Arithmetic - Part 2

Duration: 27 min

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Inside: a video lesson and guided study material.

Module outline

  1. हिंदी / Hindi — भाषा खंड: भाषा, लिपि और वर्ण-विचार, संधि, शब्द-स्रोत और शब्द-रचना, समास, शब्द-भेद: विकारी और अविकारी, लिंग, वचन, कारक, काल और वाच्य, वाक्य-विचार और शुद्ध लेखन, शब्द-भंडार, रस, छंद, अलंकार और शब्द-शक्ति, अपठित बोध, हिंदी शिक्षणशास्त्र
  2. संस्कृत / Sanskrit — भाषा खंड: वर्ण, उच्चारण, सन्धि, शब्दरूप, धातुरूप, कारक-विभक्ति, समासप्रकरणम्, प्रत्यय, उपसर्गाः एवं अव्ययानि, वाच्य, सङ्ख्या, अव्यय, अपठित अवबोधन, वर्णविचारः एवं संज्ञाप्रकरणम्, सन्धिप्रकरणम्, शब्दरूपाणि, धातुरूपाणि, कारकाणि एवं विभक्तयः, संख्याज्ञानम्, शब्दज्ञानम् एवं अनुवादः, प्रत्ययप्रकरणम्, वाच्यप्रकरणम्, अपठितावबोधनम्
  3. अंग्रेज़ी / English — भाषा खंड: Parts of Speech, Nouns and Pronouns, Articles, Determiners and Adjectives, Verbs and Modals, Adverbs, Prepositions and Conjunctions, Tenses and Subject–Verb Agreement, Sentence Structure, Voice and Narration, Vocabulary, Sentence Correction and Writing Skills, Reading Comprehension, Sounds, Spelling and Word Formation, Pedagogy of English Language, Poetry and English Literature
  4. सामान्य ज्ञान एवं समसामयिक घटनाएँ / General Knowledge & Current Affairs — 25 प्रश्न: Static GK — Books & Authors, Awards, Sports, Important Days, Firsts, Organisations, Culture & Arts, Current Affairs — National, Current Affairs — International, Economy & Government Schemes (current), Uttar Pradesh, History, Polity, Indian Economy, Static General Knowledge, State Wise GK, GK- Current Affairs, इतिहास एवं राष्ट्रीय आंदोलन / History & National Movement, भूगोल एवं पर्यावरण / Geography & Environment, भारतीय राजव्यवस्था एवं शासन / Indian Polity & Governance, भारतीय अर्थव्यवस्था एवं विकास / Indian Economy & Development, सामान्य विज्ञान एवं प्रौद्योगिकी / General Science & Technology, कला, संस्कृति एवं विरासत / Art, Culture & Heritage, भारतीय समाज, शिक्षा एवं जनसांख्यिकी / Indian Society, Education & Demography, स्थिर सामान्य ज्ञान / Static General Knowledge, पुरस्कार एवं सम्मान / Awards & Honours, उत्तर प्रदेश / Uttar Pradesh, खेल एवं प्रतियोगिताएँ / Sports & Competitions, सरकारी योजनाएँ एवं सार्वजनिक कार्यक्रम / Government Schemes & Public Programmes, समसामयिकी एवं अंतरराष्ट्रीय संबंध / Current Affairs & International Relations
  5. गणित / Mathematics — 16 प्रश्न: Number System & Place Value, Whole Numbers & Four Operations, Factors, Multiples, Divisibility, HCF & LCM, Fractions & Decimals, Integers & Rational Numbers, Exponents, Powers, Squares, Cubes & Roots, Algebra — Expressions, Identities & Linear Equations, Ratio, Proportion & Percentage, Measurement — Length, Mass, Capacity, Time, Money, Commercial Arithmetic (Profit-Loss-Discount, SI & CI), Average, Ages & Mixtures, Time & Work, Speed-Time-Distance, Geometry — Shapes, Lines & Angles, Symmetry, Spatial Understanding, Geometry — Triangles, Quadrilaterals, Circles, Congruence & Constructions, Mensuration — Perimeter, Area, Surface Area, Volume, Data Handling, Graphs & Probability, Coordinates & Graphs, Higher Mathematics — Trigonometry, Quadratics, Polynomials, Progressions, Statistics, Logarithms, Number System, Arithmetic, Divisibility Rules, HCF LCM, Powers and Exponents (Surds and Indices), Algebra, Ratio and Proportion (Ratios), Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Mensuration and Geometry, Statistics, संख्या पद्धति एवं अंकगणितीय आधार / Number System & Arithmetic Foundations, गुणनखंड, विभाज्यता एवं HCF–LCM / Factors, Divisibility & HCF–LCM, अनुपात, समानुपात एवं प्रतिशत / Ratio, Proportion & Percentage, व्यावसायिक अंकगणित / Commercial Arithmetic, औसत, आयु एवं मिश्रण / Averages, Ages & Mixtures, समय, कार्य एवं गति / Time, Work & Motion, बीजगणित एवं समीकरण / Algebra & Equations, ज्यामिति एवं स्थानिक बोध / Geometry & Spatial Understanding, मापन एवं क्षेत्रमिति / Measurement & Mensuration, डेटा प्रबंधन, सांख्यिकी एवं प्रायिकता / Data Handling, Statistics & Probability, निर्देशांक, त्रिकोणमिति एवं उच्चतर गणित / Coordinates, Trigonometry & Higher Mathematics, गणित शिक्षाशास्त्र / Mathematics Pedagogy
