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. About the Course: About the Course
  2. Section 1 | Language (Hindi): भाषा, लिपि और वर्ण, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, पद-भेद और रूप-विकार, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, शब्द-भंडार, अपठित बोध, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): رسم الخط، حروفِ تہجی اور املا / Script, Alphabet and Spelling, اسم، ضمیر اور صفت / Nouns, Pronouns and Adjectives, الفاظ، محاورے اور ضرب الامثال / Vocabulary, Idioms and Proverbs, تفہیمِ عبارت، انشا اور ترجمہ / Comprehension, Writing and Translation, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): শব্দার্থ, বাগধারা ও ভাষাশুদ্ধি / Meaning, Idioms and Correct Usage, বাক্য ও বাচ্য / Sentences and Voice, শব্দগঠন ও শব্দভান্ডার / Word Formation and Vocabulary, অনুবাদ, বোধপরীক্ষণ ও রচনা / Translation, Comprehension and Composition
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Verbs and Tenses, Pronoun, Verb, Adverb, Prepositions and Conjunctions, Parts of Speech, Determiner, Conjunction, Modals, Transformation of Sentences, Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Structure and Common Errors, Reading Comprehension, Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, अशाब्दिक तर्क / Non-Verbal Reasoning, प्रतिशत / Percentage, औसत / Average, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, समय और कार्य / Time and Work, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, Algebra, Probability, Trigonometry, Syllogisms, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, Analytical Reasoning (Counting Figures Reasoning), गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, कैलेंडर एवं घड़ी / Calendar and Clock, Clock, घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, Data Arrangement, Inequality, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, Chemistry, History, Geography, Indian Economy, Environment, समसामयिकी / Current Affairs, Static General Knowledge
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | 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, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, कंप्यूटर नेटवर्क / Computer Networks, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), Terms & Abbreviations, प्रेज़ेंटेशन (MS PowerPoint) / Presentation Software (MS PowerPoint)
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References, OOPS with Java
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
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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