GATE CS 2024 Set 1 question paper: all 65 questions with answers and solutions

General Aptitude

10 questions, 15 marks

General AptitudeMCQ1 markEasy (estimate)
Q.1
If ' $\to$ ' denotes increasing order of intensity, then the meaning of the words [dry $\to$ arid $\to$ parched] is analogous to [diet $\to$ fast…
Verbal Ability and Grammar
General AptitudeMCQ1 markEasy (estimate)
Q.2
If two distinct non-zero real variables $x$ and $y$ are such that $(x + y)$ is proportional to $(x - y)$ then the value of $\frac{x}{y}$
Quantitative Aptitude
General AptitudeMCQ1 markEasy (estimate)
Q.3
Consider the following sample of numbers: 9, 18, 11, 14, 15, 17, 10, 69, 11, 13 The median of the sample is
Quantitative Aptitude
General AptitudeMCQ1 markEasy (estimate)
Q.4
The number of coins of Rs. 1, Rs. 5, and Rs. 10 denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in Rs. 5 coins is
Quantitative Aptitude
General AptitudeMCQ1 markEasy (estimate)
Q.5
For positive non-zero real variables $p$ and $q$ , if $lo g (p^{2} + q^{2}) = lo g p + lo g q + 2 lo g 3,$ then, the value of $\frac{p ^{4} + q ^{4}}{p ^{2} q ^{2}}$ is
Quantitative Aptitude
General AptitudeMCQ2 marksEasy (estimate)
Q.6
In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks. Steve was advised to keep his head __(i)__ before heading __(ii)__ to bat; for, wh...
Verbal Ability and Grammar
General AptitudeMCQ2 marksMedium (estimate)
Q.7
A rectangular paper sheet of dimensions $54 cm \times 4 cm$ is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube wh...
Quantitative Aptitude
General AptitudeMCQ2 marksEasy (estimate)
Q.8
The pie chart presents the percentage contribution of different macronutrients to a typical $2, 000 kcal$ diet of a person. Pie chart of Macronutrient energy contribution:...
Data Interpretation and Graphs
General AptitudeMCQ2 marksMedium (estimate)
Q.9
A rectangular paper of $20 cm \times 8 cm$ is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter...
Spatial Aptitude
General AptitudeMCQ2 marksEasy (estimate)
Q.10
The least number of squares to be added in the figure to make $AB$ a line of symmetry is Horizontal dashed line AB with 6 unit squares: on the left, one square above AB a...
Spatial Aptitude

