Concept of Reminders (Part 4)

Duration: 18 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. Mathematical Aptitude / गणितीय अभिक्षमता: Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Divisibility Rules / विभाज्यता के नियम, Percentage / प्रतिशत, Ratio and Proportion / अनुपात और समानुपात, Average / औसत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Time and Work / समय और कार्य, Solid Mensuration / घन क्षेत्रमिति, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Time, Speed and Distance / समय, चाल और दूरी, Age Problems / आयु संबंधी प्रश्न, Mixture and Alligation / मिश्रण और एलिगेशन, Algebra / बीजगणित, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Pipe and Cistern / नल और टंकी, Trigonometry / त्रिकोणमिति, Statistics / सांख्यिकी, Data Interpretation / आँकड़ा निर्वचन, Arithmetic / अंकगणित, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ
  3. Logical Reasoning / तार्किक तर्कशक्ति: Series / श्रेणी, Coding-Decoding / कूट लेखन एवं कूट वाचन, Analogy and Classification / सादृश्यता एवं वर्गीकरण, Blood Relations / रक्त संबंध, Direction and Distance / दिशा एवं दूरी, Order and Ranking / क्रम एवं रैंकिंग, Non-Verbal Reasoning / अशाब्दिक तर्क, Seating Arrangement and Puzzles / बैठक व्यवस्था एवं पहेलियाँ, Syllogisms / न्यायवाक्य, Venn Diagrams, Syllogism and Inequalities / वेन आरेख, न्याय वाक्य एवं असमानता, Mathematical Operations and Missing Numbers / गणितीय संक्रियाएँ एवं लुप्त संख्या, Alphabet and Number Test / वर्णमाला एवं संख्या परीक्षण, Statement-Based Reasoning / कथन आधारित तार्किक विवेचन, Analytical Reasoning (Counting Figures Reasoning) / विश्लेषणात्मक तर्क (आकृति गणना तर्क), Cubes, Dice and Figure Counting / घन, पासा एवं आकृतियों की गिनती, Calendar and Clock / कैलेंडर एवं घड़ी, Clock / घड़ी
  4. General Knowledge / सामान्य ज्ञान: Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान, Chemistry / रसायन विज्ञान, Biology / जीव विज्ञान, History / इतिहास, Geography / भूगोल, Polity / राजव्यवस्था, Indian Economy / भारतीय अर्थव्यवस्था, Current Affairs / समसामयिकी, Static General Knowledge / स्थैतिक सामान्य ज्ञान, State-Specific General Knowledge / राज्य विशेष सामान्य ज्ञान
  5. Art of Teaching / शिक्षण कला: Teaching-Learning Process and Classroom Management / शिक्षण-अधिगम प्रक्रिया एवं कक्षा प्रबंधन, Learners & Learning Process / अधिगमकर्ता और अधिगम प्रक्रिया, Factors Affecting Teaching / शिक्षण को प्रभावित करने वाले कारक, Teaching Methods and Approaches / शिक्षण विधियाँ एवं उपागम, Microteaching and Classroom Communication / सूक्ष्म शिक्षण एवं कक्षा संप्रेषण, Teaching Aids and Educational Technology / शिक्षण सहायक सामग्री एवं शैक्षिक तकनीकी, Assessment and Evaluation / आकलन एवं मूल्यांकन, Teacher: Qualities, Professional Ethics and Development / शिक्षक: गुण, व्यावसायिक नैतिकता एवं विकास, Educational Policies, Acts and Administration / शैक्षिक नीतियाँ, अधिनियम एवं प्रशासन, Curriculum, Arts and Co-curricular Areas / पाठ्यचर्या, कला एवं सह-शैक्षिक क्षेत्र, Guidance and Counselling / निर्देशन एवं परामर्श, Education of Children with Disabilities / दिव्यांग बच्चों की शिक्षा, Micro-Teaching & Teaching Skills / सूक्ष्म शिक्षण और शिक्षण कौशल, Lesson Planning / पाठ योजना
  6. Environmental Science / पर्यावरण विज्ञान: Environment / पर्यावरण
  7. Unit 1 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  8. Unit 2 | COA: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer
  9. Unit 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  10. Unit 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  11. Unit 4 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  12. Unit 5 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  13. Unit 6 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Transaction Management, Concurrency Control
  14. Unit 7 | 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
  15. Unit 8 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  16. Unit 9 | Object Oriented Programming: OOPS with C++
  17. Unit 10 | Web Development: HTML Basics, CSS, JavaScript-Basics, XML, Node.js, Git & Github, PHP
  18. Unit 11 | 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
  19. Unit 12 | IoT: Emerging Tech Trends, Cloud Computing, Computer Networks, Internet of Things
  20. Unit 13 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
  21. Unit 14 | E-Commerce: Electronic Data Interchange and E-Commerce, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Physical Security and Cryptography Basics, Cyber Safety and Security
  22. Unit 15 | Multimedia: Multimedia
  23. Unit 16 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  24. Full Length Mock Tests — General Paper:
  25. Full Length Mock Tests — Computer Science (Paper II):
  26. Full Length Mock Test – General + Computer Science:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video, presented by Yash Jain from Knowledge Gate, is a comprehensive tutorial on solving remainder problems in number systems, a common topic in competitive exams. The video begins with an introduction to the concept of remainders, using a simple division example (7 ÷ 2 = 3 R1) to establish the foundational idea. The main content consists of two complex problems. The first problem involves the sum of the reciprocals of the first 13 natural numbers, expressed as a fraction x/13!. The instructor demonstrates that to find the remainder when x is divided by 11, one must analyze the numerator of the sum after a common denominator is applied. The key insight is that for any term where the denominator is not divisible by 11, the corresponding numerator term will be divisible by 11, leaving only the term where the denominator is 11 as the only non-zero contributor to the remainder. The second problem asks for the remainder when N = (1! + 2! + 3! + ... + 1000!)^40 is divided by 10. The instructor explains that for n ≥ 5, n! is divisible by 10, so all terms from 5! onwards are 0 modulo 10. This simplifies the sum to (1! + 2! + 3! + 4!)^40 = (1 + 2 + 6 + 24)^40 = 33^40. The final step is to find the remainder of 33^40 when divided by 10, which is equivalent to finding the last digit of 33^40. The video concludes with a summary of the problem-solving techniques, emphasizing the use of modular arithmetic and the simplification of large expressions by identifying terms that become zero under the given modulus.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card for 'NUMBER SYSTEM' and then transitions to a presentation slide. The slide features the title 'NUMBER SYSTEM' and the tagline 'The mysterious world of numbers...'. The instructor, Yash Jain, is visible in a small window. He introduces the topic of the 'Concept of Remainders' and provides a simple example on the board: '7 ÷ 2 = 3 R1', with an arrow pointing to the '1' and labeling it 'Remainder'. This establishes the basic definition of a remainder as the leftover part of a division.

