Practice Questions

Duration: 5 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:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a focused lesson on Group Theory, specifically targeting the identification of groups and the calculation of inverses within modular arithmetic systems. The instructor begins by evaluating four distinct sets and operations to determine which satisfy the axioms of a group. He then proceeds to solve three multiple-choice problems that require applying the definition of an inverse element (a * a^-1 = e) in different modular groups. The lesson emphasizes checking closure, identity, and inverse properties through concrete examples involving addition and multiplication modulo p.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by presenting four mathematical structures labeled 15 through 18, each defining a set and an operation to test for group properties. Structure 15 is {1, ..., p-1} under multiplication. Structure 16 is {0, ..., p-1} under multiplication. Structure 17 is {1, ..., p-1} under addition. Structure 18 is {0, ..., p-1} under addition. The instructor analyzes each to determine if they form a group. He marks 15 as correct because the set of non-zero residues modulo a prime p forms a group under multiplication. He marks 16 as incorrect because the element 0 does not have a multiplicative inverse. He marks 17 as incorrect because the set lacks the identity element 0 for addition. Finally, he marks 18 as correct, as the set of all residues modulo p forms a group under addition.

  2. 2:00 – 5:00 02:00-05:00

    The lecture transitions to solving specific multiple-choice questions involving inverses. The first question asks to identify the false statement for the group {0, 1, 2, 3, 4, 5} under addition modulo 6. The options involve finding inverses. The instructor explains that for an element 'a', its inverse 'a^-1' must satisfy a + a^-1 = 0 (mod 6). He verifies that 1^-1 = 5 (since 1+5=6=0), 2^-1 = 4 (since 2+4=6=0), and 0^-1 = 0. He identifies option (c) 3^-1 = 6 as false because 6 is not in the set and 3+3=0, so the inverse of 3 is 3. The next question involves the group {1, 2, 3, 4, 5, 6} under multiplication modulo 7. He verifies that 1^-1=1, 2^-1=4 (2*4=8=1), 3^-1=5 (3*5=15=1), and 6^-1=6 (6*6=36=1). All options appear true, suggesting a potential trick or error in the question, but he moves on. The final question is about the group {1, 2, 4, 7, 8, 11, 13, 14} under multiplication modulo 15. He checks the inverses: 2^-1=8 (2*8=16=1), 4^-1=4 (4*4=16=1), 7^-1=13 (7*13=91=1). He calculates 11*14=154, which is 4 mod 15, not 1. Thus, he marks option (d) 11^-1 = 14 as the false statement. A Cayley table is displayed for the first problem to visualize the operation.

The video effectively bridges theoretical definitions with practical problem-solving. It starts by reinforcing the conditions for a set to be a group, highlighting common pitfalls like missing identity elements or zero divisors. The progression to specific MCQs demonstrates how to apply these concepts to find inverses. The instructor uses visual aids like checkmarks and crosses to indicate correctness and performs arithmetic calculations on screen to verify modular results, providing a clear, step-by-step method for students to follow when analyzing group properties.

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