Number System (Quick Revision & Practice Questions)

Duration: 1 hr 21 min

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Module outline

  1. About Course: About the Course
  2. Section A: General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, History, Geography, Indian Economy, GK- Current Affairs, Evolution of Indian Banking (Banking & Financial Awareness), Environment
  3. Section A: General Intelligence & Reasoning ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analytical Reasoning (Counting Figures Reasoning), Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Directions (Direction Test), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, TCS NQT Advanced Reasoning Ability
  4. Section A: Arithmetical & Numerical Ability: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Powers and Exponents (Surds and Indices), Algebra, Probability, Mental Ability, Age Problems, Partnership, Statistics, Arithmetic, Speed Mathematics and Basic Mathematics, Miscellaneous
  5. Section A: English Language & Comprehension: Vocabulary, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Articles, Sentence Construction, Preposition, Direct and Indirect Speech, Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Modals, Active Passive Voice (Voice), Sentence Correction (Error Correction), Adverb, Conjunction, Cloze Test (Cloze Passage)
  6. Section A: Hindi Language & Comprehension: भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, 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, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  7. Section B: Programming, Data Structures, OOP & Java: 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, Java, OOPS with C++, Language Design, Intro to Compilers, Visual Basics, Syntax Analysis: Bottom-Up, Object Oriented Technology
  8. Section B: Computer Networks, TCP/IP & Network Security: Introduction to CN, Data Communication, DLL: Flow Control, DLL: Access 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, Network Access Technologies, Network Security, Society, Law & Ethics, Mobile Computing, Net Layer:Routing Protocol, Cyber Safety and Security
  9. Section B: Teaching Methodology: Child Development, Concept of Pedagogy, Theories, Inclusive Education, Experiential Pedagogy, Assessment & Evaluation, Curriculum Framework & Reforms, National Education Policy (NEP) 2020, Psychology, Teaching-Learning Process, Personality Development, Teaching Methods & Strategies, Learning and Motivation, Learners & Learning Process, Factors Affecting Teaching, Methods of Teaching, Nature, Objectives & Characteristics of Teaching, Teaching-Learning Aids & ICT Integration, Classroom Management & Communication, Evaluation, Assessment & Measurement, Curriculum & School Environment, Inclusive Education & Special Needs, Professional Development & Ethics
  10. Section B: Digital Electronics / Boolean Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  11. Section B: Operating Systems & Linux: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, File Management, Disc Scheduling, Unix OS, Linux OS, Distributed Systems, Windows OS
  12. Section B: Data Base Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, File Organization & Indexing, Transaction Management, Concurrency Control, Database Security & Authorization, Database Recovery, Data Warehousing & Mining
  13. Section B: Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, HTML Basics, CSS, Emerging Technologies, JavaScript-Basics, .Net Programming, Electronic Data Interchange and E-Commerce, XML
  14. Section B: Computer Fundamentals, IT Basics & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer, Terms & Abbreviations, MS Office Applications, Instr Formats & Modes, Floating Point Rep, Artificial Intelligence, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), कंप्यूटर नेटवर्क / Computer Networks, प्रेज़ेंटेशन (MS PowerPoint) / Presentation Software (MS PowerPoint)
  15. Section B: Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  16. Section B: Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, extras, Fundamentals of Systems and Information Systems
  17. Section B: Design & Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  18. Section B: Mathematics: Linear Algebra, Calculus, Trigonometry, Vectors, Set Theory, Functions, Relations, Propositional and Predicate Logic, Research Process Steps, Graph Theory, Number System & Place Value, Factors, Multiples, Divisibility, HCF & LCM, Mensuration — Perimeter, Area, Surface Area, Volume, Data Handling, Graphs & Probability, Coordinates & Graphs, Higher Mathematics — Trigonometry, Quadratics, Polynomials, Progressions, Statistics, Logarithms, समतल क्षेत्रमिति / Plane Mensuration, प्रतिचयन / Sampling
  19. Section B: Computer Graphics, Multimedia & Mobile Computing: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, Multimedia
  20. Section B: Emerging Trends: Emerging Tech Trends, Knowledge Representation, Natural Language Processing, Marketing and Consumer Studies
  21. DSSSB Previous Year Paper:
  22. Business Studies and Management: Business Communication, Business Organization and Management, Financial Accounting, Business Economics, Management Information System (MIS), Knowledge Management & New Economy
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This video is a comprehensive mathematics lecture on the concepts of multiples and factors, designed for competitive exam preparation. The instructor begins by defining factors and multiples using the number 12 as an example, showing that its factors are {1, 2, 3, 4, 6, 12} and its multiples are {12, 24, 36, 48, ...}. He then introduces the fundamental formula for finding the number of factors of a number N, which is derived from its prime factorization: if N = p^a * q^b * r^c, then the number of factors is (a+1)(b+1)(c+1). The lecture progresses to solve a series of practice problems, including finding the number of factors of a sum, determining the smallest number to multiply to make a perfect square or cube, and solving remainder problems using the formula Dividend = Divisor * Quotient + Remainder. The video concludes with a problem involving the sum of digits of a large number and a unique problem about the square root of a repeating digit sequence.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card for 'NUMBER SYSTEM' followed by a presentation slide titled 'MULTIPLES AND FACTORS'. The instructor, Yash Jain Sir, begins the lesson by defining factors of a number N as all numbers that divide N completely. He introduces the concept of the number of factors and the product of factors, setting the stage for the main topic.

