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⬇ ಉಚಿತ PDF ಡೌನ್‌ಲೋಡ್ ⬇ ಅಭ್ಯಾಸ ಪತ್ರಿಕೆ PDF (50 ಪ್ರಶ್ನೆಗಳು)

2026ರ ಕಂಪ್ಯೂಟರ್ ವಿಜ್ಞಾನ ಶಿಕ್ಷಕರ (CST, 1–8ನೇ ತರಗತಿ) ನೇಮಕಾತಿಯಲ್ಲಿ ತಲಾ 100 ಅಂಕಗಳ ಎರಡು ಪತ್ರಿಕೆಗಳಿವೆ: ಪತ್ರಿಕೆ 1 ಸಾಮಾನ್ಯ (GPT ಜೊತೆ ಸಾಮಾನ್ಯ) ಮತ್ತು ಪತ್ರಿಕೆ 2 ಕಂಪ್ಯೂಟರ್ ವಿಜ್ಞಾನ. ಕೆಳಗೆ ಅಧಿಕೃತ ಪತ್ರಿಕೆ 2 ಪಠ್ಯಕ್ರಮ, ಪತ್ರಿಕೆ 1 ವಿಭಾಗಗಳು, ಪರೀಕ್ಷಾ ಮಾದರಿ ಮತ್ತು ಉಚಿತವಾಗಿ ಡೌನ್‌ಲೋಡ್ ಮಾಡಬಹುದಾದ 50 ಪ್ರಶ್ನೆಗಳ ಅಭ್ಯಾಸ ಪತ್ರಿಕೆ ಇದೆ. (ಅಧಿಕೃತ ಪತ್ರಿಕೆ 2 ಪಠ್ಯಕ್ರಮ ಇಂಗ್ಲಿಷ್‌ನಲ್ಲಿ ಮಾತ್ರ ಲಭ್ಯ.)

ಪರೀಕ್ಷಾ ಮಾದರಿ

ಪತ್ರಿಕೆಪ್ರಶ್ನೆಗಳುಅಂಕಗಳುಅವಧಿ
ಪತ್ರಿಕೆ 1 — ಸಾಮಾನ್ಯ (GPT ಜೊತೆ ಸಾಮಾನ್ಯ)1001002 ಗಂಟೆ
ಪತ್ರಿಕೆ 2 — ಕಂಪ್ಯೂಟರ್ ವಿಜ್ಞಾನ (1–8ನೇ ತರಗತಿ)1001002 ಗಂಟೆ
  • ಎರಡೂ ಪತ್ರಿಕೆಗಳು ಕಡ್ಡಾಯ; ಪ್ರತಿ ಪತ್ರಿಕೆಯಲ್ಲಿ ಕನಿಷ್ಠ ಶೇ 35 ಅಂಕ ಅಗತ್ಯ.
  • ವಸ್ತುನಿಷ್ಠ ಬಹು ಆಯ್ಕೆ ಪ್ರಶ್ನೆಗಳು, OMR ಹಾಳೆ; ಪ್ರಶ್ನೆಪತ್ರಿಕೆ ಕನ್ನಡ ಮತ್ತು ಇಂಗ್ಲಿಷ್‌ನಲ್ಲಿ (ವ್ಯತ್ಯಾಸವಿದ್ದರೆ ಇಂಗ್ಲಿಷ್ ಆವೃತ್ತಿ ಅಂತಿಮ).
  • ತಪ್ಪು ಉತ್ತರಕ್ಕೆ ಋಣಾತ್ಮಕ ಅಂಕ ಇಲ್ಲ. ಆದರೆ ಪ್ರತಿ ಪ್ರಶ್ನೆಗೆ ಒಂದು ವೃತ್ತ ತುಂಬಬೇಕು — 4 ಆಯ್ಕೆಗಳಲ್ಲಿ ಒಂದು ಅಥವಾ 5ನೇ “ಉತ್ತರಿಸುತ್ತಿಲ್ಲ” ವೃತ್ತ; ಯಾವುದನ್ನೂ ತುಂಬದ ಪ್ರತಿ ಪ್ರಶ್ನೆಗೆ 0.25 ಅಂಕ ಕಡಿತ.
  • ಆಯ್ಕೆ ಪಟ್ಟಿ: ಪರೀಕ್ಷೆಯ ಅಂಕಗಳಿಗೆ ಶೇ 85 + ಪದವಿ ಅಂಕಗಳಿಗೆ ಶೇ 15 ಮಹತ್ವ; ಸಮಾನ ಅಂಕಗಳಿದ್ದರೆ ಹಿರಿಯರಿಗೆ ಆದ್ಯತೆ.
  • ಪರೀಕ್ಷೆ: 24.09.2026ರ ಪ್ರಕಟಣೆಯಂತೆ ನವೆಂಬರ್/ಡಿಸೆಂಬರ್ 2026ಕ್ಕೆ ಮುಂದೂಡಲಾಗಿದೆ; ಹೊಸ ವೇಳಾಪಟ್ಟಿ ಪ್ರಕಟವಾಗಬೇಕಿದೆ. ಅರ್ಜಿ ಸಲ್ಲಿಸುವ ಕೊನೆಯ ದಿನಾಂಕಕ್ಕೆ ಅಧಿಕೃತ ವೆಬ್‌ಸೈಟ್ ನೋಡಿ.

