Practice Question Strings

Duration: 3 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper-2 | Programming & Data Structures: 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
  3. Paper-2 | Databases / DBMS & SQL: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  4. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  5. Paper-2 | Computer Networks & Security: 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, Network Access Technologies, Network Security
  6. Paper-2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  7. Paper-2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  8. Paper-2 | Theory of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines
  9. Paper-2 | Computer Organization & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  10. Paper-2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  11. Paper-1 | General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, GK- Current Affairs, History, Geography, Indian Economy, Environment
  12. Paper-1 | Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Data Interpretation, Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Clock, Calendar, Cubes & Dices, Directions (Direction Test), Analogy, Seating Arrangements, Analytical Reasoning (Counting Figures Reasoning)
  13. Paper-1 | Quantitative Aptitude: Ratio and Proportion (Ratios), Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Speed Time and Distance, Average, Age Problems, Percentage, Profit and Loss, Time and Work, Pipe and Cistern, Simple Interest and Compound Interest, Powers and Exponents (Surds and Indices), Mensuration and Geometry, Probability, Statistics, Arithmetic, Algebra
  14. Paper-1 | English: Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Cloze Test (Cloze Passage)
  15. Coal India Previous Year Paper:
  16. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus
  17. Coal India Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video presents a discrete mathematics problem concerning binary strings without consecutive zeros. The instructor defines $x_n$ as the count of such strings of length $n$ and asks to identify the correct recurrence relation from four options. He systematically calculates the first few terms ($x_0$ through $x_3$) by listing valid strings to verify the base cases. By testing these values against the given options, he eliminates incorrect formulas and identifies the Fibonacci-like recurrence $x_n = x_{n-1} + x_{n-2}$. Finally, he uses this recurrence to compute $x_5$, selecting the correct numerical answer from the provided choices.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the problem statement: finding the recurrence for binary strings of length $n$ with no consecutive 0s. He writes down the four options on the screen: $x_n = 2x_{n-1}$, $x_n = x_{\lfloor n/2 floor} + 1$, $x_n = x_{\lfloor n/2 floor} + n$, and $x_n = x_{n-1} + x_{n-2}$. He begins by determining base cases, writing $x_0 = 1$ for the empty string and $x_1 = 2$ for strings "0" and "1". He then lists valid strings for length 2 ("01", "10", "11") to find $x_2 = 3$. For length 3, he lists "010", "011", "101", "110", "111" to find $x_3 = 5$. He tests option (a) $x_n = 2x_{n-1}$ and finds it fails for $x_2$ since $3 eq 4$. He tests option (b) and (c) and finds they fail. He tests option (d) $x_n = x_{n-1} + x_{n-2}$, verifying $x_2 = x_1 + x_0$ ($3 = 2+1$) and $x_3 = x_2 + x_1$ ($5 = 3+2$), confirming it is the correct recurrence.

  2. 2:00 – 3:06 02:00-03:06

    The instructor proceeds to the second question asking for the value of $x_5$. He continues the sequence established by the recurrence relation $x_n = x_{n-1} + x_{n-2}$. He calculates $x_4$ by adding $x_3$ and $x_2$ ($5 + 3 = 8$). Then he calculates $x_5$ by adding $x_4$ and $x_3$ ($8 + 5 = 13$). He circles the value 13 on the board. He identifies 13 as the correct answer, corresponding to option (c), and marks it.

The lesson demonstrates a standard method for solving recurrence relation problems: calculating initial terms to identify the pattern. By explicitly listing small cases, the instructor validates the Fibonacci sequence structure inherent in the problem constraints. The progression from identifying the recurrence to applying it for a specific term ($x_5$) reinforces the practical application of the derived formula.

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