem-solving skills. I also provide handwritten notes, important questions, sample papers, and chapter-wise assignments to help students practice regularly. I monitor students’ performance individually and guide them according to their strengths and weaknesses. Many students who initially found Chemistry difficult became more confident and improved their academic performance after attending my classes. Apart from subject knowledge, I focus on motivating students and developing disciplined study habits. I believe that every student can perform well when taught with patience, clarity, and proper guidance. My goal as a Class 11 tutor is not only to help students score good marks but also to develop genuine interest and confidence in the subject. Through continuous interaction with students and updated teaching methods, I have gained valuable experience in understanding the learning needs of Class 11 students and helping them achieve academic success effectively.

I take classes for grade 11 of Karnataka State PUC, CBSE, ISC, NIOS and Cambridge or IGCSE AS Levels. I have 4 years of teaching experience.

I am Aaina Nandal, an experienced, qualified teacher and tutor, worked as an Assistant Professor in an engineering college. With a dynamic and engaging teaching style, I strive to create an environment where curiosity is nurtured, and knowledge is not just acquired but embraced. Education is not just about memorizing facts; it's about understanding and applying knowledge. I am deeply passionate about my subjects, and I bring that enthusiasm into every lesson. Recognizing that every student is unique, my teaching methodology is adaptive. I tailor lessons to suit individual learning styles, ensuring that each student progresses at their own pace. My classes are designed to be interactive and exciting, encouraging students to actively participate and enjoy the learning process. My goal is to equip students with the skills they need to thrive in all aspects of life. • Who Can Benefit High school students aiming for academic excellence. College students seeking additional support or a fresh perspective. Online tuition classes for students with backlogs, year-back students for the subject or topics of their need with one-to-one teaching. The syllabus will be covered in detail to make the student understand the concepts correctly. Last minute preparation/ crash course classes can also be conducted upon request for any subject. I can hold tuition classes for engineering subjects as per syllabus during weekends and semester vacation Please feel free to ask for a free demo online class Courses Offered: • B.Tech (All ECE Subjects and 1st year subjects which is common to all branches. • Diploma (Branch-ECE) • UGC-NET (Paper 1 & Paper 2 (Electronic Science)) • Class IX-X (Subjects: Mathematics & Science) • Class XI-XII ( Subjects: Mathematics ) • Class XI-XII ( Subjects: Computer science & Informatics Practices)

I am a Chartered Accountant by profession and have been teaching Commerce subjects—primarily Accounting and Economics—for the past 4 years. I work with BCom/BSc students and CA aspirants, helping them build strong conceptual clarity and practical understanding. Teaching is my passion and hobby, and I focus on delivering quality education by maintaining small group sizes (2–3 students at a time). This allows me to give individual attention, ensuring that every student understands the concepts thoroughly and gains confidence. My teaching approach is practical-based, designed to bridge the gap between academic theories and real-world industry applications. I emphasize how concepts are applied in actual business environments—both in private and public sectors—so students can connect textbook knowledge to real scenarios. I prefer conducting online, individual sessions to provide personalized support and address each student’s learning style and pace. I teach using a whiteboard for clear and visual explanations. For CA students, I recommend specific books aligned with the syllabus. For Class 11 and 12, I rely on their existing school books but provide additional notes or references on request to avoid overloading them. While I haven't pursued awards in teaching, the positive feedback from my students and their academic success bring me immense satisfaction. My goal is to make learning effective, relevant, and engaging for every student I teach.

Hi, I am Neeraj Dwivedi Top Tutor and partner at Urban Pro . Into profession of teaching since last four years. Expertise and specialization in guiding students on subjects like History, Political Science, Economics and Hindi. These subjects were my strength in my journey of Civil Services and later helped in shaping future of students. Apart from teaching guidance I have been doing career counselling of students as to what to pursue/not pursue after school based on individual interests and capabilities.