8.5 Practice Question

Duration: 2 min

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Module outline

  1. HPSC Interview Preparation: Interview Preparation
  2. Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  3. Data Structure & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Sorting Algorithms, Minimum Spanning Trees, Time Complexity Analysis, Graph Theory, Shortest Path Algos
  4. Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security
  5. Computer System & Organisation: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  6. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Transaction Management, Concurrency Control
  7. Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling
  8. Digital Logic & Circuits: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  9. Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Pushdown Automata & CFG, Turing Machines, Moore & Mealy Machines
  10. 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. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Data Warehousing & Mining
  12. Introduction to Emerging Trends: Emerging Tech Trends, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, कंप्यूटर नेटवर्क / Computer Networks
  13. Digital Society & Cyber Law: Society, Law & Ethics, साइबर सुरक्षा / Cyber Safety and Security
  14. HPSC PGT Previous Year Paper:
  15. HPSC Assistant Professor Previous Year Paper:
  16. Live Sessions: HPSC Live Sessions, EMRS TGT/PGT Live Class
  17. Full Mock Test:
  18. HPSC PGT - MOCK Test Series:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This video segment presents a practice problem applying the Handshaking Lemma in graph theory. The instructor works through a specific question involving a simple graph with 35 edges and vertices of varying degrees. The core concept demonstrated is that the sum of all vertex degrees in a graph must equal twice the number of edges. The problem asks to find the unknown number of vertices with degree 2, given specific counts for other degrees.

Chapters

  1. 0:00 – 1:58 00:00-01:58

    The instructor solves a graph theory problem using the Handshaking Lemma. Visible on-screen text states: 'Q Consider a simple graph with 35 edges such that 4 vertex of degree 5, 5 vertex of degree 4, 4 vertex of degree 3,…'. The instructor sets up the equation '4 x 5 + 5 x 4 + 4 x 3 + x x 2 = 35 x 2'. Key visible events include correcting the edge count to 35 and writing '4 x 5 + 5 x 4 + 41' initially before simplifying to '20 + 20 + 12 + 2x = 70'. The final calculation shows '2x = 70 - 52' leading to the circled answer 'x = 9'. The instructor applies the rule Sum of degrees = 2 * |E| to isolate x.

The instructional content focuses on the practical application of the Handshaking Lemma to solve for unknown vertex counts. The problem requires translating a word problem into an algebraic equation where the sum of products (vertex count * degree) equals twice the edge count. The video demonstrates the step-by-step simplification from '4 x 5 + 5 x 4 + 4 x 3 + x x 2 = 70' to '52 + 2x = 70', then solving for x. This reinforces the fundamental graph theory principle that every edge contributes exactly two to the total degree sum.

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