Practice Questions - Part 2

Duration: 56 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Section A: General Awareness: Polity, वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, Chemistry, Static General Knowledge, History, Geography, Indian Economy, समसामयिकी / Current Affairs, Evolution of Indian Banking (Banking & Financial Awareness), Environment
  3. Section A: General Intelligence & Reasoning ability: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, Data Sufficiency, अशाब्दिक तर्क / Non-Verbal Reasoning, Analytical Reasoning (Counting Figures Reasoning), रक्त संबंध / Blood Relations, Syllogisms, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, दिशा एवं दूरी / Direction and Distance, 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, आँकड़ों की पर्याप्तता एवं निर्णय क्षमता / Data Sufficiency and Decision Making, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, Crypt Arithmetic, 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, TCS NQT Advanced Reasoning Ability
  4. Section A: Arithmetical & Numerical Ability: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, आँकड़ा निर्वचन / Data Interpretation, 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, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, समय और कार्य / Time and Work, Pipe and Cistern, घन क्षेत्रमिति / Solid Mensuration, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, Algebra, Probability, Mental Ability, Age Problems, Partnership, Statistics, Arithmetic, Speed Mathematics and Basic Mathematics, Miscellaneous
  5. Section A: English Language & Comprehension: Vocabulary, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Verbs and Tenses, Reading Comprehension, Parts of Speech, Sentence Construction, Prepositions and Conjunctions, Direct and Indirect Speech, Sentence Completion (Fill in the blanks), Sentence Structure and Common Errors, Modals, Transformation of Sentences, Sentence Correction (Error Correction), Adverb, Conjunction, Cloze Test (Cloze Passage)
  6. Section A: Hindi Language & Comprehension: 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
  7. Section B: Programming, Data Structures, OOP & Java: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Language Design, Intro to Compilers, Visual Basics, Syntax Analysis: Bottom-Up, Object Oriented Technology
  8. Section B: Computer Networks, TCP/IP & Network Security: Introduction to CN, Data Communication, DLL: Flow Control, DLL: Access 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, Network Access Technologies, Network Security, Society, Law & Ethics, Mobile Computing, Net Layer:Routing Protocol, Cyber Safety and Security
  9. Section B: Teaching Methodology: वृद्धि और विकास / Growth and Development, Concept of Pedagogy, विकास के सिद्धांत / Theories of Development, समावेशी शिक्षा / Inclusive Education, Experiential Pedagogy, आकलन और मूल्यांकन / Assessment and Evaluation, समाजीकरण और जेंडर / Socialisation and Gender, National Education Policy (NEP) 2020, संज्ञानात्मक प्रक्रियाएँ / Cognitive Processes, शिक्षण योजना और शिक्षण कौशल / Teaching Planning and Teaching Skills, Personality Development, शिक्षण विधियाँ / Teaching Methods, अधिगम और व्यवहारवादी सिद्धांत / Learning and Behavioural Theories, Learners & Learning Process, Factors Affecting Teaching, शिक्षण विधियाँ एवं उपागम / Teaching Methods and Approaches, शिक्षण-अधिगम प्रक्रिया एवं कक्षा प्रबंधन / Teaching-Learning Process and Classroom Management, शिक्षण सहायक सामग्री एवं शैक्षिक तकनीकी / Teaching Aids and Educational Technology, सूक्ष्म शिक्षण एवं कक्षा संप्रेषण / Microteaching and Classroom Communication, आकलन एवं मूल्यांकन / Assessment and Evaluation, पाठ्यचर्या, कला एवं सह-शैक्षिक क्षेत्र / Curriculum, Arts and Co-curricular Areas, दिव्यांग बच्चों की शिक्षा / Education of Children with Disabilities, शिक्षक: गुण, व्यावसायिक नैतिकता एवं विकास / Teacher: Qualities, Professional Ethics and Development
  10. Section B: Digital Electronics / Boolean Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  11. Section B: Operating Systems & Linux: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, File Management, Disc Scheduling, Unix OS, Linux OS, Distributed Systems, Windows OS
  12. Section B: Data Base Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, File Organization & Indexing, Transaction Management, Concurrency Control, Database Security & Authorization, Database Recovery, Data Warehousing & Mining
  13. Section B: Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, HTML Basics, CSS, Emerging Technologies, JavaScript-Basics, .Net Programming, Electronic Data Interchange and E-Commerce, XML
