Concept of Reminders (Part 3)

Duration: 22 min

This video lesson is available to enrolled students.

Return to /learn/BIHAR-STET-COMPUTER-SCIENCE-COMPLETE-COURSE/mathematical-aptitude/number-system-bff2d7/concept-of-remainders/asset-concept-of-reminders-part-3 after enrolling

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 is a lecture on number systems, focusing on the concept of remainders in divisibility problems. The instructor, Yash Jain, begins by introducing the topic with a title slide and then presents two complex problems. The first problem asks for the remainder when the sum of cubes from 22^3 to 88^3 is divided by 110. The second problem involves finding the sum of remainders when the sum of seventh powers from 16^7 to 19^7 is divided by 5, 7, 14, and 35. The lecture progresses by explaining the mathematical principle that if a number is divisible by two coprime numbers, it is also divisible by their product. The instructor demonstrates this by pairing terms in the first sum (22^3 + 88^3, 23^3 + 87^3, etc.) and showing that each pair is divisible by 110, thus the entire sum is divisible by 110, resulting in a remainder of 0. The second problem is solved by noting that the sum of the numbers 16, 17, 18, and 19 is 70, which is divisible by 5, 7, 14, and 35, and since the exponent 7 is odd, the sum of their seventh powers is also divisible by these numbers, leading to a sum of remainders of 0. The video uses a digital whiteboard for all explanations and includes a final thank you screen.

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, a Knowledge Gate Educator. The slide features a colorful background with mathematical symbols and the tagline 'The mysterious world of numbers...'. The instructor, visible in a small window, introduces the topic, setting the stage for a lesson on number systems and remainders.

  2. 2:00 – 5:00 02:00-05:00

    The instructor presents two problems on the screen. The first is: 'If (22)^3 + (23)^3 + (24)^3 + ... + (87)^3 + (88)^3 is divided by 110, then the remainder will be __?'. The second is: 'If (16)^7 + (17)^7 + (18)^7 + (19)^7 is divided by 5, 7, 14 and 35 and remainders obtained are R1, R2, R3 and R4 respectively. Find R1 + R2 + R3 + R4.'. The instructor begins to analyze the first problem, writing out the sum and noting the range of numbers from 22 to 88.

  3. 5:00 – 10:00 05:00-10:00

    The instructor explains the strategy for the first problem. He identifies that the sum is from 22 to 88, which is an arithmetic sequence. He calculates the number of terms as 67. He then pairs the terms from the beginning and end of the sequence: (22^3 + 88^3), (23^3 + 87^3), and so on. He writes the formula for the nth term of an arithmetic sequence, an = a + (n-1)d, and calculates that 88 = 22 + (n-1)1, finding n=67. He then shows that 22+88=110, 23+87=110, etc., and notes that since the exponent 3 is odd, the sum of cubes a^n + b^n is divisible by a+b when n is odd.

  4. 10:00 – 15:00 10:00-15:00

    The instructor draws a diagram on the whiteboard to illustrate the divisibility rule for a^n + b^n. He shows that if n is odd, a^n + b^n is divisible by a+b. He writes the formula a^n + b^n = (a+b)(a^(n-1) - a^(n-2)b + ... + b^(n-1)). He applies this to the first problem, stating that since 22+88=110, 23+87=110, and so on, and the exponent 3 is odd, each pair (22^3 + 88^3), (23^3 + 87^3), etc., is divisible by 110. He then notes that there are 33 such pairs and one middle term, 55^3, which is also divisible by 110 because 55 is a factor of 110. Therefore, the entire sum is divisible by 110, and the remainder is 0.

  5. 15:00 – 20:00 15:00-20:00

    The instructor moves to the second problem. He writes the sum N = 16^7 + 17^7 + 18^7 + 19^7. He calculates the sum of the bases: 16+17+18+19 = 70. He notes that 70 is divisible by 5, 7, 14, and 35. He then applies the same principle: since the exponent 7 is odd, the sum of the seventh powers is divisible by the sum of the bases, which is 70. Therefore, N is divisible by 5, 7, 14, and 35, and the remainders R1, R2, R3, and R4 are all 0. The sum R1 + R2 + R3 + R4 is 0.

  6. 20:00 – 22:25 20:00-22:25

    The video concludes with a final screen. A red and blue neon-style box appears with the text 'THANK YOU FOR WATCHING'. A lightning bolt effect splits the box down the middle, and the video ends. The instructor's voice is not heard in this final segment.

The video provides a clear and structured lesson on solving remainder problems using the properties of divisibility. The core concept demonstrated is that for an odd exponent n, the sum a^n + b^n is divisible by a+b. This principle is applied to two different problems. In the first, the sum of cubes from 22 to 88 is shown to be divisible by 110 by pairing terms that sum to 110. In the second, the sum of seventh powers from 16 to 19 is shown to be divisible by 70, and since 70 is a multiple of 5, 7, 14, and 35, the sum is divisible by all of them, resulting in a sum of remainders of 0. The lecture effectively uses visual aids and step-by-step reasoning to teach a powerful mathematical shortcut.

Loading lesson…