  2. 2:00 – 5:00 02:00-05:00

    The instructor writes the title 'Concept of Multiples & Factors' on the whiteboard. He uses the number 12 as an example, writing '12 = {1, 2, 3, 4, 6, 12}' to list its factors. He then explains that the number of factors of 12 is 6 and that the product of its factors is 12^3, which is 1728. He also writes the formula for the number of factors: (a+1)(b+1)(c+1) for a number N = p^a * q^b * r^c.

  3. 5:00 – 10:00 05:00-10:00

    The instructor demonstrates the formula for the number of factors using the number 12. He shows the prime factorization of 12 as 2^2 * 3^1. Applying the formula, he calculates the number of factors as (2+1)(1+1) = 3 * 2 = 6. He then explains that the product of the factors of a number N is N^(number of factors / 2), which for 12 is 12^3. He also discusses the concept of infinite multiples and limited factors.

  4. 10:00 – 15:00 10:00-15:00

    The instructor presents a slide titled 'Number of Factors/Divisors' and reviews the basic formula for the number of factors of a number N, which is (a+1)(b+1)(c+1) where N = p^a * q^b * r^c. He then moves to a practice problem: 'The number A4531B where A & B are single digits, the given number is divisible by 72. Then the number of factors for A + B is'. He begins to solve it by factoring 72 as 2^3 * 3^2.

  5. 15:00 – 20:00 15:00-20:00

    The instructor continues solving the problem about the number A4531B. He determines that for the number to be divisible by 72, it must be divisible by both 8 and 9. He uses the divisibility rule for 8 (last three digits must be divisible by 8) to find that B must be 2. He then uses the divisibility rule for 9 (sum of digits must be divisible by 9) to find that A must be 3. He concludes that A + B = 5 and the number of factors of 5 is 2.

  6. 20:00 – 25:00 20:00-25:00

    The instructor presents a new problem: 'Let N = 162, let P be the smallest number multiplied to N such that N becomes a perfect square. Let Q be the smallest number multiplied to N such that N becomes a perfect cube. Find the product of factors of P+Q'. He begins by factoring 162 as 2 * 3^4. To make it a perfect square, he needs to multiply by 2, so P = 2. To make it a perfect cube, he needs to multiply by 2^2 * 3^2, so Q = 36.

  7. 25:00 – 30:00 25:00-30:00

    The instructor continues the problem with N=162. He calculates P = 2 and Q = 36, so P + Q = 38. He then needs to find the product of the factors of 38. He factors 38 as 2 * 19, so the number of factors is (1+1)(1+1) = 4. The product of the factors is 38^(4/2) = 38^2 = 1444. He then moves to the next problem.

  8. 30:00 – 35:00 30:00-35:00

    The instructor presents a problem: 'x is the smallest number such that x/2 is a perfect square and x/3 is a perfect cube. Find the number of divisors of x'. He sets up the equations x/2 = a^2 and x/3 = b^3. He then combines them to get x = 2a^2 = 3b^3. He deduces that x must be divisible by 2 and 3, so he lets x = 2^a * 3^b. He then uses the conditions to find that a must be odd and b must be even, and that a-1 must be divisible by 3 and b-1 must be divisible by 2.

  9. 35:00 – 40:00 35:00-40:00

    The instructor continues solving for x. He finds the smallest values for a and b that satisfy the conditions: a=3 and b=4. Therefore, x = 2^3 * 3^4 = 8 * 81 = 648. He then calculates the number of divisors of x as (3+1)(4+1) = 4 * 5 = 20.

  10. 40:00 – 45:00 40:00-45:00

    The instructor presents a new problem: 'A number is divided by 406 leaves remainder 115. What will be the remainder when it will be divided by 29?'. He writes the formula Dividend = Divisor * Quotient + Remainder, so n = 406q + 115. He then divides this expression by 29 to find the remainder. He calculates 406 / 29 = 14, so 406q is divisible by 29. He then finds the remainder of 115 / 29, which is 28.

