GATE CS 2026 Set 1 question paper: all 65 questions with answers and solutions

General Aptitude

10 questions, 15 marks

General AptitudeMCQ1 markEasy (estimate)
Q.1
The antonym of the word protagonist is ________.
Verbal Ability and Grammar
General AptitudeMCQ1 markEasy (estimate)
Q.2
The figure shows two 4-tile patterns. Two 4-tile patterns: a 2 by 2 square of 4 tiles on the left, and a 4 by 1 vertical strip of 4 tiles on the right. Either one or both of the...
Spatial Aptitude
General AptitudeMCQ1 markEasy (estimate)
Q.3
Consider a knock-out women's badminton singles tournament where there are no ties. The loser in each game is eliminated from the tournament. Every player plays until she is defe...
Analytical and Logical Reasoning
General AptitudeMCQ1 markEasy (estimate)
Q.4
A student needs to enroll for a minimum of 60 credits. A student cannot enroll for more than 70 credits. The credits are divided amongst project and three distinct sets of cours...
Quantitative Aptitude
General AptitudeMCQ1 markEasy (estimate)
Q.5
'When the teacher is in the room, all students stand silently.' If the above statement is true, which one of the following statements is not necessarily true?
Analytical and Logical Reasoning
General AptitudeMCQ2 marksEasy (estimate)
Q.6
Combinatorics deals with problems involving counting. For example, "How many distinct arrangements of N distinct objects in M spaces on a circle are possible?" is a typical prob...
Reading Comprehension and Verbal Deduction
General AptitudeMCQ2 marksMedium (estimate)
Q.7
In Panel I of the figure below, the front view and top view of a structure are shown. Which one of the 3D structures shown in Panel II possesses the views shown in Panel I? Pane...
Spatial Aptitude
General AptitudeMCQ2 marksEasy (estimate)
Q.8
For positive real numbers $S$ and $K$ , the function $H_{K} (S)$ is defined as: $H_{K} (S) = max (S - K, 0)$ . The $max$ function is defined as…
Data Interpretation and Graphs
General AptitudeMCQ2 marksMedium (estimate)
Q.9
In the 2020 summer Olympics' Javelin throw finals, Neeraj Chopra exhibited a spectacular performance to win the gold medal. The silver medal was won by Jakub Vadlejch and the br...
Analytical and Logical Reasoning
General AptitudeMCQ2 marksEasy (estimate)
Q.10
An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice in succession and the number on the top face is recorded each time. The proba...
Quantitative Aptitude

Computer Science and Information Technology

55 questions, 85 marks

Engineering MathematicsMCQ1 markEasy (estimate)
Q.11
An urn contains one red ball and one blue ball. At each step, a ball is picked uniformly at random from the urn, and this ball together with another ball of the same color is pu...
Probability and Statistics
Engineering MathematicsMCQ1 markMedium (estimate)
Q.12
Consider $4 \times 4$ matrices with their elements from ${0, 1}$ . The number of such matrices with even number of $1$ s in every row and every column is
Combinatorics, Counting, Recurrence Relations and Generating Functions
Engineering MathematicsMCQ1 markEasy (estimate)
Q.13
For $n > 1$ , the maximum multiplicity of any eigenvalue of an $n \times n$ matrix with elements from $R$ is
Linear Algebra
Computer Organization and ArchitectureMCQ1 markEasy (estimate)
Q.14
Match each addressing mode in List I with a data element or an element of a data structure (in a high-level language) in List II: List I List II P. Immediate 1. Element of an ar...
Machine Instructions and Addressing Modes
Computer Organization and ArchitectureMCQ1 markEasy (estimate)
Q.15
Consider a processor P whose instruction set architecture is the load-store architecture. The instruction format is such that the first operand of any instruction is the destina...
Machine Instructions and Addressing Modes
Computer Organization and ArchitectureMCQ1 markEasy (estimate)
Q.16
Which one of the following dependencies among the register operands of different instructions can cause a data hazard in a pipelined processor?
Instruction Pipelining and Hazards
AlgorithmsMCQ1 markMedium (estimate)
Q.17
Consider the following recurrence relations: For all $n > 1$ , $T_{1} (n) = 4 T_{1} (\frac{n}{2}) + T_{2} (n)$ $T_{2} (n) = 5 T_{2} (\frac{n}{4}) + Θ (lo g_{2} n)$ Ass...