ಅರ್ಹತೆ

  • ಕನಿಷ್ಠ ಶೇ 50 ಅಂಕಗಳೊಂದಿಗೆ (ಪ.ಜಾ/ಪ.ಪಂ/ಪ್ರವರ್ಗ-1/ವಿಕಲಚೇತನರಿಗೆ ಶೇ 45) B.Sc (ಕಂಪ್ಯೂಟರ್ ವಿಜ್ಞಾನ), BCA, ಅಥವಾ ಕಂಪ್ಯೂಟರ್ ವಿಜ್ಞಾನ / ಮಾಹಿತಿ ವಿಜ್ಞಾನ / ಎಲೆಕ್ಟ್ರಾನಿಕ್ಸ್ ಮತ್ತು ಸಂವಹನದಲ್ಲಿ B.E. / B.Tech.
  • ವಯೋಮಿತಿ: ಕನಿಷ್ಠ 21; ಗರಿಷ್ಠ 40 (ಸಾಮಾನ್ಯ), 43 (2ಎ/2ಬಿ/3ಎ/3ಬಿ), 45 (ಪ.ಜಾ/ಪ.ಪಂ/ಪ್ರವರ್ಗ-1).
  • B.Ed ಮತ್ತು TET: ಜಿಲ್ಲಾ ಅಧಿಸೂಚನೆಯ ಪ್ರಕಾರ CST ಅಭ್ಯರ್ಥಿಗಳಿಗೆ ಸದ್ಯ ವಿನಾಯಿತಿ ಇದ್ದು, ಸೇರಿದ 5 ವರ್ಷಗಳೊಳಗೆ ಪೂರೈಸಬೇಕು; ಆದರೆ ಅಭ್ಯರ್ಥಿ ಮಾರ್ಗಸೂಚಿಗಳು TET ಕಡ್ಡಾಯವೆಂದು ಹೇಳುತ್ತವೆ — ನಿಮ್ಮ ಜಿಲ್ಲಾ ಅಧಿಸೂಚನೆಯಲ್ಲಿ ಖಚಿತಪಡಿಸಿಕೊಳ್ಳಿ.
  • ವೇತನ ಶ್ರೇಣಿ: ₹44,425–83,700. ಒಟ್ಟು CST ಹುದ್ದೆಗಳು: 500 (ಕಲ್ಯಾಣ ಕರ್ನಾಟಕ 300, ಉಳಿದ ಜಿಲ್ಲೆಗಳು 200).

ಪತ್ರಿಕೆ 2 — ಕಂಪ್ಯೂಟರ್ ವಿಜ್ಞಾನ (10 ಘಟಕಗಳು)

ಅಧಿಕೃತ ಪಠ್ಯಕ್ರಮ ಇಂಗ್ಲಿಷ್‌ನಲ್ಲಿ ಮಾತ್ರ ಪ್ರಕಟವಾಗಿದೆ; ಅದನ್ನೇ ಇಲ್ಲಿ ನೀಡಲಾಗಿದೆ.