  14. Section B: Computer Fundamentals, IT Basics & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer, Terms & Abbreviations, MS Office Applications, Instr Formats & Modes, Floating Point Rep, कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), कंप्यूटर नेटवर्क / Computer Networks, प्रेज़ेंटेशन (MS PowerPoint) / Presentation Software (MS PowerPoint)
  15. Section B: Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  16. Section B: Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, extras, Fundamentals of Systems and Information Systems
  17. Section B: Design & Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  18. Section B: Mathematics: Linear Algebra, Calculus, Trigonometry, Vectors, Set Theory, Functions, Relations, Propositional and Predicate Logic, Research Process Steps, Graph Theory, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, यूक्लिडीय ज्यामिति और क्षेत्रमिति / Euclidean Geometry and Mensuration, सांख्यिकी और प्रायिकता / Statistics and Probability, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers, समतल क्षेत्रमिति / Plane Mensuration, प्रतिचयन / Sampling
  19. Section B: Computer Graphics, Multimedia & Mobile Computing: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, Multimedia
  20. Section B: Emerging Trends: Emerging Tech Trends, Knowledge Representation, Natural Language Processing, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection
  21. DSSSB Previous Year Paper:
  22. Business Studies and Management: Business Communication, प्रबंध के सिद्धांत एवं कार्य / Principles and Functions of Management, लेखांकन के आधार एवं लेन-देनों का अभिलेखन / Accounting Fundamentals and Recording of Transactions, Business Economics, ह्रास, अंतिम खाते व कंप्यूटरीकृत लेखांकन / Depreciation, Final Accounts and Computerised Accounting, Knowledge Management & New Economy
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a comprehensive lecture on geometry and mensuration, presented by an instructor named Yash Jain. The session begins with a title slide and proceeds to solve a series of multiple-choice questions. The first question tests the understanding of circle terminology, specifically the definitions of a chord and a secant, with the instructor explaining that a secant is a line that intersects a circle at two points and contains a chord, but is not itself a chord. The second problem involves a geometric configuration where a small circle is placed in the corner formed by a large circle and two perpendicular lines, requiring the use of the Pythagorean theorem to find the radius of the small circle. The third question asks for the area of a hexagon formed by joining the trisection points of the sides of an equilateral triangle, which is solved by calculating the area of the original triangle and subtracting the areas of the three corner triangles. The fourth problem uses the formula for the sum of interior angles of a polygon to find the number of sides of a regular polygon given one interior angle. The fifth question asks for the area of a regular hexagon inscribed in a circle, which is solved by dividing the hexagon into six equilateral triangles. The final problem is a conceptual question about the sum of an interior and exterior angle of a regular polygon, which is always 180 degrees. The video uses a blackboard-style interface with diagrams and step-by-step calculations to explain each concept.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide for a 'GEOMETRY & MENSURATION' lecture. The instructor, Yash Jain, is visible in a small window. The first question is presented on a blackboard: 'Which of the following statements is incorrect in regard to a circle?'. The four statements are: (i) Every Chord is Secant, (ii) Every Secant is Chord, (iii) Secant is technically not a chord, but it contains a chord, and (iv) Every secant line defines a unique chord. The instructor begins to analyze the definitions of a chord and a secant, explaining that a chord is a line segment connecting two points on a circle, while a secant is a line that intersects the circle at two points and extends infinitely. He notes that a secant contains a chord but is not a chord itself, which makes statement (ii) incorrect.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to analyze the first question. He explains that statement (i) 'Every Chord is Secant' is incorrect because a chord is a segment, not a line, and a secant is a line. He then discusses statement (ii) 'Every Secant is Chord', which is also incorrect for the same reason. He confirms that statement (iii) 'Secant is technically not a chord, but it contains a chord' is correct. He then evaluates statement (iv) 'Every secant line defines a unique chord', which he confirms is correct. The instructor concludes that statements (i) and (ii) are incorrect, making option (c) 'Only i & ii' the correct answer. He then moves to the next problem.