Asymptotic Analysis and Time/Space Complexity
Computer NetworksMCQ1 markEasy (estimate)
Q.18
With respect to a TCP connection between a client and a server, which one of the following statements is true?
Transport Layer: UDP, TCP Flow and Congestion Control, Sockets
Computer NetworksMSQ1 markEasy (estimate)
Q.19
Which of the following statements is/are true with respect to the interaction of a web browser with a web server using HTTP 1.1?
Application Layer: DNS, HTTP, SMTP, FTP
Engineering MathematicsMSQ1 markEasy (estimate)
Q.20
Let $n > 1$ . Consider an $n \times n$ matrix $M$ with its elements from $R$ . Let the vector $(0, 1, 0, 0, \dots, 0) \in R^{n}$ be in the null space of $M$ . Which...
Linear Algebra
Digital LogicMSQ1 markEasy (estimate)
Q.21
Consider the following Boolean expression of a function $F$ : $F (P, Q) = (P + Q) \oplus (P Q)$ Which of the following expressions is/are equivalent to $F$ ?
Boolean Algebra and Logic Minimization
Digital LogicMSQ1 markEasy (estimate)
Q.22
Consider the 8-bit signed integers $X$ , $Y$ and $Z$ represented using the sign-magnitude form. The binary representations of $X$ and $Y$ are as follows…
Number Representations and Computer Arithmetic
Data StructuresMSQ1 markEasy (estimate)
Q.23
Let $n$ be an odd number greater than $100$ . Consider a binary minheap with $n$ elements stored in an array $P$ whose index starts from $1$ . Which of the following indices of…
Binary Heaps and Priority Queues
Data StructuresMSQ1 markEasy (estimate)
Q.24
Consider a hash table $P [0, 1, \dots, 10]$ that is initially empty. The hash table is maintained using open addressing with linear probing. The hash function used is…
Hash Tables and Collision Resolution
Theory of ComputationMSQ1 markMedium (estimate)
Q.25
Consider the following grammar where $S$ is the start symbol, and $a$ and $b$ are terminal symbols. $S \to a S b S ∣ b S ∣ ϵ$ Which of the following statement...
Context-Free Grammars, Pushdown Automata and CFLs
Theory of ComputationMSQ1 markEasy (estimate)
Q.26
Let $M$ be a nondeterministic finite automaton (NFA) with 6 states over a finite alphabet. Which of the following options CANNOT be the number of states in the minimal determini...
Regular Expressions, Finite Automata and Regular Languages
Compiler DesignMSQ1 markEasy (estimate)
Q.27
Consider the following C statements: char str1 = "Hello; / Statement S1 */ char str2 = "Hello;"; / Statement S2 */ int str3 = "Hello"; / Statement S3 */ Which of the follo...
Lexical Analysis
Compiler DesignMSQ1 markEasy (estimate)
Q.28
Which of the following statements is/are true?
Parsing and Syntax Analysis (LL and LR)
Operating SystemsMSQ1 markEasy (estimate)
Q.29
With respect to deadlocks in an operating system, which of the following statements is/are FALSE?
Deadlock Prevention, Avoidance and Detection
DatabasesMSQ1 markEasy (estimate)
Q.30
Let $P, Q, R$ and $S$ be the attributes of a relation in a relational schema. Let $X ⟶ Y$ indicate functional dependency in the context of a relational database, w...
Functional Dependencies and Normalization
DatabasesMSQ1 markEasy (estimate)
Q.31
In the context of relational database normalization, which of the following statements is/are true?
Functional Dependencies and Normalization
Engineering MathematicsNAT1 markEasy (estimate)
Q.32
Consider the function $f : R \to R$ defined as follows…
Calculus
Data StructuresNAT1 markEasy (estimate)
Q.33
The height of a binary tree is the number of edges in the longest path from the root to a leaf in the tree. The maximum possible height of a full binary tree with 23 nodes is __...
Binary Trees, Binary Search Trees and Balanced Trees
Programming in CNAT1 markEasy (estimate)
Q.34
Consider the following program in C: #include <stdio.h> void func(int i, int j) { if(i < j) { int i = 0; while (i < 10) { j += 2; i++; } } printf("%d", i); } int main() { int i...
Functions, Recursion, Scope and Storage Classes
Operating SystemsNAT1 markEasy (estimate)
Q.35
Consider a system consisting of $k$ instances of a resource $R$ , being shared by 5 processes. Assume that each process requires a maximum of two instances of resource $R$ and a...