ಘಟಕ 1: Fundamentals of Computers
  • Introduction, Functional Components of a computer (Working of each unit) Evolution Of Computers, Generations Of Computers, Classification Of Computers Applications Of Computers, Input, Output and Memory devices, Software Concepts Problem Solving Methodology, Word Processing, Spreadsheets, power point presentation, Typical configuration of Computer system, Introduction to Motherboard, Types of Motherboards, Components of Motherboard, Memory, Power supply to the computer system, Assembling the computer system
ಘಟಕ 2: Discrete Structures and Optimization
  • Mathematical Logic: Propositional and Predicate Logic, Propositional Equivalences, Normal Forms, Predicates and Quantifiers, Nested quantifiers, Rules of Inference.
  • Sets and Relations: Set Operations, Representation and Properties of Relations, Equivalence Relations, Partially Ordering.
  • Counting, Mathematical Induction and Discrete Probability: Basics of Counting, Pigeonhole Principle, Permutations and Combinations, Inclusion – Exclusion Principle, Mathematical Induction, Probability, Bayes’ Theorem.
  • Graph Theory: Simple Graph, Multigraph, Weighted Graph, Paths and Circuits, Shortest Paths in Weighted Graphs, Euclidian Paths and Circuits, Hamiltonian Paths and Circuits, Planner graph, Graph Colouring, Bipartite Graphs, Trees and Rooted Trees, Prefix Codes, Tree Traversals, Spanning Trees and cut-Sets.
  • Boolean algebra: Boolean Functions and its Representation, Simplifications of Boolean Functions.
ಘಟಕ 3: Computer System Architecture
  • Digital Logic Circuits and Components: Digital Computers, Logic Gates, Map Simplifications, Combinational Circuits, Flip-Flops, Sequential Circuits, Integrated Circuits, Decoders, Multiplexers, Registers and Counters, Memory Unit.
  • Data Representation: Data Types, Number Systems and Conversion, Complements, Fixed Point Representation, Floating Point Representation, Error Detection Codes, Computer Arithmetic – Addition, Subtraction, Multiplication and Division Algorithms.
  • Basic Computer Organization and Design: Stored Program Organization and Instruction Codes, Computer Registers, Computer Instructions, Timing and Control, Instruction Cycle, Memory- Reference Instructions, Input-Output, Interrupt.
  • Programming the Basic Computer: Machine Language, Assembly Language, Assembler, Program Loops Subroutines, Input-Output Programming.
  • Central Processing Unit : General Register Organization, Stack Organization, Instruction Formats, Addressing Modes, RISC Computer, CISC Computer.
  • Input-Output Organization: Peripheral Devices, Input-Output Interface, Asynchronous Data Transfer, Modes of Transfer, Priority Interrupt, DMA, Serial Communication.
  • Memory Hierarchy: Main Memory, Auxiliary Memory, Associative Memory, Cache Memory, Virtual Memory, Memory Management Hardware.
ಘಟಕ 4: Programming Languages and Computer Graphics
  • Language Design and Translation Issues: Programming Language Concepts, Paradigms and Models, Programming Environments, Programming Languages Syntax, Stages in Translation, Formal Transition Models.
  • Elementary Data Types: Properties of Types and Objects: Scalar and Composite Data Types.
  • Programming in C: Tokens, Identifiers, Data Types, Sequence Control, Subprogram Control, Arrays, Structures, Union, String, Pointers, Functions, File Handling. Command Line Arguments, Preprocessors.
  • Object Oriented Programming: Class, Object, Instantiation, Inheritance, Encapsulation, Abstract Class, and Polymorphism.
  • Programming in C++: Tokens, Identifiers, variables and Constants; Data types, Operators, Control statements, Functions Parameter Passing, Virtual Functions, Class and Objects; Constructors and Destructors; Overloading, Inheritance, Templates, Exception and Event Handling; Streams and Files.
  • Web Programming: HTML, DHTML, CSS,XML, Scripting, java Script
ಘಟಕ 5: Database Management Systems
  • Database System concepts and Architecture: Data Models, Schemas, and Instances; Three- Schema Architecture and Data Independence; Database Language and Interfaces; Centralized and Client/Server Architectures for DBMS.
