Short Tricks to Find Unit Digit of an Expression (1)

Duration: 15 min

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): भाषा, लिपि और वर्ण, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, पद-भेद और रूप-विकार, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, शब्द-भंडार, अपठित बोध, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): رسم الخط، حروفِ تہجی اور املا / Script, Alphabet and Spelling, اسم، ضمیر اور صفت / Nouns, Pronouns and Adjectives, الفاظ، محاورے اور ضرب الامثال / Vocabulary, Idioms and Proverbs, تفہیمِ عبارت، انشا اور ترجمہ / Comprehension, Writing and Translation, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): শব্দার্থ, বাগধারা ও ভাষাশুদ্ধি / Meaning, Idioms and Correct Usage, বাক্য ও বাচ্য / Sentences and Voice, শব্দগঠন ও শব্দভান্ডার / Word Formation and Vocabulary, অনুবাদ, বোধপরীক্ষণ ও রচনা / Translation, Comprehension and Composition
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Verbs and Tenses, Pronoun, Verb, Adverb, Prepositions and Conjunctions, Parts of Speech, Determiner, Conjunction, Modals, Transformation of Sentences, Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Structure and Common Errors, Reading Comprehension, Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, अशाब्दिक तर्क / Non-Verbal Reasoning, प्रतिशत / Percentage, औसत / Average, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, समय और कार्य / Time and Work, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, Algebra, Probability, Trigonometry, 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, Data Arrangement, Inequality, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, 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
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, Chemistry, History, Geography, Indian Economy, Environment, समसामयिकी / Current Affairs, Static General Knowledge
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, कंप्यूटर नेटवर्क / Computer Networks, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), Terms & Abbreviations, प्रेज़ेंटेशन (MS PowerPoint) / Presentation Software (MS PowerPoint)
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References, OOPS with Java
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a comprehensive lecture on the concept of 'Unit Digit' in number systems, presented by an instructor from Knowledge Gate Eduventures. The video begins with an introduction to the topic, emphasizing its importance for various competitive exams such as CAT, XAT, GMAT, and government tests, where it is a crucial part of the aptitude section. The core of the lecture focuses on a method to find the unit digit of large numbers raised to high powers. The instructor explains that this is achieved by identifying the cyclicity of the unit digit of the base number. The method involves observing the pattern of unit digits as the base is raised to successive powers. The video provides a classification of single-digit numbers (0-9) into three categories based on their cyclicity: numbers with a fixed unit digit (0, 1, 5, 6), numbers with a two-number cycle (4, 9), and numbers with a four-number cycle (2, 3, 7, 8). The instructor demonstrates this concept with several examples, including 185^563, 271^6987, and 156^25369, showing how to determine the unit digit by finding the remainder when the exponent is divided by the cycle length. The video concludes with a summary of the method and a list of practice problems for the viewer.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide for 'NUMBER SYSTEM' and a subtitle 'The mysterious world of numbers...'. The instructor, Yash Jain, introduces the topic, stating that it is a fundamental concept for various competitive exams. A slide titled 'Why Study This Topic?' lists numerous exams including CAT, XAT, CMAT, NMAT, SNAP, MAT, IIFT, GMAT, GATE, and others, emphasizing that number system is a crucial part of the aptitude section, with at least two questions appearing in every exam. The instructor is visible in a small window in the bottom right corner, speaking to the camera.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to explain the importance of the topic, with a list of exams on the screen. He emphasizes that the number system is a key area for aptitude tests. The slide lists exams such as Placements, Government Exams, Civil Services Exams, Banking Exams, Railway Exams, College Entrance Exams, and others. The instructor's voiceover explains that this topic is essential for students preparing for these competitive exams. The visual focus remains on the list of exams, with the instructor's video feed in the corner.

  3. 5:00 – 10:00 05:00-10:00

    The video transitions to a new slide titled 'Concept of Unit Digit'. The instructor explains that to find the unit digit of a number raised to a power, one must understand the concept of cyclicity. He states that the unit digit of a number repeats in a pattern when the number is raised to successive powers. The slide shows an example: 'Unit Digit of 3547^153 x 251^72'. The instructor then moves to a new slide with a question: 'Q: Find the unit digit of the following:', followed by a list of 11 problems, including 185^563, 271^6987, and 154^258741369. The instructor begins to solve the first problem, 185^563, by focusing on the unit digit of the base, which is 5.

  4. 10:00 – 14:35 10:00-14:35

    The instructor explains the rule for numbers ending in 0, 1, 5, or 6: their unit digit remains the same regardless of the power. He demonstrates this with 185^563, stating the unit digit is 5. He then moves to 271^6987, noting the unit digit of the base is 1, so the answer is 1. For 156^25369, the unit digit is 6. The instructor then explains the cyclicity of 4 and 9, which have a cycle of 2. He demonstrates with 154^258741369, where the unit digit of the base is 4, and the exponent is odd, so the unit digit is 4. He then explains the cycle of 2, 3, 7, and 8, which have a cycle of 4. He demonstrates with 190^654789321, where the unit digit of the base is 0, so the answer is 0. The video ends with a 'Thank You for Watching' screen.

The video provides a structured and practical guide to solving unit digit problems, a common type of question in competitive exams. It begins by establishing the relevance of the topic, then systematically introduces the core concept of cyclicity. The instructor uses a clear, step-by-step approach, first explaining the rules for numbers with fixed unit digits (0, 1, 5, 6), then for those with a two-number cycle (4, 9), and finally for those with a four-number cycle (2, 3, 7, 8). The method is demonstrated through a series of worked examples, showing how to determine the cycle length and use the remainder of the exponent divided by the cycle length to find the correct unit digit. This logical progression from theory to application makes the concept accessible and provides a reliable method for students to solve similar problems under time pressure.

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