Deadlock Prevention, Avoidance and Detection
Computer Organization and ArchitectureMCQ2 marksMedium (estimate)
Q.36
Consider the real valued variables $X$ , $Y$ and $Z$ represented using the IEEE 754 single-precision floating-point format. The binary representations of $X$ and $Y$ in hexadecim...
ALU, Datapath and Control Unit
Digital LogicMCQ2 marksMedium (estimate)
Q.37
Consider a 2-bit saturating up/down counter that performs the saturating up count when the input $P$ is 0, and the saturating down count when $P$ is 1. The Next State table of t...
Sequential Circuits, Counters and Registers
Computer Organization and ArchitectureMCQ2 marksEasy (estimate)
Q.38
The size of the physical address space of a processor is $2^{32}$ bytes. The capacity of a cache memory unit is $2^{23}$ bytes. The cache block size is $128$ bytes. The cache me...
Memory Hierarchy: Cache, Main Memory and Secondary Storage
Data StructuresMCQ2 marksEasy (estimate)
Q.39
Consider the following code snippet in C language that computes the number of nodes in a non-empty singly linked list pointed to by the pointer variable head. struct node{ int...
Arrays and Linked Lists
Data StructuresMCQ2 marksMedium (estimate)
Q.40
Let $P$ be the set of all integers from $1$ to $15$ . Consider any order of insertion of the elements of $P$ into a binary search tree that creates a complete binary tree. Which...
Binary Trees, Binary Search Trees and Balanced Trees
AlgorithmsMCQ2 marksMedium (estimate)
Q.41
Let $G (V, E)$ be an undirected, edge-weighted graph with integer weights. The weight of a path is the sum of the weights of the edges in that path. The length of a path is the n...
Single-Source and All-Pairs Shortest Paths
Compiler DesignMCQ2 marksMedium (estimate)
Q.42
Consider the control flow graph shown in the figure. Control flow graph with ENTRY leading to basic block B1 (a = b + i), which branches to B2 (a = g * k; f = d - f; a = c * 4)...
Intermediate Code Generation, Data Flow Analysis and Code Optimization
DatabasesMCQ2 marksEasy (estimate)
Q.43
Consider a relational database schema with two relations $R (P, Q)$ and $S (X, Y)$ . Let…
Relational Algebra and Tuple Relational Calculus
Computer NetworksMCQ2 marksMedium (estimate)
Q.44
A TCP sender successfully establishes a connection with a TCP receiver and starts the transmission of segments. The TCP congestion control mechanism's slow-start threshold is se...
Transport Layer: UDP, TCP Flow and Congestion Control, Sockets
Computer NetworksMCQ2 marksEasy (estimate)
Q.45
Consider the implementation of sliding window protocol over a lossless link, with a window size of $W$ frames, where each frame is of size $1000$ bits (including header). The ba...
Data Link Layer: Framing, Error Detection and Sliding Window
Engineering MathematicsMSQ2 marksMedium (estimate)
Q.46
Let $f : R \to R$ be defined as follows: $f (x) = (\frac{∣ x ∣}{2} - x) (x - \frac{∣ x ∣}{2})$ Which of the following statements is/ar...
Calculus
Engineering MathematicsMSQ2 marksMedium (estimate)
Q.47
Let $G (V, E)$ be a simple, undirected graph. A vertex cover of $G$ is a subset $V^{'} \subseteq V$ such that for every $(u, v) \in E$ , $u \in V^{'}$ or $v \in V^{'}$ . Let the size of the...
Graph Theory
Digital LogicMSQ2 marksMedium (estimate)
Q.48
Consider a Boolean function $F$ with the following minterm expression: $F (P, Q, R, S) = \sum m (1, 2, 3, 4, 5, 7, 10, 12, 13, 14)$ Which of the following options is/are the min...
Boolean Algebra and Logic Minimization
AlgorithmsMSQ2 marksMedium (estimate)
Q.49
Let $G (V, E)$ be a simple, undirected, edge-weighted graph with unique edge weights. Which of the following statements about the minimum spanning trees (MST) of $G$ is/are true?
Minimum Spanning Trees
AlgorithmsMSQ2 marksMedium (estimate)
Q.50
Consider the following pseudocode for depth-first search (DFS) algorithm which takes a directed graph $G (V, E)$ as input, where $d [v]$ and $f [v]$ are the discovery time and fini...