  6. विज्ञान / Science — 8 प्रश्न: Food, Nutrition & Components of Food, Plants — Nutrition, Transport, Reproduction, Animals & Human Body — Systems, Organs, Nutrition, Health, Diseases, Microorganisms & Hygiene, Cell, Tissues & Classification of Living Beings, Reproduction & Adolescence, Physical Quantities, Units & Measurement, Materials, Matter, Mixtures & Separation, Atoms, Molecules & Structure of Matter, Elements, Compounds, Acids-Bases-Salts, Metals & Non-metals, Physical & Chemical Changes, Combustion, Fuels, Carbon & Organic Compounds, Motion, Force, Pressure & Friction, Heat & Temperature, Light, Shadows, Mirrors & Lenses, Work, Energy & Power, Sound, Electricity & Magnetism, Earth, Universe & Solar System, Natural Resources, Environment, Ecosystem & Pollution, Science & Technology in Daily Life (inventions, space, defence), Biology, Chemistry, Physics, वैज्ञानिक आधार, मापन और प्रौद्योगिकी / Scientific Foundations, Measurement & Technology, भोजन, पोषण एवं स्वास्थ्य / Food, Nutrition and Health, पदार्थ और दैनिक उपयोग की सामग्री / Matter & Materials of Daily Use, रासायनिक अभिक्रियाएँ, अम्ल, क्षार एवं लवण / Chemical Reactions, Acids, Bases and Salts, बल, दाब, कार्य एवं ऊर्जा / Force, Pressure, Work and Energy, प्रकाश / Light, विद्युत एवं चुंबकत्व / Electricity and Magnetism, सजीव जगत: वर्गीकरण, कोशिका एवं ऊतक / Living World: Classification, Cell and Tissues, पादपों में पोषण, परिवहन एवं जनन / Plants: Nutrition, Transport and Reproduction, मानव शरीर एवं अंग तंत्र / Human Body and Organ Systems, पर्यावरण एवं पारिस्थितिकी / Environment and Ecology, विज्ञान शिक्षण और शिक्षाशास्त्र / Science Pedagogy
  7. पर्यावरण एवं सामाजिक अध्ययन / Environment & Social Studies — 8 प्रश्न: Environment Conservation, Waste & Pollution, Natural Disasters & Safety, Water (sources, conservation), Air, Weather, Sky & Seasons, यात्रा, परिवहन और संचार / Travel, Transport and Communication, Festivals, Culture & Heritage (India), Food & Nutrition, Health & Hygiene, Plants (types, parts, uses), Animals (habitats, features, care), History — Sources, Prehistory & Harappan Civilisation, History — Vedic Age, Mahajanapadas, Religions (Buddhism/Jainism), History — Mauryas, Guptas & Post-Gupta Kingdoms, History — Medieval India (Sultanate, Mughals, Regional Kingdoms, Bhakti-Sufi), History — Modern India & Colonial Rule, History — Indian National Movement (1857–1947), History — India Since Independence, Geography — Earth, Globe, Maps, Latitudes-Longitudes, Geography — Landforms, Atmosphere, Hydrosphere, Climate, Natural Vegetation & Biomes, Geography — Physical & Political India (rivers, mountains, soils, vegetation, climate), Geography — Resources, Agriculture, Industries, Transport, Geography — World (continents, countries, oceans), Geography — Population, Settlements & Census, Polity — Democracy, Diversity, Social Justice & Gender, Polity — Constitution, Preamble, Fundamental Rights & Duties, DPSP, Polity — Union & State Government, Parliament, Judiciary, Elections, Polity — Local Government (Panchayati Raj, Urban bodies), Polity — International Relations & Organisations, Economy — Basic Concepts, Money, Banking, Budget, Schemes, Economy — Consumer Rights & Protection, Geography, Environment, परिवार, मित्र और समुदाय / Family, Friends and Community, पौधे / Plants, जंतु / Animals, भोजन और पोषण / Food and Nutrition, जल / Water, आवास / Shelter, मानचित्र, दिशाएँ और भारत / Maps, Directions and India, हम क्या बनाते और करते हैं / Things We Make and Do, पृथ्वी, आकाश और आपदाएँ / Earth, Sky and Disasters, पर्यावरण, पारिस्थितिकी और वन्यजीव / Environment, Ecology and Wildlife, प्राकृतिक संसाधन, प्रदूषण और जलवायु परिवर्तन / Natural Resources, Pollution and Climate Change, पर्यावरण अध्ययन का शिक्षणशास्त्र / Pedagogy of Environmental Studies
