Number Systems - HOT Questions (2)

Duration: 6 min

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Inside: a video lesson and guided study material.

Module outline

  1. Language Skills (English): Vocabulary, Verbal Analogy (Word Based Analogy), Noun, Pronoun, Verb, Adjectives, Adverb, Preposition, Articles, Conjunction, Tenses, Modals, Subject Verb Agreement (Verb Noun Agreement), Determiner, Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage)
  2. General Aptitude (Quantitative Ability): Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Speed Time and Distance, Mixture and Alligation, Age Problems, Partnership, Number System, HCF LCM, Divisibility Rules, Powers and Exponents (Surds and Indices), Algebra, Data Interpretation, Statistics, Sequence and Series (Series), Logarithm, Arithmetic, Speed Mathematics and Basic Mathematics
  3. General Aptitude (Reasoning Ability): Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Syllogisms, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Inequality, Logical Sequence Of Words, Seating Arrangements, Puzzle Solving (Puzzles), Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Cubes & Dices, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Analytical Reasoning (Counting Figures Reasoning), Clock, Calendar, Data Sufficiency, Analogy
  4. Technical Skills MCQ - Data Structure: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  5. Technical Skills MCQ - Networking: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, Application Layer, Mobile Technology, Network Security
  6. Technical Skills MCQ - Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, File Management, Windows OS, Linux OS, Security, Virtual Machines
  7. Technical Skills MCQ - DBMS: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), File Organization & Indexing, Relational Algebra, SQL, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, NoSQL
  8. Technical Skills MCQ - Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  9. Technical Skills MCQ - Cloud Computing: Emerging Tech Trends, Cloud Computing and IoT
  10. Technical Skills MCQ - Cyber Security: Cyber and Info Security, Security in Mobile and Wireless Computing
  11. Technical Skills (Coding): Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir, Object Oriented Programming (OOPS)
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video, presented by Yash Jain from Knowledge Gate, is a tutorial on solving a specific type of number system problem. The video begins with an introduction to the topic, followed by a detailed analysis of a question asking for the sum of 'n' and 'p' where the square root of the number 12345678987654321 is expressed as a repeating digit 'n' repeated 'p' times. The instructor uses a step-by-step approach, first demonstrating the pattern by calculating the squares of numbers composed of repeated 1s (e.g., 11, 111, 1111) to show that 111111111 squared equals 12345678987654321. This reveals that the square root is 111111111, which is the digit '1' repeated 9 times. Therefore, 'n' is 1 and 'p' is 9, making their sum 10. The video concludes with a final answer and a thank you message.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card displaying 'NUMBER SYSTEM' in a stylized font against a grey background. It then transitions to a presentation slide with a colorful, patterned background. The slide is titled 'NUMBER SYSTEM' and includes the text 'The mysterious world of numbers...' and 'Basic To Advance'. The instructor, Yash Jain, is visible in a small window in the bottom right corner. The main content area of the slide shows a question: 'q. The square root of 12345678987654321 is nnnnn... upto 'p' times, find sum of n and p ?'. The instructor begins to explain the problem, writing the square root symbol and the number 12345678987654321 on the screen.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to work on the problem, writing the equation '√12345678987654321 = nnnnn... p times' on the screen. He then begins to analyze the pattern of the number 12345678987654321. He writes a series of equations on the left side of the screen to demonstrate the pattern: '(11)^2 = 121', '(111)^2 = 12321', and '(1111)^2 = 1234321'. He then extends this pattern to the full number, writing '(111111111)^2 = 12345678987654321'. This shows that the number is the square of a number composed of nine 1s. He then writes 'n = 1' and 'p = 9' to identify the values of n and p.

  3. 5:00 – 6:10 05:00-06:10

    The instructor completes the solution by calculating the sum of n and p. He writes 'n + p = 1 + 9 = 10' on the screen. He then circles the number 10 to emphasize the final answer. The video concludes with a black screen displaying a red neon-style text box that says 'THANK YOU FOR WATCHING'. The instructor's voiceover confirms the answer is 10.

The video presents a clear, step-by-step solution to a number theory problem. It begins by identifying the problem: finding the sum of 'n' and 'p' where the square root of a large, palindromic number is a repeating digit. The core of the solution lies in recognizing a mathematical pattern: the square of a number composed of 'k' ones results in a palindrome that increases from 1 to k and then decreases back to 1. By applying this pattern to the given number, the instructor deduces that the square root is 111111111, which is the digit 1 repeated 9 times. This directly gives n=1 and p=9, leading to the final answer of 10. The video effectively uses visual aids and a logical progression to teach a problem-solving technique for a specific class of number system questions.

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