GATE CSE 2026 Set 2 | Complexity Analysis and Asymptotic Notations Question 1 | Algorithms

GATE CSE 2026 Set 2

MCQ (Single Correct Answer)

-0

Consider the following functions, where $n$ is a positive integer.

$$ n^{1 / 3}, \log (n), \log (n!), 2^{\log (n)} $$

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

Note: Assume the base of log to be 2 .

$\log (n), n^{1 / 3}, 2^{\log (n)}, \log (n!)$

$n^{1 / 3}, \log (n), \log (n!), 2^{\log (n)}$

$\log (n), n^{1 / 3}, \log (n!), 2^{\log (n)}$

$2^{\log (n)}, n^{1 / 3}, \log (n), \log (n!)$

GATE CSE 2026 Set 2

MCQ (More than One Correct Answer)

-0

Which of the following can be recurrence relation(s) corresponding to an algorithm with time complexity $\Theta(n)$ ?

$T(n)=T(n-1)+1, \quad T(1)=1$

$T(n)=2 T\left(\frac{n}{2}\right)+1, T(1)=1$

$\quad T(n)=2 T\left(\frac{n}{2}\right)+n, \quad T(1)=1$

$T(n)=T(n-1)+n, \quad T(1)=1$

GATE CSE 2025 Set 2

MCQ (Single Correct Answer)

-0.33

Consider an unordered list of $N$ distinct integers. What is the minimum number of element comparisons required to find an integer in the list that is NOT the largest in the list?

$N-1$

$2 N-1$

GATE CSE 2025 Set 1

MCQ (Single Correct Answer)

-0.33

Consider the following recurrence relation :

$$T(n)=2 T(n-1)+n 2^n \text { for } n>0, T(0)=1$$

Which ONE of the following options is CORRECT?

$T(n)=\Theta\left(n^2 2^n\right)$

$T(n)=\Theta\left(n 2^n\right)$

$T(n)=\Theta\left((\log n)^2 2^n\right)$

$T(n)=\Theta\left(4^n\right)$

GATE CSE Subjects

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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

Syntax Directed Translation Parsing Lexical Analysis Code Generation and Optimization

Web Technologies

General Aptitude

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