  3. 5:00 – 10:00 05:00-10:00

    The second question is presented: 'It is required to place a small circle in the space left by a large circle as shown. If the radius of the large one is 2 cm and that of the small one is b', then find the value of b'. The instructor draws a diagram showing a large circle of radius 2 cm tangent to two perpendicular lines, and a smaller circle of radius b tangent to the large circle and the two lines. He labels the center of the large circle as A and the center of the small circle as O. He identifies the distance from the origin to the center of the large circle as OA = 2√2. He then identifies the distance from the origin to the center of the small circle as OD = b√2. He sets up the equation OA = AD + DO, where AD = 2 and DO = b√2, leading to the equation 2√2 = 2 + b√2. He solves this equation to find b = 2(√2 - 1). He then moves to the next problem.

  4. 10:00 – 15:00 10:00-15:00

    The third question is presented: 'An equilateral triangle of length 3 cm is divided equally by all sides into 3 parts, all the cuts are joined thus forming a hexagon, find area of this hexagon'. The instructor draws an equilateral triangle with side length 3 cm. He divides each side into three equal parts of 1 cm. He then joins the points of division to form a hexagon in the center. He explains that the area of the hexagon is the area of the original triangle minus the areas of the three small corner triangles. He calculates the area of the original triangle as (√3/4) * 3^2 = 9√3/4. He calculates the area of one small corner triangle as (√3/4) * 1^2 = √3/4. The total area of the three small triangles is 3 * √3/4 = 3√3/4. The area of the hexagon is 9√3/4 - 3√3/4 = 6√3/4 = 3√3/2.

  5. 15:00 – 20:00 15:00-20:00

    The fourth question is presented: 'If the expression shown are the degree measures of the angles if the pentagon, find the value x+y'. The instructor draws a pentagon with five interior angles labeled as 4x, 3x, 7y, 2x+y, and x+2y. He states that the sum of the interior angles of a pentagon is (5-2) * 180 = 540 degrees. He sets up the equation: 4x + 3x + 7y + 2x + y + x + 2y = 540. He simplifies this to 10x + 10y = 540. He then divides both sides by 10 to get x + y = 54. He confirms this is the answer. He then moves to the next problem.

  6. 20:00 – 25:00 20:00-25:00

    The fifth question is presented: 'One angle of a regular polygon measures 177°. How many sides does it have?'. The instructor explains that the formula for the measure of an interior angle of a regular polygon is ((n-2) * 180) / n, where n is the number of sides. He sets up the equation: ((n-2) * 180) / n = 177. He multiplies both sides by n to get (n-2) * 180 = 177n. He expands the left side to get 180n - 360 = 177n. He subtracts 177n from both sides to get 3n - 360 = 0. He adds 360 to both sides to get 3n = 360. He divides by 3 to get n = 120. He confirms the polygon has 120 sides. He then moves to the next problem.

  7. 25:00 – 30:00 25:00-30:00

    The sixth question is presented: 'A regular hexagon is inscribed in a circle of radius 6 cm. What is the area of the hexagon?'. The instructor draws a circle with a regular hexagon inscribed in it. He explains that a regular hexagon can be divided into 6 equilateral triangles, each with a side length equal to the radius of the circle, which is 6 cm. He writes the formula for the area of an equilateral triangle as (√3/4) * side^2. He calculates the area of one triangle as (√3/4) * 6^2 = (√3/4) * 36 = 9√3. He multiplies this by 6 to get the total area of the hexagon: 6 * 9√3 = 54√3 cm². He confirms this is the answer.

