Practice Question - 2

Duration: 4 min

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Inside: a video lesson and guided study material.

Module outline

  1. General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
  2. General Awareness: Physics, Chemistry, Biology, History, Geography, Polity, Indian Economy, Environment, Static General Knowledge, GK- Current Affairs, Artificial Intelligence, MS Office Applications, Terms & Abbreviations, Keyboard Shortcuts, Evolution of Indian Banking (Banking & Financial Awareness), Emerging Tech Trends
  3. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Probability, Statistics, Signal Space and Optimum Detection, Probability, Statistics
  4. Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
  5. Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
  6. 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, HTML Basics, OOPS with C++, Java, Object Oriented Technology
  7. Databases: 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, Database Recovery, Database Security & Authorization
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. 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, Complexity Theory
  10. 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. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Security, Windows OS, Distributed Systems, Unix OS, Linux OS
  12. Computer Networks: Introduction to CN, 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, Data Communication, Website, Browser & Services, Web Design & Development, Network Security, Cyber Threats and Malware Attacks, Cyber Safety and Security
  13. Full Length Mock Tests:
  14. Sectional Tests:
  15. Paper 2 - Full-length Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video features an instructor from Knowledge Gate solving a problem in automata theory. The task is to identify the language accepted by a Pushdown Automaton (PDA) given its transition mapping. The instructor systematically converts the mathematical notation of the transition function into a visual state diagram. He then analyzes the paths within this diagram to determine the structural properties of the accepted strings, such as their ending character and the parity of specific symbols. By testing specific examples against the diagram, he eliminates incorrect options and identifies the correct language definition.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by presenting the problem on a slide titled 'Q consider the following mapping and find the correct language?'. The slide lists seven transition rules for a PDA, such as $\delta(q_0, a, z_0) = (q_1, z_0)$ and $\delta(q_1, \epsilon, z_0) = (q_f, z_0)$. He starts drawing the state diagram on the right side of the screen. He draws circles for states $q_0, q_1, q_2$ and adds arrows representing the transitions. He draws an arrow from $q_0$ to $q_1$ labeled 'a', and from $q_0$ to $q_2$ labeled 'b'. He continues by adding a self-loop on $q_1$ for 'a' and an arrow from $q_1$ to $q_2$ for 'b'. He also draws a self-loop on $q_2$ for 'a' and an arrow from $q_2$ back to $q_0$ for 'b'. Finally, he draws an epsilon transition from $q_1$ to a final state $q_f$. The multiple-choice options are visible at the bottom: (a) ending with a, (b) ending with a, contain even number of a, (c) ending with a, contain odd number of a, (d) ending with a, contain even number of b.

  2. 2:00 – 4:19 02:00-04:19

    The instructor analyzes the diagram to find the correct option. He notes that the only way to reach the final state $q_f$ is via an epsilon transition from $q_1$. This implies the string must end with a transition that lands in $q_1$. Since transitions to $q_1$ occur on input 'a' (from $q_0$ or $q_1$), the string must end with 'a'. He then tests the string 'bba'. Tracing the path: $q_0 \xrightarrow{b} q_2 \xrightarrow{b} q_0 \xrightarrow{a} q_1 \xrightarrow{\epsilon} q_f$. This string is accepted. It has one 'a' (odd) and two 'b's (even). This eliminates option (b) which requires an even number of 'a's. He tests 'aa': $q_0 \xrightarrow{a} q_1 \xrightarrow{a} q_1 \xrightarrow{\epsilon} q_f$. This is accepted and has two 'a's (even). This eliminates option (c) which requires an odd number of 'a's. He observes that to return to $q_0$ from $q_2$, a 'b' is needed. Since $q_2$ is entered by 'b' from $q_0$, 'b's must come in pairs to return to the start state. Thus, the number of 'b's must be even. This confirms option (d) 'ending with a, contain even number of b' is the correct answer.

The lecture demonstrates a methodical approach to solving PDA problems by converting transition mappings into state diagrams and testing sample strings to deduce the language properties. The key takeaway is understanding how state transitions constrain the input string structure, specifically how 'b' transitions must occur in pairs to return to the start state, while 'a' transitions allow entry into the accepting state.

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