Q1:

Let $A = \{1, 2, 3,...,14\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : 3x – y = 0, \text{where } x, y \in A\}$. Write down its domain, codomain and range.

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I teach Mathematics to CBSE board students in Classes 9 to 12, and I also teach Applied Mathematics to students in Classes 11 and 12. I have been teaching for the past 25 years, and over this time I have worked with students at different learning levels and helped them build strong academic foundations. My primary focus is on making concepts clear, developing problem-solving abilities, and helping students approach their examinations with confidence. I have completed my Master of Science (M.Sc.) along with a Bachelor of Education (B.Ed.). My academic qualifications, combined with my extensive teaching experience, have given me a strong understanding of the subjects I teach as well as the different ways in which students learn. Over my 25 years in teaching, I have gained experience in several aspects of the education field. I have worked as a visiting faculty member and have also been involved in boarding and examination-related responsibilities, including paper checking. These experiences have given me valuable exposure to assessment, examination patterns, student performance, and the academic expectations of different levels. My aim is to take students from zero to hero by helping them strengthen their fundamentals, develop confidence, and improve their problem-solving skills over time. Whether a student needs support in CBSE Mathematics 9 to 12, or Applied Mathematics for Classes 11 and 12, I provide structured guidance with a strong focus on conceptual clarity, consistent practice, and examination preparation. Why Join My Classes? Math isn't about memorizing formulas—it's about understanding the "WHY" behind every concept. Whether you are struggling to keep up with school lectures or aiming for a 95+ in your Board Exams, my structured, step-by-step approach is designed to take you from zero to hero. Here is what makes learning with me different: 💡 Real Conceptual Clarity: Say goodbye to rote learning. We start from absolute ground zero and build up to advanced, high-order thinking problems (HOTS) so you actually understand what you're solving. 🎯 Inside Secrets from a Board Evaluator: Having checked CBSE board answer scripts for years, I don't just teach you how to solve a problem—I teach you how to present your answers to win maximum step-marking, avoid silly errors, and manage time like a pro. 🔍 Diagnostic & Tailored Learning: No two students learn at the same pace. I assess your specific strengths and blind spots to customize a learning plan that works for you. ⚡ Active Problem-Solving: My sessions are 100% interactive. You will actively solve questions in class, catch your own mistakes, and build the self-reliance needed for exams. 🚫 Zero-Gap Policy: Regular practice tests and dedicated doubt-solving sessions ensure you never move to a new topic with unresolved questions. Transform Math from a Subject You Fear to a Subject You Master! 25+ Years of Teaching Excellence | CBSE Mathematics (Classes 9–12) & Applied Mathematics (Classes 11–12) M.Sc. (Maths) | B.Ed. | Ex-Board Paper Evaluator Ready to turn Math into your highest-scoring subject? Book a demo session today, and let's build your path to top board exam results!