  8. शिक्षण कौशल / Teaching Skills — 8 प्रश्न: Nature, Objectives & Characteristics of Teaching, Learners & Learning Process, Factors Affecting Teaching, Classroom Management & Communication, Teaching-Learning Aids & ICT Integration, Curriculum & School Environment, Lesson Planning, Micro-Teaching & Teaching Skills, Evaluation, Assessment & Measurement, Inclusive Education & Special Needs, Policies, Acts & Contemporary Issues
  9. बाल मनोविज्ञान / Child Psychology — 8 प्रश्न: Concept of Pedagogy, Psychology, Child Development, Theories, Personality Development, Individual Differences, Learning and Motivation, Understanding Diverse Learners, Inclusive Education, Teaching-Learning Process, Teaching Methods & Strategies, Experiential Pedagogy, Assessment & Evaluation, National Education Policy (NEP) 2020, Curriculum Framework & Reforms, Miscellaneous Topics
  10. जीवन कौशल, प्रबन्धन एवं अभिवृत्ति / Life Skills, Management & Attitude — 8 प्रश्न: Professional Development & Ethics, Guidance, Counselling & Mental Health, Mental Health & Life Skills
  11. तार्किक ज्ञान / Logical Reasoning — 5 प्रश्न: Number/Alphabet Test, Mathematical Operations, Cubes & Dices, Inequality, Selection Decision Table (Decision Making), Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Western Logic, 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, Venn Diagram, Syllogism, Analogy, Ranking, Order and Sequence, Mirror & Water Image, Embedded/Figure Completion, Paper Folding & Cutting, Data Interpretation, वर्णमाला और श्रृंखला / Alphabet and Series, सादृश्य और वर्गीकरण / Analogy and Classification, कूटलेखन और कूटवाचन / Coding and Decoding, रक्त संबंध, दिशा और क्रम / Blood Relations, Directions and Order, गणितीय संक्रिया और संख्या पहेली / Mathematical Operations and Number Puzzles, वेन आरेख और तार्किक निगमन / Venn Diagrams and Logical Deduction, बैठक व्यवस्था और तार्किक पहेली / Seating Arrangements and Logical Puzzles, कैलेंडर और घड़ी / Calendars and Clocks, कथन आधारित तर्क और निर्णय / Statement Reasoning and Decisions, अशाब्दिक तर्क / Non-Verbal Reasoning, घन और पासा / Cubes and Dice, तर्कशक्ति का शिक्षण / Pedagogy of Reasoning
  12. सूचना तकनीकी / Information Technology — 4 प्रश्न: Terms & Abbreviations, MS Office Applications, Keyboard Shortcuts, Emerging Tech Trends, Digital India & e-Gov, कंप्यूटर मूलतत्त्व / Computer Fundamentals, कंप्यूटर आर्किटेक्चर और डिजिटल लॉजिक / Computer Architecture & Digital Logic, ऑपरेटिंग सिस्टम और फ़ाइल प्रबंधन / Operating Systems & File Management, वर्ड प्रोसेसिंग / Word Processing, स्प्रेडशीट और डेटा प्रस्तुतीकरण / Spreadsheets & Data Presentation, प्रस्तुतीकरण और ऑफिस उपकरण / Presentations & Office Tools, इंटरनेट, नेटवर्क और संचार / Internet, Networks & Communication, साइबर सुरक्षा, कानून और डिजिटल नागरिकता / Cyber Safety, Law & Digital Citizenship, डिजिटल सेवाएँ और ICT शिक्षा / Digital Services & ICT in Education, डेटाबेस और डेटा प्रबंधन / Databases & Data Management, प्रोग्रामिंग और सॉफ्टवेयर विकास / Programming & Software Development, उभरती प्रौद्योगिकियाँ और AI / Emerging Technologies & AI
  13. अतिरिक्त अभ्यास (वैकल्पिक) / Extra Practice — beyond the 2026 syllabus: संस्कृत साहित्य-कवि-ग्रन्थ, History — World History (basic), संस्कृतसाहित्यम् एवं काव्यशास्त्रम्, संस्कृतशिक्षणशास्त्रम्, हिंदी साहित्य
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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