  11. 45:00 – 50:00 45:00-50:00

    The instructor presents a problem: 'A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21. What is the remainder left, when twice the number is divided by 3D?'. He sets up the equations n = Dx + 8 and n = 3Dy + 21. He equates them to get Dx + 8 = 3Dy + 21, which simplifies to D(x - 3y) = 13. He then considers the possible values for D and x-3y, finding D=13 and x-3y=1. He then finds n = 13*1 + 8 = 21, so 2n = 42. Finally, he divides 42 by 3D = 39 to get a remainder of 3.

  12. 50:00 – 55:00 50:00-55:00

    The instructor presents a problem: 'If n is a natural number such that 10^100 < n < 10^101 and the sum of the digits on n is 2, then the number of values n can take is'. He explains that n is a 101-digit number. The sum of its digits is 2, so the only possibilities are a 1 followed by 100 zeros, or a 2 followed by 100 zeros, or a 1 followed by a 1 and then 99 zeros. He calculates the number of such numbers as 100 (for 1 followed by 1 and 99 zeros) + 1 (for 2 followed by 100 zeros) + 1 (for 1 followed by 100 zeros) = 102.

  13. 55:00 – 60:00 55:00-60:00

    The instructor presents a problem: 'The square root of 12345678987654321 is nnnnnn... upto p times, find the sum of n and p?'. He shows that the square root of 121 is 11, the square root of 12321 is 111, and the square root of 1234321 is 1111. He identifies the pattern: the square root of a number that reads 123...n...321 is a number with n ones. The given number is 12345678987654321, which has 9 digits in the middle, so the square root is 111111111, which is 9 ones. Therefore, n=1 and p=9, so n+p=10.

  14. 60:00 – 65:00 60:00-65:00

    The instructor continues the problem about the square root of 12345678987654321. He confirms that the number is a palindrome and that its square root is a number with 9 ones, which is 111111111. He then states that the sum of n and p is 1 + 9 = 10. He then moves to the next problem.

  15. 65:00 – 70:00 65:00-70:00

    The instructor presents a problem: 'If n is a natural number such that 10^100 < n < 10^101 and the sum of the digits on n is 2, then the number of values n can take is'. He explains that n is a 101-digit number. The sum of its digits is 2, so the only possibilities are a 1 followed by 100 zeros, or a 2 followed by 100 zeros, or a 1 followed by a 1 and then 99 zeros. He calculates the number of such numbers as 100 (for 1 followed by 1 and 99 zeros) + 1 (for 2 followed by 100 zeros) + 1 (for 1 followed by 100 zeros) = 102.

  16. 70:00 – 75:00 70:00-75:00

    The instructor continues the problem about the number of values n can take. He explains that n is a 101-digit number. The sum of its digits is 2, so the only possibilities are a 1 followed by 100 zeros, or a 2 followed by 100 zeros, or a 1 followed by a 1 and then 99 zeros. He calculates the number of such numbers as 100 (for 1 followed by 1 and 99 zeros) + 1 (for 2 followed by 100 zeros) + 1 (for 1 followed by 100 zeros) = 102.

  17. 75:00 – 80:00 75:00-80:00

    The instructor presents a problem: 'The square root of 12345678987654321 is nnnnnn... upto p times, find the sum of n and p?'. He shows that the square root of 121 is 11, the square root of 12321 is 111, and the square root of 1234321 is 1111. He identifies the pattern: the square root of a number that reads 123...n...321 is a number with n ones. The given number is 12345678987654321, which has 9 digits in the middle, so the square root is 111111111, which is 9 ones. Therefore, n=1 and p=9, so n+p=10.

  18. 80:00 – 81:02 80:00-81:02

    The video ends with a closing screen showing the 'KG' logo for Knowledge Gate and the website www.knowledgegate.in. The background is a dark, abstract design with glowing orange lines, signifying the end of the lecture.

This video is a structured and comprehensive lecture on the topic of number systems, specifically focusing on multiples and factors. The instructor begins with foundational definitions and formulas, using the number 12 as a primary example to illustrate the concepts of factors, multiples, and the formula for the number of factors. The core of the video is a series of practice problems that progressively increase in complexity, covering topics such as divisibility rules, finding the smallest multiplier to form a perfect square or cube, and solving remainder problems using the fundamental division algorithm. The lecture also includes a unique problem involving the square root of a palindromic number, demonstrating a pattern recognition skill. The overall teaching style is methodical, with clear step-by-step solutions, making it an effective resource for students preparing for competitive exams.

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