Practice Question

Duration: 3 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper-2 | Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  3. Paper-2 | Databases / DBMS & SQL: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  4. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  5. Paper-2 | Computer Networks & Security: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware Basics, Network Access Technologies, Network Security
  6. Paper-2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  7. Paper-2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  8. Paper-2 | Theory of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines
  9. Paper-2 | Computer Organization & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  10. Paper-2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  11. Paper-1 | General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, GK- Current Affairs, History, Geography, Indian Economy, Environment
  12. Paper-1 | Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Data Interpretation, Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Clock, Calendar, Cubes & Dices, Directions (Direction Test), Analogy, Seating Arrangements, Analytical Reasoning (Counting Figures Reasoning)
  13. Paper-1 | Quantitative Aptitude: Ratio and Proportion (Ratios), Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Speed Time and Distance, Average, Age Problems, Percentage, Profit and Loss, Time and Work, Pipe and Cistern, Simple Interest and Compound Interest, Powers and Exponents (Surds and Indices), Mensuration and Geometry, Probability, Statistics, Arithmetic, Algebra
  14. Paper-1 | English: Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Cloze Test (Cloze Passage)
  15. Coal India Previous Year Paper:
  16. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus
  17. Coal India Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video segment presents a practice problem in abstract algebra, specifically focusing on group theory properties. The instructor guides students through verifying the identity element and inverse elements for a binary operation defined on positive rational numbers. The core task involves identifying the false statement among four options regarding an abelian group structure where a*b = (a.b)/3. The teaching method emphasizes algebraic derivation and logical elimination of incorrect options to solve the multiple-choice question.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video introduces a multiple-choice question concerning positive rational numbers under the operation a*b = (a.b)/3. The instructor highlights this formula by boxing it on screen to emphasize its role in defining the group structure. The problem asks students to identify which statement is not true regarding identity elements and inverses for this abelian group. Visible text displays four options: (a) identity element e = 3, (b) inverse of a = 9/a, (c) inverse of 2/3 = 6, and (d) inverse of 3 = 3. The instructor begins the solution process by writing a*e = a to derive the identity element, showing that e must equal 3. This step confirms option (a) is a true statement within the group context.

  2. 2:00 – 2:35 02:00-02:35

    In the final segment, the instructor completes the verification of group properties by calculating specific inverse values. The derivation shows that for any element a, the inverse is 9/a, confirming option (b) as true. The instructor then checks specific cases like the inverse of 2/3, which equals 6, validating option (c). By systematically verifying these properties through algebraic manipulation of fractions and the operation definition, the instructor identifies that option (d) claiming the inverse of 3 is 3 is false. The video concludes by crossing out options (a), (b), and (c) as correct statements, leaving option (d) as the answer to the question asking which statement is not true.

The lecture effectively demonstrates how to apply group axioms to a custom binary operation. Key concepts include the definition of an identity element where a*e = a, and the inverse property where a*a^-1 = e. The instructor uses algebraic substitution to solve for unknowns, such as setting (a.e)/3 = a to find e=3. This methodical approach allows students to verify each option against the group definition. The critical takeaway is that not all intuitive assumptions about inverses hold true for non-standard operations, requiring rigorous calculation. The problem reinforces the importance of checking all group axioms when analyzing algebraic structures.

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