Graph Traversals, Topological Sort and Connectivity
Theory of ComputationMSQ2 marksEasy (estimate)
Q.51
Let $L_{1}$ and $L_{2}$ be two languages over a finite alphabet, such that $L_{1} \cap L_{2}$ and $L_{2}$ are regular languages. Which of the following statements is/are always true?
Context-Free Grammars, Pushdown Automata and CFLs
Theory of ComputationMSQ2 marksMedium (estimate)
Q.52
Consider the following context-free grammar $G$ . $S \to aba A B A bba$ $A \to aa B B A b ∣ b B abaa$ $B \to a B b ∣ ab$ In the above grammar, $S$ is the...
Context-Free Grammars, Pushdown Automata and CFLs
Compiler DesignMSQ2 marksMedium (estimate)
Q.53
Consider the following two syntax-directed definitions SDD1 and SDD2 for type declarations. SDD1 Grammar (G1) SDD1 Semantic Rules SDD2 Grammar (G2) SDD2 Semantic Rules…
Syntax-Directed Translation
Operating SystemsMSQ2 marksMedium (estimate)
Q.54
Consider a system that has a cache memory unit and a memory management unit (MMU). The address input to the cache memory is a physical address. The MMU has a translation lookasi...
Memory Management and Virtual Memory
AlgorithmsMSQ2 marksEasy (estimate)
Q.55
An undirected, unweighted, simple graph $G (V, E)$ is said to be 2-colorable if there exists a function $c : V \to {0, 1}$ such that for every $(u, v) \in E$ …
Graph Traversals, Topological Sort and Connectivity
Computer NetworksMSQ2 marksMedium (estimate)
Q.56
An ISP having an address block 202.16.0.0/15 assigns a block of $6000$ IP addresses to a client, using the classless internet domain routing (CIDR) super-netting approach. Whi...
IPv4/IPv6 Addressing, Subnetting, CIDR, ARP, ICMP and NAT
Engineering MathematicsNAT2 marksMedium (estimate)
Q.57
Let $G$ be an undirected graph, which is a path on 8 vertices. The number of matchings in $G$ is ______. (answer in integer)
Combinatorics, Counting, Recurrence Relations and Generating Functions
Engineering MathematicsNAT2 marksEasy (estimate)
Q.58
Let $X$ be a random variable which takes values in the set ${1, 2, 3, 4, 5, 6, 7, 8}$ . Further, $Pr (X = 1) = Pr (X = 2) = Pr (X = 5) = Pr (X = 7) = \frac{1}{6}$ and…
Probability and Statistics
Operating SystemsNAT2 marksMedium (estimate)
Q.59
Consider a hard disk with a rotational speed of $15000$ rpm. The time to move the read/write head from a track to its adjacent track is $1$ millisecond. Initially, the head is o...
File Systems, I/O and Disk Scheduling
Computer Organization and ArchitectureNAT2 marksMedium (estimate)
Q.60
The EX stage of a pipelined processor performs the memory read operations for LOAD instructions, and the operations for the arithmetic and logic instructions. Let $t_{E X}$ denot...
Instruction Pipelining and Hazards
Programming in CNAT2 marksMedium (estimate)
Q.61
Consider the recursive functions represented by the following code segment: int bar(int n){ if (n == 1) return 0; else return 1 + bar(n/2); } int foo(int n){ if (n == 1) return...
Functions, Recursion, Scope and Storage Classes
Data StructuresNAT2 marksMedium (estimate)
Q.62
The following sequence corresponds to the preorder traversal of a binary search tree $T$ : $50, 25, 13, 40, 30, 47, 75, 60, 70, 80, 77$ The position of the element $60$ in the...
Binary Trees, Binary Search Trees and Balanced Trees
Operating SystemsNAT2 marksEasy (estimate)
Q.63
Consider the following program snippet. Assume that the program compiles and runs successfully. Further, assume that the fork() system call is always successful in creating a...
Processes, Threads and System Calls
Operating SystemsNAT2 marksMedium (estimate)
Q.64
Consider a CPU that has to execute two types of processes. The first type, Actuators (A), requires a CPU burst of 6 seconds. The second type, Controllers (C), requires a CPU bur...
CPU Scheduling
DatabasesNAT2 marksEasy (estimate)
Q.65
Consider a relational database schema with a relation $R (A, B, C, D)$ . If ${A, B}$ and ${A, C}$ are the only two candidate keys of the relation $R$ , then the number of super...
Functional Dependencies and Normalization