Tricks to Calculate Number of Triangles in Any Figure

Duration: 11 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 video is a tutorial on solving a common aptitude test problem: counting the number of triangles in a given figure. The instructor, Yash Jain Sir, begins by presenting a sequence of four diagrams, each showing a large triangle subdivided into smaller triangles by horizontal lines. He explains that the number of triangles in each figure follows a pattern based on the number of horizontal divisions. For the first figure with one horizontal line, he counts the triangles as 1 (small) + 2 (medium) = 3. For the second with two horizontal lines, he counts 1 + 2 + 3 = 6. He then generalizes this pattern, stating that for a figure with 'n' horizontal lines, the total number of triangles is the sum of the first 'n+1' natural numbers, which is given by the formula n(n+1)/2. He demonstrates this with a final example of a triangle divided into 4 horizontal levels, where the total is 1+2+3+4 = 10. The video uses on-screen diagrams and handwritten annotations to illustrate the counting process and the mathematical formula.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card reading "SPEED MATHS". It then transitions to a screen with a daily quiz announcement and a sequence of four diagrams. The diagrams show a large triangle divided into smaller triangles by horizontal lines. The first has one horizontal line, the second has two, the third has three, and the fourth has four. The instructor, Yash Jain Sir, appears in a small window and begins to explain the problem, which is to count the number of triangles in each figure. He states that the quiz is about questions asked in IT companies and encourages viewers to follow their Instagram.

  2. 2:00 – 5:00 02:00-05:00

    The instructor begins to solve the first problem. He focuses on the first diagram, which has one horizontal line dividing the large triangle. He counts the small triangles at the top (1) and the larger triangles formed by combining the top and bottom sections (2), arriving at a total of 3. He then moves to the second diagram, which has two horizontal lines. He counts the triangles: 1 small one at the top, 2 medium ones in the middle, and 3 large ones at the bottom, summing to 6. He writes the equation 1+2+3=6 on the screen. He then explains that the pattern is the sum of the first 'n' natural numbers, where 'n' is the number of horizontal lines plus one.

  3. 5:00 – 10:00 05:00-10:00

    The instructor generalizes the pattern. He explains that for a figure with 'n' horizontal lines, the total number of triangles is the sum of the first (n+1) natural numbers. He writes the formula n(n+1)/2 on the screen. He then applies this to the third diagram, which has three horizontal lines. He counts the triangles as 1+2+3+4=10. He then moves to the fourth diagram, which has four horizontal lines, and states that the total number of triangles is 1+2+3+4+5=15. He uses red lines to highlight the different levels of triangles in the diagrams to aid the counting process.

  4. 10:00 – 10:32 10:00-10:32

    The video concludes with a final summary of the formula. The instructor reiterates that the total number of triangles in a figure with 'n' horizontal lines is given by the formula n(n+1)/2. He shows a final example of a triangle with 4 horizontal lines, where the total is 1+2+3+4+5=15. The video ends with a "THANKS FOR WATCHING" screen over a blue, abstract background with mathematical equations.

The video presents a clear, step-by-step method for solving a classic aptitude problem. It starts with a visual pattern of triangles, guides the viewer through the counting process for the first few cases, and then reveals the underlying mathematical formula. The progression from a specific example to a general rule is logical and effective. The use of on-screen diagrams and handwritten annotations makes the explanation easy to follow, demonstrating that a complex counting problem can be solved efficiently using a simple arithmetic series formula.

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