Practice Question

Duration: 4 min

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Inside: a video lesson and guided study material.

Module outline

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. 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
  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. 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
  12. 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
  13. Full Length Mock Tests:
  14. Sectional Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video segment focuses on solving graph theory problems involving simple non-isomorphic regular graphs. The instructor begins by presenting a problem requiring the identification of all possible configurations for 6 vertices and 6 edges where every vertex maintains an identical degree. The core constraint is that the graph must be regular, meaning each vertex connects to the same number of edges. The instructor systematically explores solutions by visualizing cycle graphs and disjoint unions, ensuring the total vertex count and edge count match the problem statement while maintaining regularity.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with the instructor displaying a practice question on screen asking for the number of simple non-isomorphic graphs possible with 6 vertices and 6 edges where every vertex has the same degree. Key constraints highlighted include 'simple', 'non-isomorphic', and the requirement for a regular graph structure. The instructor begins visualizing solutions by drawing a hexagonal cycle graph labeled C6, which satisfies the condition of 6 vertices and 6 edges with a degree of 2 for each vertex. Subsequently, the instructor draws two separate triangles (K3 + K3) to illustrate a second valid configuration where vertices also maintain a uniform degree of 2. These drawings are labeled G1 and G2 on the whiteboard to distinguish between the connected cycle graph and the disconnected union of cycles.

  2. 2:00 – 4:14 02:00-04:14

    The problem statement shifts to a new scenario involving 8 vertices and 8 edges with the same regularity constraint. The instructor draws a large octagon representing a single cycle graph C8, which serves as the first solution. Next, two disjoint squares are drawn and labeled C4 - C4 to demonstrate a configuration where the total vertex count is 8 and edges are distributed equally. The instructor then explores further combinations by drawing a house-shaped graph (a pentagon C5) alongside a separate triangle (C3), indicating that the sum of vertices and edges must equal 8. The final visual evidence shows three distinct configurations drawn in red ink: a single 8-cycle (C8), two disjoint 4-cycles (2C4), and a combination of a 5-cycle and a 3-cycle (C5 + C3). These drawings represent the complete set of non-isomorphic regular graphs satisfying the 8-vertex, 8-edge constraint.

The lecture demonstrates a methodical approach to enumerating regular graphs by decomposing the total number of vertices and edges into disjoint cycles. For a graph with n vertices and n edges where every vertex has degree 2, the solution space consists of all partitions of n into cycle lengths. The instructor uses visual aids to show that a single connected component (C6 or C8) is one solution, while disconnected components formed by combining smaller cycles (like two triangles for n=6 or a pentagon and triangle for n=8) are other valid solutions. This technique highlights the importance of checking both connectivity and degree constraints when determining non-isomorphic graph counts.

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