  2. 2:00 – 5:00 02:00-05:00

    The video presents the first problem: 'The expression sigma(1/n) from n=1 to 13 can also be written as x/13!. What would be the remainder if x is divided by 11?'. The instructor begins to solve this by writing the sum as 1/1 + 1/2 + 1/3 + ... + 1/13. He then multiplies the entire sum by 13! to get x, which results in the expression x = 13!/1 + 13!/2 + 13!/3 + ... + 13!/13. He explains that to find x mod 11, he needs to evaluate each term in the sum modulo 11.

  3. 5:00 – 10:00 05:00-10:00

    The instructor analyzes the terms of the sum x = 13!/1 + 13!/2 + ... + 13!/13 modulo 11. He explains that 13! is divisible by 11, so 13! ≡ 0 (mod 11). For any term where the denominator is not 11, the numerator 13! is divisible by 11, making the entire term 0 modulo 11. The only term that is not divisible by 11 is the one where the denominator is 11, which is 13!/11. He simplifies this term to 13 × 12 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 13 × 12 × 10!. He then states that the remainder is the value of 13 × 12 × 10! modulo 11, which he will calculate in the next step.

  4. 10:00 – 15:00 10:00-15:00

    The instructor calculates the remainder of 13 × 12 × 10! when divided by 11. He uses the property that (p-1)! ≡ -1 (mod p) for a prime p (Wilson's Theorem). Since 11 is prime, 10! ≡ -1 (mod 11). He then simplifies 13 × 12 modulo 11: 13 ≡ 2 (mod 11) and 12 ≡ 1 (mod 11). Therefore, the expression becomes 2 × 1 × (-1) = -2. Since the remainder must be positive, he adds 11 to get 9. The final answer for the first problem is 9. He then transitions to the second problem.

  5. 15:00 – 18:29 15:00-18:29

    The second problem is introduced: 'What is the remainder when N = (1! + 2! + 3! + ... + 1000!)^40 is divided by 10?'. The instructor explains that for n ≥ 5, n! is divisible by 10 (since it contains both 2 and 5 as factors), so n! ≡ 0 (mod 10). This means all terms from 5! to 1000! are 0 modulo 10. The sum simplifies to (1! + 2! + 3! + 4!)^40 = (1 + 2 + 6 + 24)^40 = 33^40. The problem now is to find 33^40 mod 10, which is the last digit of 33^40. He notes that the last digit of 33 is 3, so he needs to find the last digit of 3^40. He then calculates the pattern of the last digit of powers of 3: 3^1=3, 3^2=9, 3^3=7, 3^4=1, and the cycle repeats every 4. Since 40 is divisible by 4, the last digit is 1. The final answer is 1. The video ends with a 'Thank You for Watching' screen.

The video provides a clear and structured lesson on applying modular arithmetic to solve complex remainder problems. It begins with a fundamental concept and progresses to two distinct, challenging problems. The first problem demonstrates the power of simplification by identifying that only one term in a large sum contributes to the remainder when the modulus is a prime number, leveraging Wilson's Theorem. The second problem illustrates the technique of reducing a sum by recognizing that terms beyond a certain point become zero modulo the divisor. The core teaching method is the step-by-step breakdown of complex expressions into manageable parts, using properties of factorials and modular arithmetic to arrive at the solution. The progression from a simple example to two advanced problems effectively builds the viewer's problem-solving skills for competitive exams.

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