GATE Exam (Mechanical) Asked Question on Alligation Rule

Duration: 13 min

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Module outline

  1. Numerical Ability & Problem Solving: Speed Mathematics and Basic Mathematics, Arithmetic, Number System, HCF LCM, Divisibility Rules, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Mixture and Alligation, Time and Work, Pipe and Cistern, Speed Time and Distance, Age Problems, Partnership, Data Interpretation, Mental Ability, Sequence and Series (Series), Powers and Exponents (Surds and Indices), Algebra, Statistics, Logarithm, Mensuration and Geometry, Permutation and Combination, Probability, Sequences and Series, Powers, Surds and Logarithms, Subject-Verb Agreement, Sentence Completion, Geometry, Sentence Structure and Correction, Data Sufficiency, Trigonometry, Measurement and Quantity Take-Off, Signal Space and Optimum Detection, Probability, Statistics, Algebra, Time and Work, Speed, Time and Distance, Data Interpretation, Combinatorics
  2. Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Logical Sequence Of Words, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, Selection Decision Table (Decision Making), Alphabet and Word Tests, Numerical Reasoning, Number System, Averages, Mixtures and Alligation, Percentages, Series Completion, Analogy and Classification, Patterns in Two-Dimensional Figures, Coding and Decoding, Mathematical Operations, Direction Sense, Logical Deduction and Induction, Syllogisms and Venn Diagrams, Critical Reasoning, Order, Ranking and Sequence, Reading Comprehension, Profit, Loss and Discount, Constraint Puzzles, Traverse Surveying, Ratio and Proportion, Mensuration, Permutations and Combinations, Clocks and Calendars, Assembling and Grouping of Shapes, Transformation of Shapes, Three-Dimensional Patterns and Visualization, Cubes and Dice, Vocabulary, Blood Relations
  3. General Knowledge & Current Affairs (India + Rajasthan): History, Geography, Polity, Indian Economy, Static General Knowledge, State Wise GK, GK- Current Affairs, Environment, Physics
  4. Computer Fundamentals & Operating Systems: Basics of COA, Floating Point Rep, Digital Systems & Boolean Basics, Number Representation, Number System, Introduction to OS, File Management, Windows OS, Unix OS, Linux OS, Register Transfer and Microoperations, Virtual Memory
  5. Computer Networks: Introduction to CN, Data Communication, DLL: Error Control, DLL: Access Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Application Layer, Hardware Basics, Network Security
  6. Cyber Security: Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security, Ethical Hacking
  7. Programming (C & OOP): C Fundamentals, Control Flow, Arrays & Pointers, Functions, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++, Operators & Expressions, Sorting Algorithms, Java Fundamentals, Java
  8. MS Office & Data Processing: MS Office Applications, Basics of DBMS
  9. Internet & Web Technology: Society, Law & Ethics, Terms & Abbreviations, Keyboard Shortcuts, Emerging Tech Trends, Artificial Intelligence, Emerging Technologies, Internet Fundamentals, Website, Browser & Services, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video is an educational lecture on the topic of 'Mixtures & Alligations,' presented by an instructor named Yash Jain. The lecture begins with an introduction to the topic, followed by a detailed explanation of how to solve a problem involving the average weight of two combined classes. The instructor uses the alligation method, a technique for finding the mean value of a mixture, to solve the problem. He demonstrates the method by setting up a diagram with the given values (30 and 15) and the number of students (40 and 20), then calculates the difference and ratio to find the combined average. The video also shows the application of the standard weighted average formula as an alternative method. The lecture concludes with a final answer and a thank you message.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with an animated title card featuring a cartoon scientist in a lab, with the word 'MIXTURE' visible at the bottom. This transitions to a presentation slide with a geometric background. The slide displays the title 'MIXTURES & ALLIGATIONS' and credits the instructor as 'By Yash Jain'. A small video window in the bottom right corner shows the instructor, Yash Jain, who is wearing glasses and a red shirt. He introduces the topic of mixtures and alligations, explaining that it is a common topic in competitive exams like the GATE exam, particularly for the Mechanical Branch.

  2. 2:00 – 5:00 02:00-05:00

    The instructor presents a problem on the screen: 'Q: The average weight of a class of 40 students is 30 and the average weight of a class of 20 students is 15. Find the average weight of the combined class?'. He states that this is a question asked in the GATE Exam for the Mechanical Branch. He begins to solve the problem using the alligation method. He writes the two average weights, 30 and 15, on a diagram. He then writes the number of students, 40 and 20, next to their respective weights. He explains that the difference between the two values is 15 (30 - 15), which he writes on the diagram.

  3. 5:00 – 10:00 05:00-10:00

    The instructor continues to solve the problem using the alligation method. He writes the difference (15) and the number of students (40 and 20) on the diagram. He then explains that the ratio of the two groups is 40:20, which simplifies to 2:1. He uses this ratio to find the combined average. He writes the formula for the weighted average: (40*30 + 20*15) / (40+20). He calculates the numerator as 1200 + 300 = 1500 and the denominator as 60. He then divides 1500 by 60 to get 25. He confirms that the combined average weight is 25.

  4. 10:00 – 12:54 10:00-12:54

    The instructor reiterates the solution, showing the final answer of 25 on the screen. He explains that the combined average is 25, which is closer to 30 than to 15, because there are more students in the class with an average weight of 30. He then shows the standard formula for weighted average: x = (n1*x1 + n2*x2) / (n1 + n2). He substitutes the values into the formula and arrives at the same answer, 25. The video ends with a 'THANKS FOR WATCHING' screen.

The video provides a clear and structured lesson on solving mixture and alligation problems. It begins with an introduction to the topic and then presents a specific, exam-relevant problem. The instructor effectively demonstrates two methods to solve the problem: the alligation method, which uses a visual diagram to find the ratio and average, and the standard weighted average formula. The progression from problem statement to solution, with clear step-by-step calculations, makes the concept accessible. The video successfully connects the theoretical method to a practical application, reinforcing the learning objective.

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