13.1 Practice Question

Duration: 2 min

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Module outline

  1. About Course: About the Course
  2. General Aptitude & Reasoning: Number System, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Speed Time and Distance, Mixture and Alligation, Data Interpretation, Algebra, Probability, Permutation and Combination, Venn Diagram, HCF LCM, Divisibility Rules, Age Problems, Pipe and Cistern, Partnership, Linear Algebra, Sequence and Series (Series), Statistics, Powers and Exponents (Surds and Indices), Arithmetic, Mensuration and Geometry, Calculus, Trigonometry, Vectors, Speed Mathematics and Basic Mathematics, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analogy, Series (Number and Letter Series) (Numerical Relations and Reasoning), Puzzle Solving (Puzzles), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Calendar, Seating Arrangements, Coding Decoding, Blood Relations, Directions (Direction Test), Clock, Analytical Reasoning (Counting Figures Reasoning), Ranking, Order and Sequence, Logical Sequence Of Words, Inequality, Data Sufficiency, Cubes & Dices
  3. Computer Networks & Cybersecurity: 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 Security
  4. Programming, Data Structures & Algorithms: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++, 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, Advanced Algorithms
  5. AI, Machine Learning, Big Data & Cloud: Emerging Tech Trends, Artificial Intelligence, Big Data Systems, Approaches to AI, Search Algorithms, Knowledge Representation, Cloud Computing
  6. Digital Logic & Computer Organization: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer
  7. TOC & Compiler: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory, 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
  8. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  9. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS, Distributed Systems
  10. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Object Oriented Technology, HTML Basics, JavaScript-Basics, Java, XML
  11. Database Management System: 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, Database Recovery, Data Warehousing & Mining, Enhanced Data Models, NoSQL
  12. Other Recurring CS Topics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, Multimedia
  13. Live Classes: ISRO Live classes
  14. Full Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture segment focuses on solving practice problems in graph theory, specifically concerning the relationship between a simple graph G and its complement Gc. The instructor demonstrates how to calculate the number of vertices or edges using fundamental formulas involving complete graphs.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces a problem where a simple graph G has 30 edges and its complement Gc has 36 edges, asking for the number of vertices n. The visible text displays the question 'Q A simple graph G has 30 edges and Gc has 36 edges, the number of vertices in G will be?'. The instructor writes the core formula |E(G)| + |E(Gc)| = n(n-1)/2, representing the total edges in a complete graph. Substituting 30 + 36 = n(n-1)/2, the instructor derives the quadratic equation n^2 - n = 132. The solution process involves factoring: n^2 - 12n + 11n - 132 = 0, leading to n(n-12) + 11(n-12) = 0, and finally (n+1)(n-12) = 0. The instructor notes x = -1 as a rejected solution, implying n=12 is the valid vertex count.

  2. 2:00 – 2:29 02:00-02:29

    The second problem asks to find the number of edges in the complement |E(Gc)| given a simple graph G with |V|=8 and |E|=12. The instructor calculates the total possible edges for a complete graph with 8 vertices using the formula 8(8-1)/2, which equals 28. The visible calculation shows the subtraction step: 28 - 12, resulting in a final answer of 16. This value is circled on the screen as the solution for |E(Gc)|.

The lecture effectively demonstrates two distinct applications of the complement graph edge formula. The first example requires solving a quadratic equation to find the number of vertices n when given edge counts for both G and Gc. The second example is a direct arithmetic application where the total edges of a complete graph are calculated and the known edges of G are subtracted to find the complement's edge count. Both problems rely on the foundational concept that |E(G)| + |E(Gc)| equals n(n-1)/2.

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