  • Data Modelling: Entity-Relationship Diagram, Relational Model – Constraints, Languages, Design, and Programming, Relational Database Schemes, Update Operations and constraints
  • Relational Algebra and Relational Calculus; SQL: Data Definition and Data Types; Types of data base Languages, aggregate functions, Constraints, Queries, Insert, Delete, and Update Statements; Views, Stored Procedures and Functions; Database Triggers, SQL Injection.
  • Normalization for Relational Databases: Anomalies in relational data base design data, Functional Dependencies and Normalizations; algorithms for Query Processing and Optimization; Transaction Processing, Concurrency Control Techniques, Database Recovery Techniques
  • Data Warehousing and Data Mining: Data Modelling for Data Warehouse, Concept Hierarchy, OLAP and OLTP, Association Rules, Classification, Clustering, Regression.
ಘಟಕ 6: System Software and Operating system
  • System Software: Machine, Assembly and High-Level Languages; Compilers and Interpreters; Loading, Linking and Relocation; Macros, Debuggers.
  • Basics of Operating Systems: Operating System Structure, Operations and Services; System Calls, Operating-System Design and Implementation; System Boot.
  • Process Management: Process Scheduling and Operations; Inter process Communication, Communication in Client-Server Systems, Process Synchronization, Critical-Section Problem, Peterson’s Solution, Semaphores, Synchronization.
  • Threads: Multicore Programming, Multithreading Models, Thread Libraries, Implicit Threading, Threading Issues.
  • CPU Scheduling: Scheduling Criteria and Algorithms; Thread Scheduling, Multiple-Processor Scheduling, Real-time CPU Scheduling.
  • Deadlocks: Deadlock Characterization, Methods for Handing Deadlocks, Deadlock Prevention, Avoidance and Detection; Recovery from Deadlock.
  • Memory Management: Contiguous Memory Allocation, Swapping, Paging, Segmentation, Demand Paging, Page Replacement, Allocation of Frames, Thrashing, Memory-Mapped Files.
  • Storage Management: Mass-Storage Structure, Disk Structure, Scheduling and Management, RAID Structures.
  • File and Input /Output Systems: Access Methods, Directory and Disk Structure; File-System Mounting, File Sharing, File-System Structure and Implementation; Directory Implementation, Allocation Methods, Free-Space Management, Efficiency and Performance; Recovery, I/O Hardware, Application I/O Interface, Kernel I/O Subsystem, Transforming I/O Requests to Hardware Operations.
  • Security: Protection, Access Matrix, Access Control, Revocation of Access Rights, Program Threats, System and Network Threats; Cryptography as a Security Tool, user Authentication, Implementing Security Defenses.
  • Linux Operating Systems: Design Principles, Kernel Modules, Process Management, Scheduling, Memory Management, File Systems, Input and Output; Interprocess Communication, Network Structure.
  • Windows Operating Systems: Design Principles, System Components, Terminal Services and Fast User Switching; File System Networking.
ಘಟಕ 7: Software Engineering
  • Software Process Models: Software Process, Generic Process Model- Framework Activity, Task Set and Process Patterns; Process Lifecycle, Prescriptive Process Models, Project Management, Component Based Development, Aspect-Oriented Software Development, Formal Methods, Agile Process Models- Extreme Programming (XP), Adaptive Software Development, Scrum, Dynamics System Development Model, Feature Driven Development
  • Software Requirement: Functional and Non-Functional Requirements; Eliciting Requirements, Developing Use Cases, Requirement Analysis and Modelling; Requirements Review, Software Requirement and Specification (SRS) Document.
  • Software Design: Abstraction, Architecture, Patterns, Separation of Concerns, Modularity, Information Hiding, Functional Independence, Cohesion and Coupling; Object-Oriented Design, Data Design, Architectural Design, User Interface Design, Component Level Design.
