9.2 Practice Question
Duration: 2 min
This video lesson is available to enrolled students.
Inside: a video lesson and guided study material.
Module outline
- General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
- General Awareness: Physics, Chemistry, Biology, History, Geography, Polity, Indian Economy, Environment, Static General Knowledge, GK- Current Affairs, Artificial Intelligence, MS Office Applications, Terms & Abbreviations, Keyboard Shortcuts, Evolution of Indian Banking (Banking & Financial Awareness), Emerging Tech Trends
- Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Probability, Statistics, Signal Space and Optimum Detection, Probability, Statistics
- Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
- Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
- 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, HTML Basics, OOPS with C++, Java, Object Oriented Technology
- Databases: 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, Database Security & Authorization
- Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
- 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, Complexity Theory
- 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
- Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Security, Windows OS, Distributed Systems, Unix OS, Linux OS
- Computer Networks: Introduction to CN, 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, Data Communication, Website, Browser & Services, Web Design & Development, Network Security, Cyber Threats and Malware Attacks, Cyber Safety and Security
- Full Length Mock Tests:
- Sectional Tests:
- Paper 2 - Full-length Mock Tests:
AI summary & chapters
AI Summary
An AI-generated summary of this video lecture.
This educational video segment focuses on solving graph theory practice problems using the Handshaking Lemma. The instructor demonstrates how to determine vertex constraints based on edge counts and degree limits. Key concepts include the relationship where the sum of all vertex degrees equals twice the number of edges (2|E|). The session covers two primary problem types: finding maximum vertices given a minimum degree constraint and finding minimum vertices given a maximum degree constraint. The instructor applies inequalities to bound the number of vertices, ensuring results are rounded appropriately for integer solutions.
Chapters
0:00 – 2:00 00:00-02:00
The instructor begins by addressing a problem asking for the maximum number of vertices in a simple graph with 35 edges where each vertex has a degree of at least 3. The on-screen text displays the question: 'Q Maximum no of vertex in a simple graph with 35 edges and degree of each vertex is at least 3 is ____?'. The instructor applies the Handshaking Lemma, calculating the sum of degrees as 35 * 2 = 70. To find the upper bound for vertices, they divide this sum by the minimum degree (3), resulting in 70/3. The calculation is shown as '20 / 3' on screen, which the instructor rounds down to find the maximum possible integer vertices. The final answer is circled as 23, though the arithmetic shown suggests a discrepancy or specific rounding logic used in class.
2:00 – 2:25 02:00-02:25
The video transitions to a second problem asking for the minimum number of vertices possible in a simple graph with 41 edges where each vertex has a degree of at most 5. The text on screen reads: 'Q Minimum number of vertices possible in a simple graph if 41 edges and degree of each vertex is at most 5?'. The instructor calculates the total degree sum as 41 * 2 = 82. They set up an inequality where the maximum degree (5) times the number of vertices (|V|) must be at least 82, written as '5 x |V| >= 82'. Solving for |V| gives approximately 16.4, which is displayed as '< 16.4'. Since vertices must be whole numbers, the instructor rounds up to conclude the minimum number of vertices is 17.
The lecture effectively demonstrates the practical application of the Handshaking Lemma for bounding graph parameters. The instructor consistently uses the formula sum(degrees) = 2 * edges to establish a total degree budget. For maximum vertex counts, the strategy involves dividing this budget by the minimum allowed degree per vertex and rounding down. Conversely, for minimum vertex counts, the instructor divides the budget by the maximum allowed degree and rounds up. This approach ensures that the resulting integer vertex count satisfies the given edge and degree constraints simultaneously.