Computer Science and Information Technology

55 questions, 85 marks

Engineering MathematicsMCQ1 markEasy (estimate)
Q.11
Let $f : R \to R$ be a function such that $f (x) = max {x, x^{3}}, x \in R$ , where $R$ is the set of all real numbers. The set of al...
Calculus
Engineering MathematicsMCQ1 markEasy (estimate)
Q.12
The product of all eigenvalues of the matrix $147258369$ is
Linear Algebra
Digital LogicMCQ1 markEasy (estimate)
Q.13
Consider a system that uses 5 bits for representing signed integers in 2's complement format. In this system, two integers $A$ and $B$ are represented as $A = 01010$ and $B = 11010$ ...
Number Representations and Computer Arithmetic
Engineering MathematicsMCQ1 markEasy (estimate)
Q.14
Consider a permutation sampled uniformly at random from the set of all permutations of ${1, 2, 3, \dots, n}$ for some $n \geq 4$ . Let $X$ be the event that $1$ occurs before…
Probability and Statistics · Combinatorics, Counting, Recurrence Relations and Generating Functions
Computer Organization and ArchitectureMCQ1 markEasy (estimate)
Q.15
Which one of the following statements is FALSE?
I/O Interface, Interrupts and DMA
Computer NetworksMCQ1 markEasy (estimate)
Q.16
A user starts browsing a webpage hosted at a remote server. The browser opens a single TCP connection to fetch the entire webpage from the server. The webpage consists of a top-...
Application Layer: DNS, HTTP, SMTP, FTP · Transport Layer: UDP, TCP Flow and Congestion Control, Sockets
AlgorithmsMCQ1 markEasy (estimate)
Q.17
Given an integer array of size $N$ , we want to check if the array is sorted (in either ascending or descending order). An algorithm solves this problem by making a single pass t...
Asymptotic Analysis and Time/Space Complexity · Searching and Sorting Algorithms
Programming in CMCQ1 markEasy (estimate)
Q.18
Consider the following C program: #include <stdio.h> int main(){ int a = 6; int b = 0; while(a < 10) { a = a / 12 + 1; a += b;} printf("%d", a); return 0;} Which one of the foll...
Data Types, Operators and Control Flow
Programming in CMCQ1 markEasy (estimate)
Q.19
Consider the following C program: #include <stdio.h> void fX(); int main(){ fX(); return 0;} void fX(){ char a; if((a=getchar()) != '\n') fX(); if(a != '\n') putchar(a);} Assume...
Functions, Recursion, Scope and Storage Classes
DatabasesMCQ1 markEasy (estimate)
Q.20
Let S be the specification: "Instructors teach courses. Students register for courses. Courses are allocated classrooms. Instructors guide students." Which one of the following...
ER Model and Relational Schema Design
DatabasesMCQ1 markEasy (estimate)
Q.21
In a B+ tree, the requirement of at least half-full (50%) node occupancy is relaxed for which one of the following cases?
File Organization, B-Trees and B+ Trees Indexing
DatabasesMSQ1 markEasy (estimate)
Q.22
Which of the following statements about a relation R in first normal form (1NF) is/are TRUE ?
Functional Dependencies and Normalization
Theory of ComputationMSQ1 markEasy (estimate)
Q.23
Let $L_{1}, L_{2}$ be two regular languages and $L_{3}$ a language which is not regular. Which of the following statements is/are always TRUE?
Regular Expressions, Finite Automata and Regular Languages
Operating SystemsMSQ1 markEasy (estimate)
Q.24
Which of the following statements about threads is/are TRUE?
Processes, Threads and System Calls
Operating SystemsMSQ1 markEasy (estimate)
Q.25
Which of the following process state transitions is/are NOT possible?
Processes, Threads and System Calls · CPU Scheduling
Compiler DesignMSQ1 markEasy (estimate)
Q.26
Which of the following is/are Bottom-Up Parser(s)?
Parsing and Syntax Analysis (LL and LR)
Engineering MathematicsMSQ1 markEasy (estimate)
Q.27
Let $A$ and $B$ be two events in a probability space with $P (A) = 0.3, P (B) = 0.5$ , and $P (A \cap B) = 0.1$ . Which of the following statements is/are TRUE?
Probability and Statistics
Digital LogicMSQ1 markMedium (estimate)
Q.28
Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of th...
Combinational Circuits
Computer NetworksMSQ1 markEasy (estimate)
Q.29
TCP client P successfully establishes a connection to TCP server Q. Let $N_{P}$ denote the sequence number in the SYN sent from P to Q. Let $N_{Q}$ denote the acknowledgement number...
Transport Layer: UDP, TCP Flow and Congestion Control, Sockets
Computer Organization and ArchitectureMSQ1 markEasy (estimate)
Q.30
