Interesting Facts About Perfect Squares & Perfect Cubes

Duration: 12 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. Course Overview: About the Course
  2. Paper - 1 | Unit - 1 | Teaching Aptitude: Nature, Objectives & Characteristics of Teaching, Learners & Learning Process, Factors Affecting Teaching, Methods of Teaching, Teaching-Learning Aids & ICT Integration, Evaluation, Assessment & Measurement
  3. Paper - 1 | Unit - 2 | Research Aptitude: Introduction to Research, Validity & Reliability, Research Paradigms & Types of Research, Research Process Steps, Research Ethics, Writing & Publication
  4. Paper - 1 | Unit - 3 | Comprehension: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions)
  5. Paper - 1 | Unit - 4 | Communication: Communication Basics, Language and Semiotics, Types of Communication, Communication Models, Mass Communication, Mass Media, Journalism, General Knowledge and General Studies related to Communication
  6. Paper - 1 | Unit - 5 | Mathematical Reasoning and Aptitude: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Number System, Percentage, Ratio and Proportion (Ratios), Simple Interest and Compound Interest, Speed Time and Distance, Powers and Exponents (Surds and Indices), Profit and Loss, Average, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Verbal Analogy (Word Based Analogy), Divisibility Rules, Calendar, Miscellaneous, Time and Work, Algebra
  7. Paper - 1 | Unit - 6 | Logical Reasoning: Syllogisms, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Venn Diagram, School Of Thoughts, Fallacy, Western Logic
  8. Paper - 1 | Unit - 7 | Data Interpretation: Data Interpretation
  9. Paper - 1 | Unit - 8 | Information and Communication Technology: MS Office Applications, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Electronic Data Interchange and E-Commerce, Internet Fundamentals, Web Design & Development, Web Publishing & Hosting, Emerging Technologies, Terms & Abbreviations, Artificial Intelligence, Society, Law & Ethics, Keyboard Shortcuts, Website, Browser & Services
  10. Paper - 1 | Unit - 9 | People Development and Environment: Ecosystem, Biomes & Environmental Issues, MDG & SDG, Air Pollution, Water Pollution, Soil, Noise Pollution and Waste Management, Natural Resources, Energy & Disaster Management, Global Environmental Conventions – COP, Protocols & ISA
  11. Paper - 1 | Unit - 10 | Higher Education System: Vedic Education, Jainism & Buddhism, Ancient Universities, Pre-Independence Commissions, Post-Independence Policy, Higher Education Structure & Accreditation, Universities & Learning Programmes, Types of Education & NEP 2020
  12. Paper 2 | Unit 1 | Discrete Structures and Optimization: Propositional and Predicate Logic, Set Theory, Relations, Functions, Permutation and Combination, Probability, Graph Theory, Group Theory, Digital Systems & Boolean Basics, Boolean Expression, Boolean Minimization, Optimization
  13. Paper 2 | Unit 2 | Computer System Architecture: Logic Gates & Hardware, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Basics of COA, Register Transfer and Microoperations, Programming the Basic Computer, Instr Formats & Modes, Control Unit Design, Pipelining, Input Output Organisation, Cache Memory Organization, Multiprocessors
  14. Paper 2 | Unit 3 | Programming Languages and Computer Graphics: Language Design, C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, HTML Basics, XML, JavaScript-Basics, Java, Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, OOPS with C++, Java Fundamentals
  15. Paper 2 | Unit 4 | Database Management Systems: 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, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  16. Paper 2 | Unit 5 | System Software and 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, Linux OS, Security, Distributed Systems, Virtual Machines
  17. Paper 2 | Unit 6 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  18. Paper 2 | Unit 7 | Data Structures and Algorithms: 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
  19. Paper 2 | Unit 8 | Theory of Computation and Compilers: 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
  20. Paper 2 | Unit 9 | Data Communication and 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, Network Security, Mobile Technology, Cloud Computing and IoT, Cloud Computing
  21. Paper 2 | Unit 10 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Fuzzy Sets, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
  22. Live Classes: NTA UGC NET 2025 Live Class
  23. Paper 1 | Full Mock Tests:
  24. Paper 2 | Full Mock Tests:
  25. Paper 1 | Previous Year Papers:
  26. Paper 2 | Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video, presented by Yash Jain from Knowledge Gate Eduventures, provides a comprehensive lesson on number systems, focusing on the concepts of multiples and factors. The lecture begins with an introduction to the topic, followed by a detailed explanation of multiples, using the number 2 as a primary example. The instructor demonstrates how to find the multiples of 2 by listing them (2, 4, 6, 8, 10, etc.) and then shows how to identify the factors of a number, such as 4, by breaking it down into its prime factors (2 x 2). The video then transitions to a more complex example, analyzing the number 64, which is a multiple of 2, and its factors. The instructor uses a systematic approach, writing out the powers of 2 (2^1=2, 2^2=4, 2^3=8, 2^4=16, 2^5=32, 2^6=64) to illustrate that 64 is a multiple of 2. The lesson also covers the concept of a number being a multiple of another number, using the example of 64 being a multiple of 2. The video concludes with a summary of the key concepts and a thank you message to the viewers.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide for a lecture on 'NUMBER SYSTEM' by Yash Jain from Knowledge Gate Eduventures. The instructor, visible in a small window, introduces the topic of 'The mysterious world of numbers' and the concept of 'Basic To Advance' learning. The main content slide appears, titled 'MULTIPLES AND FACTORS', setting the stage for the lesson. The instructor begins by explaining the concept of multiples, using the number 2 as an example, and starts writing the sequence of multiples of 2 on the screen: '2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100'. He explains that these are all the numbers that can be obtained by multiplying 2 by any whole number.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to explain the concept of multiples, writing the sequence '4, 8, 12, 16' on the screen as examples of multiples of 4. He then demonstrates how to find the factors of a number, using 4 as an example. He writes '4 = 2 x 2' and circles the number 2, explaining that 2 is a factor of 4. He then moves to the number 8, writing '8 = 2 x 2 x 2' and circling the number 2, explaining that 2 is a factor of 8. He continues this process for the number 12, writing '12 = 2 x 2 x 3' and circling the number 2, explaining that 2 is a factor of 12. He then moves to the number 16, writing '16 = 2 x 2 x 2 x 2' and circling the number 2, explaining that 2 is a factor of 16. The instructor then introduces the concept of a number being a multiple of another number, using the example of 64 being a multiple of 2.

