Concept of Reminders (Part 3)

Duration: 22 min

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Module outline

  1. 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, Relational Calculus, Transaction Management, Concurrency Control
  2. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  3. Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  4. Computer Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  5. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Virtual Memory, Disc Scheduling, File Management, Memory Management, Threads & Process Creation
  6. Computer Networks: Introduction to CN, 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, Network Security, Hardware Basics
  7. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  8. Algorithms: Algorithm Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Time Complexity Analysis
  9. 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, Complexity Theory
  10. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  11. C language: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums
  12. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. Emerging Trends & AI: Emerging Tech Trends, Artificial Intelligence, Cloud Computing
  14. Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing
  15. Aptitude: Percentage, Ratio and Proportion (Ratios), Logarithm, HCF LCM, Divisibility Rules, Average, Sequence and Series (Series), Number System, Powers and Exponents (Surds and Indices), Algebra, Permutation and Combination, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Speed Time and Distance, Mixture and Alligation, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Statistics, Data Interpretation, Arithmetic, Speed Mathematics and Basic Mathematics, TCS NQT Advanced Quantitative Ability, Gamified / Game Based Aptitude, Linear Algebra, Trigonometry
  16. Reasoning: Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), 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
  17. English (Verbal Ability): Vocabulary, Noun, Pronoun, Adjectives, Preposition, Articles, Direct and Indirect Speech, Tenses, Conjunction, Subject Verb Agreement (Verb Noun Agreement), Modals, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Sentence Construction, Active Passive Voice (Voice), Determiner, Facts, Inference and Judgements, Adverb, Interjection, Verb, English Writing Ability
  18. Engineering Mathematics: Calculus, Vectors
  19. GATE Live Class Recordings 2026: GATE 2026 Live Class
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.

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