11.3 Practice Question

Duration: 3 min

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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 on binary operations defined over the set {p, q, r, s}. The instructor guides students through analyzing a Cayley table to determine if the operation is commutative and associative. The core task involves checking algebraic properties using specific element pairs from the table to verify conditions like a*b = b*a for commutativity and (a*b)*c = a*(b*c) for associativity. The video demonstrates how to disprove these properties by finding counterexamples where the equality does not hold, ultimately leading to a multiple-choice selection.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video introduces a binary operation * defined on the set {p, q, r, s} via an operation table. The instructor displays the Cayley table with rows and columns labeled p, q, r, s, showing entries such as row P containing 'p r s p' and row q containing 'q p q r s'. The problem asks to identify true statements regarding commutativity and associativity. Key visible text includes the question prompt 'Q let {p, q, r, s} be the set' and the table header '* p q r s'. The instructor begins by explaining that commutativity requires symmetry across the main diagonal, noting that a*b must equal b*a for all elements. He points out specific entries like p*q and q*p to set up the verification process.

  2. 2:00 – 2:55 02:00-02:55

    The instructor performs specific calculations to test the properties. He first checks commutativity by comparing p*q and q*p, observing from the table that p*q equals r while q*p equals p. Since 'r!= p', he concludes the operation is not commutative. Next, he tests associativity using elements p and q, calculating (p*q)*q which equals q based on table lookups. He then calculates p*(q*q), finding the result is s. Because 'q!= s', the associative property fails. The instructor selects option (d) as the correct answer, indicating the operation is neither commutative nor associative. Handwritten notes on screen show 'p*q = r, q*p = p' and '(p*q)*q = q', confirming the step-by-step substitution method used to disprove both properties.

The lecture effectively demonstrates the procedural approach to verifying algebraic properties of binary operations using Cayley tables. The critical takeaway is that commutativity can be quickly assessed by checking diagonal symmetry, while associativity requires explicit calculation of nested operations. The instructor uses counterexamples—specifically the pairs (p, q) for commutativity and the triple (p, q, q) for associativity—to efficiently disprove both properties without exhaustive testing. This method highlights the importance of selecting strategic elements to find discrepancies, a common strategy in discrete mathematics exams. The visual evidence of the table entries and handwritten calculations reinforces the logical steps required to solve such problems.

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