  3. 5:00 – 10:00 05:00-10:00

    The instructor begins to list the powers of 2, writing '2^1 = 2', '2^2 = 4', '2^3 = 8', '2^4 = 16', '2^5 = 32', '2^6 = 64' on the screen. He explains that 64 is a multiple of 2 because it can be expressed as 2 raised to the power of 6. He then moves to the number 3, writing '3^1 = 3', '3^2 = 9', '3^3 = 27', '3^4 = 81', '3^5 = 243', '3^6 = 729' on the screen. He explains that 243 is a multiple of 3 because it can be expressed as 3 raised to the power of 5. The instructor then discusses the concept of a number being a multiple of another number, using the example of 64 being a multiple of 2. He explains that a number is a multiple of another number if it can be divided by that number without leaving a remainder.

  4. 10:00 – 11:49 10:00-11:49

    The instructor summarizes the key concepts of the lesson, emphasizing the importance of understanding multiples and factors. He reiterates that a multiple of a number is a product of that number and an integer, and a factor of a number is an integer that divides the number without leaving a remainder. He uses the example of 64 being a multiple of 2 and 2 being a factor of 64 to illustrate this point. The video concludes with a thank you message to the viewers, displayed in a red neon sign on a black background.

The video provides a clear and structured lesson on the fundamental concepts of number systems, specifically focusing on multiples and factors. The instructor uses a step-by-step approach, starting with simple examples and gradually moving to more complex ones, to ensure that the concepts are well understood. The use of visual aids, such as writing out the sequences of multiples and the powers of numbers, helps to reinforce the learning. The lesson is well-organized and easy to follow, making it an effective resource for students learning about number systems.

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