GATE CSE 1996 | Set Theory & Algebra Question 86 | Discrete Mathematics

GATE CSE 1996

MCQ (Single Correct Answer)

-0.3

Suppose $$X$$ and $$Y$$ are sets and $$\left| X \right|$$ and $$\left| Y \right|$$ are their respective cardinalities. It is given that there are exactly 97 functions from $$X$$ to $$Y$$. From this one can conclude that

$$\left| X \right| = 1,\,\,\,\,\,\,\,\,\,\left| Y \right| = 97$$

$$\left| X \right| = 97,\,\,\,\,\,\,\,\,\,\left| Y \right| = 1$$

$$\left| X \right| = 97,\,\,\,\,\,\,\,\,\,\left| Y \right| = 97$$

None of the above

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

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 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

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GATE CSE Subjects

Theory of Computation

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

Operating Systems

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

Algorithms

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

Digital Logic

Number Systems Boolean Algebra K Maps Combinational Circuits Sequential Circuits

Database Management System

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

Data Structures

Trees Hashing Arrays Linked List Graphs Stacks and Queues

Computer Networks

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

Software Engineering

Compiler Design

Lexical Analysis Parsing Syntax Directed Translation Code Generation and Optimization

Web Technologies

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability

Discrete Mathematics

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

Programming Languages

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

Computer Organization

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