GATE CSE 1996 | Set Theory & Algebra Question 93 | Discrete Mathematics

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GATE CSE 1996

MCQ (Single Correct Answer)

-0.3

Which of the following statements is false?

The set of rational numbers is an abelian group under addition.

The set of integers is an abelian group under addition.

The set of rational numbers from an abelian group under multiplication.

The set of real numbers excluding zero is an abelian group under multiplication.

GATE CSE 1995

MCQ (Single Correct Answer)

-0.3

The number of elements in the power set $$P(S)$$ of the set $$S = \left\{ {\left\{ \phi \right\},1,\left\{ {2,3} \right\}} \right\}$$ is

$$2$$

$$4$$

$$8$$

None of the above

GATE CSE 1995

MCQ (Single Correct Answer)

-0.3

Let $$R$$ be a symmetric and transitive relation on a set $$A$$. Then

$$R$$ is reflexive and hence an equivalence relation.

$$R$$ is reflexive and hence partial order.

$$R$$ is not reflexive and hence not an equivalence relation.

None of the above.

GATE CSE 1993

MCQ (Single Correct Answer)

-0.3

Let $${\rm A}$$ be a finite set of size $$n$$. The number of elements in the power set of $${\rm A} \times {\rm A}$$ is

$${2^{{2^n}}}$$

$${2^{{n^2}}}$$

$${2^n}$$

$${n^2}$$

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Theory of Computation

Finite Automata and Regular Language Push Down Automata and Context Free Language Undecidability Recursively Enumerable Language and Turing Machine

Operating Systems

Process Concepts and Cpu Scheduling Synchronization and Concurrency Deadlocks Memory Management File System IO and Protection

Algorithms

P and NP Concepts Searching and Sorting Greedy Method Dynamic Programming Complexity Analysis and Asymptotic Notations Divide and Conquer Method

Digital Logic

Sequential Circuits Boolean Algebra K Maps Combinational Circuits Number Systems

Database Management System

Er Diagrams Functional Dependencies and Normalization Structured Query Language Relational Algebra Transactions and Concurrency File Structures and Indexing

Data Structures

Arrays Stacks and Queues Linked List Trees Graphs Hashing

Computer Networks

Concepts of Layering Data Link Layer and Switching Network Layer Application Layer Protocol Routing Algorithm TCP UDP Sockets and Congestion Control Lan Technologies and Wi-Fi Network Security

Software Engineering

Compiler Design

Lexical Analysis Parsing Syntax Directed Translation Code Generation and Optimization

Web Technologies

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Verbal Ability Logical Reasoning Numerical Ability

Discrete Mathematics

Set Theory & Algebra Linear Algebra Graph Theory Combinatorics Mathematical Logic Probability Calculus

Programming Languages

Basic of Programming Language Pointer and Structure in C Function and Recursion

Computer Organization

Computer Arithmetic Pipelining Machine Instructions and Addressing Modes Memory Interfacing IO Interface Alu Data Path and Control Unit Secondary Memory