What is Variation, What is Direct & Indirect Variation

Duration: 13 min

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, Logarithm, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, प्रतिशत / Percentage, औसत / Average, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, Statistics, Probability, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समय और कार्य / Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  3. Paper-1 & 2 | Data Interpretation: आँकड़ा निर्वचन / Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, Data Sufficiency, अशाब्दिक तर्क / Non-Verbal Reasoning, Syllogisms, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, Analytical Reasoning (Counting Figures Reasoning), गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, कैलेंडर एवं घड़ी / Calendar and Clock, Clock, घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Data Arrangement, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: आँकड़ों की पर्याप्तता एवं निर्णय क्षमता / Data Sufficiency and Decision Making
  7. Paper-1 | General Science: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, समसामयिकी / Current Affairs
  9. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Combinational Circuit, Sequential Circuits
  10. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Calculus, Relational Algebra, SQL, NoSQL
  11. Paper-2 | Data Structures & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Algorithm Analysis, Sorting Algorithms, Intro to Compilers, Hashing
  12. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, Data Link Layer - Ethernet, DLL: Error Control, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Application Layer, Hardware basics, Network Security, Ethical Hacking
  13. Paper-2 | Operating Systems: Introduction to OS, Process Management, Memory Management, File Management, Deadlock
  14. Paper-2 | Computer Organization and Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer, Number System, Number Representation
  15. Paper 2 | System Analysis and Design: Fundamentals of Systems and Information Systems, Fundamentals of Software Engineering, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance, Software Testing
  16. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Paper 2 | OOPS , C++ , JAVA: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  18. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  19. Emerging Trends and AI: Emerging Tech Trends, कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection
  20. Paper-2 | Data Processing (Ms-Office): MS Office Applications, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), प्रेज़ेंटेशन (MS PowerPoint) / Presentation Software (MS PowerPoint)
  21. Paper-2 | Internet and Web Technologies: HTML Basics, CSS, XML, JavaScript-Basics, Internet Fundamentals, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, Terms & Abbreviations, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर नेटवर्क / Computer Networks
  22. Paper 2 | Pedagogy: वृद्धि और विकास / Growth and Development, विकास के सिद्धांत / Theories of Development, Concept of Pedagogy, समावेशी शिक्षा / Inclusive Education, Experiential Pedagogy, आकलन और मूल्यांकन / Assessment and Evaluation, संज्ञानात्मक प्रक्रियाएँ / Cognitive Processes, समाजीकरण और जेंडर / Socialisation and Gender, National Education Policy (NEP) 2020
  23. Live Classes: RSSB Live Sessions
  24. Paper 1 - Full Mock Tests:
  25. Paper 2 - Full Mock Tests:
  26. BCI Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture introduces variation within the Ratio and Proportion unit, defining it as a relationship where two or more quantities depend on each other such that if one changes, the other also changes. The instructor uses everyday examples—dairy products, sweets, and car speed—to build intuition before formally distinguishing direct variation (quantities change together) from indirect/inverse variation (one increases as the other decreases). The core formulas are presented: for direct variation, A ∝ B, so A = kB and A/B = k, giving the ratio chain A1/B1 = A2/B2; for indirect variation, A ∝ 1/B, so AB = k (constant), giving the product chain A1B1 = A2B2. Two worked examples demonstrate application: a direct variation problem (A varies directly as B; A=12 when B=6, find A when B=12) solved via k = 2 and the ratio form to get A2 = 24, with a shortcut doubling method; and an inverse variation problem (Y inversely proportional to X; Y=0.4 when X=5, find Y when X=4) solved via the product rule 5(0.4)=4(Y2), yielding Y2 = 0.5.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a 'RATIO & PROPORTION' title slide by Yash Jain, showing a hand-drawn green 'Ratio' graphic and the line 'a comparison of 2 quantities.' It then shifts to a coral background with rocket and planet doodles under the heading 'Concept of Variation' (page 37). The definition slide reads: 'When two or more quantities depend each other and if one of them changes other item also changes, this is called variation,' with 'variation' highlighted in red. This establishes the foundational definition before any formulas appear.

  2. 2:00 – 5:00 02:00-05:00

    The instructor builds intuition with real-world examples. Red handwritten symbols 'A ∝ 1/B' and a boxed 'A ∝ B' appear beneath the definition. A photograph of dairy items (milk pitcher, cheese, butter, cream) and a platter of Indian sweets illustrate how related quantities change together. A car-driving example with a speedometer inset introduces motion, followed by two digital clock times 11:07:42 and 11:00:11 with a downward arrow, setting up the time-based speed discussion.

  3. 5:00 – 10:00 05:00-10:00

    The lesson formalizes the two types. The formula S = d/t is written, noting speed relates to time as S ∝ 1/t. A summary slide contrasts Direct Variation and Indirect Variation with letters A and B circled in red. For direct variation, handwritten notes show 'A ∝ B,' boxed 'A = kB,' 'k = const,' 'A/B = k,' and the ratio chain 'A1/B1 = A2/B2 = A3/B3.' For indirect variation, notes show 'A ∝ 1/B,' boxed 'AB = const,' 'AB = K,' and the product chain 'A1B1 = A2B2 = A3B3.' Red arrows and labels like 'Ratio → RD / Direct' and a boxed 'IR' mark reinforce the distinction.

  4. 10:00 – 12:52 10:00-12:52

    Two worked examples are solved on an orange board. First, 'A varies directly as B. A is 12 when B is 6, what is the value of A when B is 12?' The solution writes 'A ∝ B,' 'A = kB,' '12 = k(6),' a circled 'K=2' with a check, then the ratio form 'A1/B1 = A2/B2' leading to 'A2 = 24.' A shortcut with columns A and B holding 12 and 6, 'x2' markers, and a circled '24' is drawn. Second, 'Y is inversely proportional to X and Y=0.4 when X=5. Find Y when X=4?' shows 'Y ∝ 1/X,' an '(IP)' tag, 'XY = const,' and the product rule 'X1Y1 = X2Y2' giving '5(0.4) = 4(Y2)' and a checked 'Y2 = 5/10 = 0.5.' The video ends with a 'THANKS FOR WATCHING' overlay.

The lecture progresses from definition to intuition to formal rules to application. The central idea is that variation describes dependent quantities, split into direct (same-direction change) and inverse (opposite-direction change). The key exam-ready tools are the constant-ratio form for direct variation (A/B = k, so A1/B1 = A2/B2) and the constant-product form for inverse variation (AB = k, so A1B1 = A2B2). The worked examples show two solution paths: finding the constant k first, or using the proportionality chain directly. The shortcut doubling method for direct variation is a useful time-saver. Students should memorize the proportionality symbol ∝, the constant forms, and which chain (ratio vs. product) applies to each type.

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