Number Systems - HOT Questions (2)

Duration: 6 min

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Inside: a video lesson and guided study material.

Module outline

  1. Section A | English: Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Preposition, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Articles, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Verbal Analogy (Word Based Analogy)
  2. Section A | Quant Aptitude: Ratio and Proportion (Ratios), Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Arithmetic, Algebra, Powers and Exponents (Surds and Indices), Average, Age Problems, Percentage, Profit and Loss, Partnership, Time and Work, Simple Interest and Compound Interest, Mensuration and Geometry, Probability, Pipe and Cistern
  3. Section A | Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Calendar, Clock, Blood Relations, Directions (Direction Test), Seating Arrangements, Ranking, Order and Sequence, Puzzle Solving (Puzzles)
  4. Section B | C Programming: C Programming by Yash Sir, Coding Questions by Yash Sir
  5. Section B | Data Structures: Algorithm Analysis, Greedy Algorithms, Time Complexity Analysis, Sorting Algorithms, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs
  6. Section B | OOP (C++): Object Oriented Programming (OOPS), Programming in C++
  7. Section B | OS: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS
  8. Section B | 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, TL: Congestion & UDP, Application Layer, Hardware basics
  9. Section B | AI & Big Data Basics: AI & ML by Arun Sir, Big Data Systems
  10. Section C | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  11. Section A, C | Comp. Fundamentals, COA: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Multiprocessors, Programming the Basic Computer
  12. MOCK TEST:
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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