8.7 Practice Question

Duration: 2 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 focuses on solving a graph theory practice problem involving simple non-directed graphs. The instructor presents a question asking for the possible number of vertices in a graph with 24 edges where every vertex has an identical degree K. The core concept applied is the Handshaking Lemma, which states that the sum of all vertex degrees equals twice the number of edges. The instructor demonstrates how to translate this theorem into an algebraic equation by defining |V| = x for the number of vertices and deg(v) = K for the degree. Through this derivation, he establishes that x * K must equal 48 (since 24 edges multiplied by 2 equals 48). The solution process involves identifying that the number of vertices x must be a divisor of 48. By testing the provided multiple-choice options (20, 15, 10, and 8), the instructor eliminates values that do not divide 48 evenly. Specifically, he crosses out options a) 20, b) 15, and c) 10 because they are not factors of 48. The remaining option d) 8 is identified as the correct answer since 8 divides 48 to yield an integer degree K of 6. This exercise reinforces the relationship between edges, vertices, and regular graph properties.

Chapters

  1. 0:00 – 1:58 00:00-01:58

    The instructor introduces a graph theory problem displayed on screen asking for the possible number of vertices in a simple non-directed graph with 24 edges where every vertex has degree K. He immediately applies the Handshaking Lemma, writing '24 x 2' to represent twice the number of edges. He assigns variables |V| = x and deg(v) = K to set up the equation x * K = 48. The instructor then systematically evaluates the multiple-choice options a) 20, b) 15, c) 10, and d) 8. He crosses out options a), b), and c) because they are not divisors of 48, leaving d) 8 as the only valid solution where x * K results in an integer degree.

The video provides a concise demonstration of applying the Handshaking Lemma to determine graph properties. The central takeaway is that for a regular graph, the product of vertices and degree must equal twice the number of edges. This creates a divisibility constraint where the vertex count must be a factor of 2E. The instructor's method highlights a practical strategy for multiple-choice questions: calculate the total degree sum (2E), then check which option divides this sum evenly. This approach efficiently filters incorrect answers without needing to construct the actual graph, emphasizing algebraic verification over geometric visualization.

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