8.7 Practice Question

Duration: 2 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. CS | 01 | Digital Logic and Circuits and Discrete Mathematical Structures: Digital Systems & Boolean Basics, Number System, Number Representation, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Permutation and Combination / क्रमचय और संचय
  3. CS | 02 | Computer Organization and Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Multiprocessors
  4. CS | 03 | Data Structures and Algorithm: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Complexity Theory, Advanced Algorithms
  5. CS | 04 | Problem Solving through C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. CS | 05 | Object Oriented Techniques: Object Oriented Technology, Java
  7. CS | 06 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Unix OS
  8. CS | 07 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Query Processing & Optimization, File Organization & Indexing
  9. CS | 08 | Computer Networks: 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
  10. CS | 09 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  11. CS | 10 | Internet Technology, Web Design and Web Technology: Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, JavaScript-Basics, HTML Basics
  12. CS | 11 | System Analysis And Design: Fundamentals of Systems and Information Systems, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance
  13. CS | 12 | Information Security and Cyber Laws: 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
  14. CS | 13 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  15. GS Paper | 01 | Indian and World Geography / भारत एवं विश्व का भूगोल: Geography / भूगोल
  16. GS Paper | 02 | History / इतिहास: History / इतिहास
  17. GS Paper | 03 | Indian Economy & Social Development / भारतीय अर्थव्यवस्था एवं सामाजिक विकास: Indian Economy / भारतीय अर्थव्यवस्था
  18. GS Paper | 04 | General Science / सामान्य विज्ञान: Biology / जीव विज्ञान, Chemistry / रसायन विज्ञान, Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान
  19. GS Paper | 05 | Elementary Maths / प्रारंभिक गणित: Number System / संख्या पद्धति, Divisibility Rules / विभाज्यता के नियम, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Percentage / प्रतिशत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Ratio and Proportion / अनुपात और समानुपात, Average / औसत, Time and Work / समय और कार्य, Time, Speed and Distance / समय, चाल और दूरी, Algebra / बीजगणित, Solid Mensuration / घन क्षेत्रमिति, Data Interpretation / आँकड़ा निर्वचन, Arithmetic / अंकगणित, Statistics / सांख्यिकी, Probability / प्रायिकता, Sequences, Series and Combinatorics / अनुक्रम, श्रेणी और संयोजन, Mixture and Alligation / मिश्रण और एलिगेशन, Calculus / कलन, Trigonometry / त्रिकोणमिति, Vectors / सदिश, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Euclidean Geometry and Mensuration / यूक्लिडीय ज्यामिति और क्षेत्रमिति, Statistics and Probability / सांख्यिकी और प्रायिकता, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ, Plane Mensuration / समतल क्षेत्रमिति, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित
  20. GS Paper | 06 | Indian Polity and Governance / भारतीय राजव्यवस्था एवं शासन: Polity / राजव्यवस्था
  21. GS Paper | 07 | Current Events / समसामयिक घटनाएँ: Current Affairs / समसामयिकी
  22. UPLT Live Classes Notes: UPLT Live Classes
  23. UPLT Full Mock Tests Tier 1:
  24. UPLT Full Mock Tests Tier 2:
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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