GATE CSE 2023 | Complexity Analysis and Asymptotic Notations Question 4 | Algorithms

GATE CSE 2023

MCQ (More than One Correct Answer)

-0

Let $$f$$ and $$g$$ be functions of natural numbers given by $$f(n)=n$$ and $$g(n)=n^2$$. Which of the following statements is/are TRUE?

$$f \in O(g)$$

$$f \in \Omega (g)$$

$$f \in o(g)$$

$$f \in \Theta (g)$$

GATE CSE 2022

MCQ (Single Correct Answer)

-0.33

Which one of the following statements is TRUE for all positive functions f(n) ?

f(n²) = $$\theta$$(f(n)²), when f(n) is a polynomial

f(n²) = o(f(n)²)

f(n²) = O(f(n)²), when f(n) is an exponential function

f(n²) = $$\Omega$$(f(n)²)

GATE CSE 2021 Set 1

MCQ (Single Correct Answer)

-0.33

Consider the following three functions.

f₁ = 10ⁿ, f₂ = n^logn, f₃ = n^√n

Which one of the following options arranges the functions in the increasing order of asymptotic growth rate?

f₁ , f₂, f₃

f₂, f₁, f₃

f₃, f₂, f₁

f₂, f₃, f₁

GATE CSE 2020

MCQ (Single Correct Answer)

-0.33

For parameters a and b, both of which are $$\omega \left( 1 \right)$$,
T(n) = $$T\left( {{n^{1/a}}} \right) + 1$$, and T(b) = 1.
Then T(n) is

$$\Theta \left( {{{\log }_a}{{\log }_b}n} \right)$$

$$\Theta \left( {{{\log }_{ab}}n} \right)$$

$$\Theta \left( {{{\log }_b}{{\log }_a}n} \right)$$

$$\Theta \left( {{{\log }_2}{{\log }_2}n} \right)$$

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GATE CSE Subjects

Theory of Computation

Undecidability Finite Automata and Regular Language Push Down Automata and Context Free Language 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

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

Digital Logic

K Maps Boolean Algebra Combinational Circuits Number Systems Sequential Circuits

Database Management System

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

Data Structures

Trees Hashing Arrays Linked List Graphs Stacks and Queues

Computer Networks

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

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