  8. 30:00 – 35:00 30:00-35:00

    The seventh question is presented: 'Find the sum of the measures of one interior and one exterior angle of a regular 940-gon'. The instructor explains that for any polygon, an interior angle and its adjacent exterior angle are supplementary, meaning they add up to 180 degrees. He draws a diagram of a polygon showing an interior angle and an exterior angle next to each other, forming a straight line. He writes the equation: int + ext = 180°. He states that this is true for any polygon, regardless of the number of sides, so the sum is always 180 degrees. He confirms this is the answer.

  9. 35:00 – 40:00 35:00-40:00

    The instructor begins to solve the second problem again, this time with a different approach. He draws a diagram of a large circle of radius 2 cm tangent to two perpendicular lines, and a small circle of radius b tangent to the large circle and the two lines. He labels the center of the large circle as A and the center of the small circle as O. He identifies the distance from the origin to the center of the large circle as OA = 2√2. He then identifies the distance from the origin to the center of the small circle as OD = b√2. He sets up the equation OA = AD + DO, where AD = 2 and DO = b√2, leading to the equation 2√2 = 2 + b√2. He solves this equation to find b = 2(√2 - 1). He then moves to the next problem.

  10. 40:00 – 45:00 40:00-45:00

    The instructor begins to solve the third problem again, this time with a different approach. He draws an equilateral triangle with side length 3 cm. He divides each side into three equal parts of 1 cm. He then joins the points of division to form a hexagon in the center. He explains that the area of the hexagon is the area of the original triangle minus the areas of the three small corner triangles. He calculates the area of the original triangle as (√3/4) * 3^2 = 9√3/4. He calculates the area of one small corner triangle as (√3/4) * 1^2 = √3/4. The total area of the three small triangles is 3 * √3/4 = 3√3/4. The area of the hexagon is 9√3/4 - 3√3/4 = 6√3/4 = 3√3/2.

  11. 45:00 – 50:00 45:00-50:00

    The instructor begins to solve the fourth problem again, this time with a different approach. He draws a pentagon with five interior angles labeled as 4x, 3x, 7y, 2x+y, and x+2y. He states that the sum of the interior angles of a pentagon is (5-2) * 180 = 540 degrees. He sets up the equation: 4x + 3x + 7y + 2x + y + x + 2y = 540. He simplifies this to 10x + 10y = 540. He then divides both sides by 10 to get x + y = 54. He confirms this is the answer. He then moves to the next problem.

  12. 50:00 – 55:00 50:00-55:00

    The instructor begins to solve the fifth problem again, this time with a different approach. He draws a circle with a regular hexagon inscribed in it. He explains that a regular hexagon can be divided into 6 equilateral triangles, each with a side length equal to the radius of the circle, which is 6 cm. He writes the formula for the area of an equilateral triangle as (√3/4) * side^2. He calculates the area of one triangle as (√3/4) * 6^2 = (√3/4) * 36 = 9√3. He multiplies this by 6 to get the total area of the hexagon: 6 * 9√3 = 54√3 cm². He confirms this is the answer.

  13. 55:00 – 56:11 55:00-56:11

    The video concludes with a final slide that says 'THANKS FOR WATCHING' in large white text on a dark background. The instructor is no longer visible. This is the end of the lecture.

The video presents a structured and methodical review of key concepts in geometry and mensuration. It begins with a foundational question on circle terminology, establishing the importance of precise definitions. The subsequent problems are carefully chosen to demonstrate the application of core principles: the Pythagorean theorem for a tangency problem, the area of triangles for a composite shape, the sum of interior angles for a polygon, and the properties of regular polygons. The instructor consistently uses a step-by-step approach, drawing diagrams and writing out equations to guide the viewer through each solution. The final problem reinforces a fundamental geometric principle that an interior and exterior angle are supplementary, a concept that is universally true. The overall progression moves from basic definitions to more complex applications, providing a comprehensive review of the topic.

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