Arithmetic - Part 2

Duration: 27 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 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Combinational Circuit, Sequential Circuits
  10. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Calculus, Relational Algebra, SQL, NoSQL
  11. Paper-2 | Data Structures & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Algorithm Analysis, Sorting Algorithms, Intro to Compilers, Hashing
  12. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, Data Link Layer - Ethernet, DLL: Error Control, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Application Layer, Hardware basics, Network Security, Ethical Hacking
  13. Paper-2 | Operating Systems: Introduction to OS, Process Management, Memory Management, File Management, Deadlock
  14. Paper-2 | Computer Organization and Architecture: 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, Number System, Number Representation
  15. Paper 2 | System Analysis and Design: Fundamentals of Systems and Information Systems, Fundamentals of Software Engineering, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance, Software Testing
  16. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Paper 2 | OOPS , C++ , JAVA: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  18. 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
  19. Emerging Trends and AI: Emerging Tech Trends, कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection
  20. Paper-2 | Data Processing (Ms-Office): MS Office Applications, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), प्रेज़ेंटेशन (MS PowerPoint) / Presentation Software (MS PowerPoint)
  21. Paper-2 | Internet and Web Technologies: HTML Basics, CSS, XML, JavaScript-Basics, Internet Fundamentals, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, Terms & Abbreviations, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर नेटवर्क / Computer Networks
  22. Paper 2 | Pedagogy: वृद्धि और विकास / Growth and Development, विकास के सिद्धांत / Theories of Development, Concept of Pedagogy, समावेशी शिक्षा / Inclusive Education, Experiential Pedagogy, आकलन और मूल्यांकन / Assessment and Evaluation, संज्ञानात्मक प्रक्रियाएँ / Cognitive Processes, समाजीकरण और जेंडर / Socialisation and Gender, National Education Policy (NEP) 2020
  23. Live Classes: RSSB Live Sessions
  24. Paper 1 - Full Mock Tests:
  25. Paper 2 - Full Mock Tests:
  26. BCI Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a lecture on solving a problem related to finding the number of common terms between two arithmetic progressions (APs). The instructor, Yash Jain Sir from Knowledge Gate Eduventures, begins by presenting a question from the TCS NQT 2020 exam: "Find the number of common terms" between the sequences A) 17, 21, 25, 29, ..., 417 and B) 16, 21, 26, 31, ..., 466. The core of the lesson is a step-by-step algorithm. First, the common difference (d) of each sequence is identified: d1 = 4 for sequence A and d2 = 5 for sequence B. The first common term is found to be 21. The key insight is that the common terms form a new arithmetic progression with a common difference equal to the Least Common Multiple (LCM) of the original two differences, which is LCM(4, 5) = 20. The final step is to use the formula for the nth term of an AP, n = (l - a) / d + 1, where 'l' is the last common term, 'a' is the first common term, and 'd' is the common difference of the new sequence. The instructor demonstrates this by calculating the last common term as 417, then applying the formula: n = (417 - 21) / 20 + 1 = 396 / 20 + 1 = 19.8 + 1, which is not an integer, indicating a need to find the actual last common term. The video also includes a brief, unrelated segment on a different topic, 'THE BADMAAASH BACCHHA', which appears to be a mnemonic or a separate example, but the main focus remains on the AP problem.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide showing a man writing on a green chalkboard filled with mathematical equations, with the word "ARITHMETIC" at the bottom. This transitions to a black screen with the title "PLAYING WITH AP/GP" in red text. The instructor, Yash Jain Sir, is introduced in a small window, and the video is identified as copyrighted content from Knowledge Gate Eduventures.

  2. 2:00 – 5:00 02:00-05:00

    The main problem is presented on a blackboard: "QUE: FIND THE NUMBER OF COMMON TERMS". The two sequences are given as A) 17 21 25 29 .... 417 and B) 16 21 26 31 .... 466. The instructor states the question was asked in TCS NQT 2020. The video shows the sequences being written out, with the first common term, 21, being highlighted.

  3. 5:00 – 10:00 05:00-10:00

    The instructor begins to solve the problem. He identifies the common difference of sequence A as 4 (21-17) and sequence B as 5 (21-16). He explains that the common terms will form a new AP with a common difference equal to the LCM of 4 and 5, which is 20. He writes the formula for the nth term of an AP: a_n = a + (n-1)d. He then identifies the first common term as 21 and the last common term as 417, which is the last term of sequence A.

  4. 10:00 – 15:00 10:00-15:00

    The instructor writes the formula for the number of terms: n = (l - a) / d + 1. He substitutes the values: l = 417, a = 21, d = 20. He calculates (417 - 21) / 20 + 1 = 396 / 20 + 1 = 19.8 + 1 = 20.8. He notes that this is not an integer, which is a problem. He then realizes that 417 might not be a common term and needs to find the actual last common term that is less than or equal to 417.

  5. 15:00 – 20:00 15:00-20:00

    The instructor corrects the approach. He states that the last common term must be a multiple of 20, starting from 21. He calculates the last common term by finding the largest multiple of 20 that is less than or equal to 417. He finds that 400 is the largest such number. He then applies the formula: n = (400 - 21) / 20 + 1 = 379 / 20 + 1 = 18.95 + 1 = 19.95. He realizes this is still not an integer. He then correctly identifies that the last common term is 401, which is 21 + 19*20. He calculates n = (401 - 21) / 20 + 1 = 380 / 20 + 1 = 19 + 1 = 20. The number of common terms is 20.

  6. 20:00 – 25:00 20:00-25:00

    The video transitions to a different topic, titled "THE BADMAAASH BACCHHA". The instructor draws a circle and writes numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 inside it. He then writes a formula: (a+b)-1, and applies it to the numbers 2 and 3, getting (2+3)-1 = 4. He then writes (5+1)-1 = 5, and 6-1-1 = 4. This appears to be a separate example or a mnemonic for a different concept, possibly related to counting or combinations.

  7. 25:00 – 26:42 25:00-26:42

    The video ends with a final slide that says "THANKS FOR WATCHING" over a blue, abstract background with mathematical symbols. The instructor's video window is still visible in the corner, and the copyright notice for Knowledge Gate Eduventures remains at the bottom.

The video provides a clear, step-by-step solution to a common problem in arithmetic progression. It begins by identifying the key components of the two given sequences: their first terms, common differences, and last terms. The central concept is that the common terms of two APs form a new AP, whose common difference is the LCM of the original two differences. The instructor correctly identifies the first common term and then applies the standard formula for the number of terms in an AP. The video demonstrates a common pitfall: assuming the last term of the original sequence is also a common term, and shows the correct method of finding the actual last common term by checking the sequence of common terms. The final answer is 20. The latter part of the video, on 'THE BADMAAASH BACCHHA', seems to be an unrelated example or a mnemonic, but the core lesson on APs is well-structured and pedagogically sound.

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