  • Software Testing: Verification and Validation; Error, Fault, Bug and Failure; Unit and Integration Testing; White-box and Black-box Testing; Basis Path Testing, Control Structure Testing, Deriving Test Cases, Alpha and Beta Testing; Regression Testing, Performance Testing, Stress Testing.
ಘಟಕ 8: Data Structures and Algorithms
  • Data Structures : Arrays and their Applications; sparse, Matrix, Stacks, Queues, Priority Queues, Linked Lists, Trees, Forest, Binary Tree, Threaded Binary Tree, Binary Search Tree, AVL Tree, Data Structure for Sets, Graphs, Sorting and Searching Algorithms; Hashing.
  • Performance Analysis of Algorithms and Recurrences: Time and Space Complexities; Asymptotic Notation, Recurrence Relations.
  • Design Techniques: Divide and Conquer; Dynamic Programming, Greedy Algorithms, Backtracking, Branch and Bound.
  • Graph Algorithms: Breadth –First Search, Depth-First Search, Shortest Paths, Maximum Flow, Minimum Spanning Trees.
  • Complexity Theory: P and NP Class Problems; NP-completeness and Reducibility.
ಘಟಕ 9: Data Communication and Computer Networks
  • Data Communication: Components of a Data Communication System, Simplex, Half-Duplex and Duplex Modes of Communication; Analog and Digital Signals; Noiseless and Noisy Channels; Bandwidth, Throughput and Latency; Digital and Analog Transmission; Data Encoding and Modulation Techniques; Broadband and Baseband Transmission; Multiplexing, Transmission Media, Transmission Errors, Error Handling Mechanisms.
  • Computer Networks: Network Topologies, Local Area Networks, Metropolitan Area Networks, Wide Area Network, Wireless Networks, Internet.
  • Network Models: Layered Architecture, OSI Reference Model and its Protocols; TCP/IP Protocol Suite, Physical, Logical, Port and Specific Addresses; Switching Techniques.
  • Functions of OSI and TCP/IP Layers: Framing Error Detection and Correction; Flow and Error Control; Sliding Window Protocol, HDLC, Multiple Access – CSMA/CD, CSMA/CA, Reservation, Polling, Token Passing, FDMA, CDMA, TDMA, Network Devices, Backbone Networks, Virtual LANs. IPv4 Structure and Address Space; Classful and Classless Addressing; Datagram, Fragmentation and Checksum; IPv6 Packet Format, Mapping Logical to Physical Address (ARP), Direct and Indirect Network Layer Delivery; Routing Algorithms, TCP, UDP and SCTP Protocols; Flow Control, Error Control and Congestion Control in TCP and SCTP.
  • World Wide Web (WWW): Internet, working of internet, Uniform Resource Locator (URL), Domain Name Service (DNS), Resolution – Mapping Names to Address and Address to Names; Electronic Mail Architecture, SMTP, POP and IMAP; TELNET and FTP.
  • Network Security: Malwares, Cryptography and Steganography; Secret-Key Algorithms, Public- Key Algorithms, Digital Signature, Virtual Private Networks, Firewalls.
  • Mobile Technology: GSM and CDMA; Services and Architecture of GSM and Mobile Computing; Middleware and Gateway for Mobile Computing; Mobile IP and Mobile Communication Protocol; Communication Satellites, Wireless Networks and Topologies; Cellular Topology, Mobile Adhoc Networks, Wireless Transmission and Wireless LANs.
  • Cloud Computing and IoT: SaaS, Paas, Iaas, Public and Private Cloud; Virtualization, Virtual Server, Cloud Storage, Database Storage, Basics of IoT.
ಘಟಕ 10: Artificial Intelligence (AI)
  • Approaches to AI: Turing Test and Rational Agent Approaches; State Space Representation of Problems, Heuristic Search Techniques, Game Playing.
  • Knowledge Representation: Logic, Semantic Network, Frames, Rules, Scripts, Conceptual Dependency and Ontologies; Expert Systems
  • Problem solving by searching: Agents, Problem& Solutions, Breadth first and death first search, A*, Bidirectional search greedy best first search, heuristic functions
  • Natural Language Processing: Grammar and Language; Parsing Techniques, Semantic Analysis and Pragmatics.
  • Artificial Neural Networks (ANN): Supervised, Unsupervised and Reinforcement Learning; Applications of AI.

