Number System (Quick Revision & Practice Questions)

Duration: 1 hr 21 min

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, Logarithm, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, प्रतिशत / Percentage, औसत / Average, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, Statistics, Probability, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समय और कार्य / Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy, 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
  3. Paper-1 & 2 | Data Interpretation: आँकड़ा निर्वचन / Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, Data Sufficiency, अशाब्दिक तर्क / Non-Verbal Reasoning, 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, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Data Arrangement, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: आँकड़ों की पर्याप्तता एवं निर्णय क्षमता / Data Sufficiency and Decision Making
  7. Paper-1 | General Science: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, समसामयिकी / Current Affairs
  9. Paper-2 | Fundamentals of Computer: Basics of COA, Number System, Floating Point Rep, Number Representation
  10. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits
  11. Paper-2 | Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Linux OS, Distributed Systems
  12. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  13. Paper-2 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  14. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  15. Paper 2 | Oops, C++, Java: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  16. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  17. Paper 2 | Emerging Trends and AI: Emerging Tech Trends, कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, कंप्यूटर नेटवर्क / Computer Networks
  18. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Advanced Algorithms
  19. Paper 2 | Data Communication and Network Security: 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, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security, Ethical Hacking
  20. Paper-2 I Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  21. Paper-2 | Computer Organization and Architecture: Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations
  22. Paper-2 | Web Development: JavaScript-Basics, HTML Basics, CSS, XML
  23. Pedagogy: वृद्धि और विकास / Growth and Development, Concept of Pedagogy, संज्ञानात्मक प्रक्रियाएँ / Cognitive Processes, विकास के सिद्धांत / Theories of Development, समावेशी शिक्षा / Inclusive Education, Experiential Pedagogy, समाजीकरण और जेंडर / Socialisation and Gender, National Education Policy (NEP) 2020
  24. Live Sessions: RSSB Live Sessions
  25. RSSB Paper 1 - Full Mock Tests:
  26. RSSB Paper 2 - Full Mock Tests:
  27. SCI Previous Year Papers:
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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