ಪತ್ರಿಕೆ 1 — ಸಾಮಾನ್ಯ (100 ಅಂಕಗಳು)

ವಿಭಾಗಅಂಕಗಳು
ಸಾಮಾನ್ಯ ಜ್ಞಾನ15
ಪ್ರಚಲಿತ ವಿದ್ಯಮಾನಗಳು15
ಸಾಮಾನ್ಯ ಕನ್ನಡ10
ಸಾಮಾನ್ಯ ಇಂಗ್ಲಿಷ್10
ಶೈಕ್ಷಣಿಕ ಮನೋವಿಜ್ಞಾನ ಮತ್ತು ಮಾನವ ವಿಕಾಸ15
ಕಂಪ್ಯೂಟರ್ ಸಾಕ್ಷರತೆ15
ಮೌಲ್ಯ ಶಿಕ್ಷಣ ಮತ್ತು ಆರೋಗ್ಯ ಶಿಕ್ಷಣ20

ವಿಷಯವಾರು ಪತ್ರಿಕೆ 1 ಪಠ್ಯಕ್ರಮಕ್ಕೆ ಅಧಿಕೃತ ಪತ್ರಿಕೆ 1 ಪಠ್ಯಕ್ರಮ PDF ನೋಡಿ.

CST ಅಭ್ಯಾಸ ಪತ್ರಿಕೆ — 50 ಪ್ರಶ್ನೆಗಳು (ಉಚಿತ PDF)

ಪತ್ರಿಕೆ 2ರ ಎಲ್ಲಾ 10 ಘಟಕಗಳಿಂದ ತಲಾ 5 ಪ್ರಶ್ನೆಗಳು, ಸರಿ ಉತ್ತರ ಮತ್ತು ವಿವರಣೆಯೊಂದಿಗೆ (ಇಂಗ್ಲಿಷ್). ಮೊದಲ 10 ಪ್ರಶ್ನೆಗಳನ್ನು ಇಲ್ಲೇ ಪ್ರಯತ್ನಿಸಿ.

⬇ ಅಭ್ಯಾಸ ಪತ್ರಿಕೆ PDF ಡೌನ್‌ಲೋಡ್
  1. Which Act gave legal validity to electronic commerce (e-commerce) in India?

    1. Companies Act
    2. Consumer Protection Act
    3. Information Technology Act
    4. Cyber Act
    ಉತ್ತರ ತೋರಿಸಿ

    ಉತ್ತರ C. Information Technology Act

    • The Information Technology Act, 2000 gave legal recognition to electronic records and digital signatures, enabling e-commerce in India.
    • It was based on the UNCITRAL Model Law on Electronic Commerce adopted by the United Nations.
    • The Act also defines cyber offences and their penalties, and it was amended in 2008.
    • India has no separate law called the Cyber Act; cyber law is mainly the IT Act.

  2. Which of the following is a type of secondary memory?

    1. Hard disk drive (HDD)
    2. Cache memory
    3. Registers
    4. Processor
    ಉತ್ತರ ತೋರಿಸಿ

    ಉತ್ತರ A. Hard disk drive (HDD)

    • A hard disk drive is secondary memory, used to store data and programs permanently in large amounts.
    • Other examples of secondary storage are SSDs, CDs, DVDs, pen drives and memory cards.
    • Cache memory and registers are fast, small, volatile memories closely tied to the CPU, and a processor is not memory at all.

  3. Why is debugging an essential part of problem solving in programming?

    1. To find and fix errors in the code
    2. To write the algorithm
    3. To reduce the size of the program
    4. To develop the problem statement
    ಉತ್ತರ ತೋರಿಸಿ

    ಉತ್ತರ A. To find and fix errors in the code

    • Debugging is the process of locating and correcting errors, called bugs, in a program.
    • Errors may be syntax errors, logical errors or runtime errors.
    • A program that has not been debugged may crash or quietly give wrong results.

  4. What is the primary function of an operating system?

    1. To manage computer hardware and software resources
    2. To develop new software
    3. To provide internet security only
    4. To create graphics
    ಉತ್ತರ ತೋರಿಸಿ

    ಉತ್ತರ A. To manage computer hardware and software resources

    • An operating system is system software that manages hardware and software resources and provides common services to programs.
    • Its tasks include process management, memory management, file management and device management.
    • It also provides the user interface, such as a command line or a GUI, through which users work with the computer.

  5. What is a common effect of improper posture while using digital devices?

    1. Improved mental health
    2. Better physical fitness
    3. Back and neck pain and fatigue
    4. Sharper concentration
    ಉತ್ತರ ತೋರಿಸಿ

    ಉತ್ತರ C. Back and neck pain and fatigue

    • Improper posture while using devices, such as bending the neck over a phone, leads to back and neck pain and general fatigue.
    • Sitting upright with the screen at eye level and feet flat on the floor reduces such physical strain.
    • Using ergonomically designed chairs and desks and taking short stretching breaks also help.

  6. The proposition ¬(P ∧ Q) ⇔ (¬P ∨ ¬Q) is a

    1. Tautology
    2. Contradiction
    3. Contingency
    4. Invalid formula
    ಉತ್ತರ ತೋರಿಸಿ

    ಉತ್ತರ A. Tautology

    • This is De Morgan's law, so both sides have the same truth value in every row of the truth table and the biconditional is always true: a tautology.
    • A tautology is true for every assignment of truth values; a contradiction is false for every assignment.
    • A contingency is true for some assignments and false for others.
    • The companion law is ¬(P ∨ Q) ⇔ (¬P ∧ ¬Q), also a tautology.

  7. Let S = {1, 2, 3, 6, 12} with the operation a * b = GCD(a, b). Which element is the identity element of (S, *)?

    1. 1
    2. 2
    3. 6
    4. 12
    ಉತ್ತರ ತೋರಿಸಿ

    ಉತ್ತರ D. 12

    • 12 is the identity because GCD(a, 12) = a for every a in S, since every element of S divides 12.
    • GCD is associative and commutative, so (S, *) is a commutative semigroup; having the identity 12 makes it a commutative monoid.
    • The element 1 behaves as a zero, not an identity: GCD(a, 1) = 1 for every a.

  8. Let X and Y be two sets having n elements each. The total number of bijective functions from X to Y is

    1. n
    2. 2n
    3. n!
    4. 2ⁿ
    ಉತ್ತರ ತೋರಿಸಿ

    ಉತ್ತರ C. n!

    • A bijection pairs each element of X with a distinct element of Y: n choices for the first, n − 1 for the second and so on, giving n!.
    • A bijective function is both one-one (injective) and onto (surjective), so it has an inverse function.
    • A bijection between two finite sets exists only when both sets have the same number of elements.
    • The total number of all functions from X to Y is nⁿ, which is much larger than n!.

  9. Which rule of inference is used in the argument "It is foggy and cloudy now; therefore it is foggy now"?

    1. Addition
    2. Simplification
    3. Resolution
    4. Conjunction
    ಉತ್ತರ ತೋರಿಸಿ

    ಉತ್ತರ B. Simplification

    • Simplification lets us conclude p from p ∧ q, so from "foggy and cloudy" we may conclude "foggy".
    • Addition works the other way: from p we may conclude p ∨ q.
    • Conjunction combines two separate premises p and q into p ∧ q.

  10. With the universal set U = {1, 2, 3, …, 10}, what is the bit string for the set {2, 4, 6, 8, 10}? (The first bit stands for 1, the last for 10.)

    1. 0101010101
    2. 1010101010
    3. 1010010101
    4. 0010010101
    ಉತ್ತರ ತೋರಿಸಿ

    ಉತ್ತರ A. 0101010101

    • Bit i is 1 when the number i is in the set; the even numbers 2, 4, 6, 8, 10 occupy positions 2, 4, 6, 8 and 10, giving 0101010101.
    • Bit strings make set operations easy: union is bitwise OR, intersection is bitwise AND and complement flips every bit.
    • 1010101010 would represent the odd numbers {1, 3, 5, 7, 9}, the complement of the given set.

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