Consider a 5-stage pipelined processor with Instruction Fetch (IF), Instruction Decode (ID), Execute (EX), Memory Access (MEM), and Register Writeback (WB) stages. Which of the...
Instruction Pipelining and Hazards
Computer NetworksMSQ1 markEasy (estimate)
Q.31
Which of the following fields is/are modified in the IP header of a packet going out of a network address translation (NAT) device from an internal network to an external network?
IPv4/IPv6 Addressing, Subnetting, CIDR, ARP, ICMP and NAT
Engineering MathematicsNAT1 markMedium (estimate)
Q.32
Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$ . The number of possible...
Sets, Relations, Functions, Partial Orders and Lattices
Compiler DesignNAT1 markEasy (estimate)
Q.33
Consider the operator precedence and associativity rules for the integer arithmetic operators given in the table below. Operator Precedence Associativity + Highest Left - High R...
Parsing and Syntax Analysis (LL and LR)
Engineering MathematicsNAT1 markEasy (estimate)
Q.34
The number of spanning trees in a complete graph of 4 vertices labelled A, B, C, and D is _________
Graph Theory
DatabasesNAT1 markEasy (estimate)
Q.35
Consider the following two relations, $R (A, B)$ and $S (A, C)$ : R.A R.B 10 20 20 30 30 40 30 50 50 95 S.A S.C 10 90 30 45 40 80 The total number of tuples obtained by evaluating th...
Relational Algebra and Tuple Relational Calculus
Computer NetworksMCQ2 marksEasy (estimate)
Q.36
Consider a network path P-Q-R between nodes P and R via router Q. Node P sends a file of size $1 0^{6}$ bytes to R via this path by splitting the file into chunks of $1 0^{3}$ bytes e...
OSI/TCP-IP Layering, Physical Layer and Switching
Compiler DesignMCQ2 marksEasy (estimate)
Q.37
Consider the following syntax-directed definition (SDD).…
Syntax-Directed Translation
Compiler DesignMCQ2 marksMedium (estimate)
Q.38
Consider the following grammar $G$ , with $S$ as the start symbol. The grammar $G$ has three incomplete productions denoted by (1), (2), and (3).…
Parsing and Syntax Analysis (LL and LR)
Compiler DesignMCQ2 marksMedium (estimate)
Q.39
Consider the following pseudo-code. L1: t1 = -1 L2: t2 = 0 L3: t3 = 0 L4: t4 = 4 * t3 L5: t5 = 4 * t2 L6: t6 = t5 * M L7: t7 = t4 + t6 L8: t8 = a[t7] L9: if t8 <= max goto L11 L...
Intermediate Code Generation, Data Flow Analysis and Code Optimization
Operating SystemsMCQ2 marksMedium (estimate)
Q.40
Consider the following two threads T1 and T2 that update two shared variables a and b. Assume that initially a = b = 1. Though context switching between threads can happen...
Process Synchronization and Concurrency
Data StructuresMCQ2 marksMedium (estimate)
Q.41
An array [82, 101, 90, 11, 111, 75, 33, 131, 44, 93] is heapified. Which one of the following options represents the first three elements in the heapified array?
Binary Heaps and Priority Queues
AlgorithmsMCQ2 marksMedium (estimate)
Q.42
Consider the following recurrence relation: $T (n) = {n T (n) + n 1 for n \geq 1, for n = 1.$ Which one of the follow...
Asymptotic Analysis and Time/Space Complexity
Data StructuresMCQ2 marksEasy (estimate)
Q.43
Consider a binary min-heap containing 105 distinct elements. Let $k$ be the index (in the underlying array) of the maximum element stored in the heap. The number of possible val...
Binary Heaps and Priority Queues
DatabasesMSQ2 marksEasy (estimate)
Q.44
The symbol $\to$ indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?
Functional Dependencies and Normalization
AlgorithmsMSQ2 marksMedium (estimate)
Q.45
Let $G$ be a directed graph and $T$ a depth first search (DFS) spanning tree in $G$ that is rooted at a vertex $v$ . Suppose $T$ is also a breadth first search (BFS) tree in $G$ ,...
Graph Traversals, Topological Sort and Connectivity
DatabasesMSQ2 marksEasy (estimate)
Q.46
Consider the following read-write schedule $S$ over three transactions $T_{1}, T_{2}$ , and $T_{3}$ , where the subscripts in the schedule indicate transaction IDs…
Transactions, Serializability and Concurrency Control
Digital LogicMSQ2 marksEasy (estimate)
Q.47
Consider a Boolean expression given by $F (X, Y, Z) = \sum (3, 5, 6, 7)$ . Which of the following statements is/are CORRECT?
Boolean Algebra and Logic Minimization
Programming in CMSQ2 marksEasy (estimate)
Q.48
Consider the following C function definition. int f(int x, int y) { for (int i=0; i<y; i++) { x=x+x+y; } return x; } Which of the following statements is/are TRUE about the abov...
Data Types, Operators and Control Flow
Engineering MathematicsMSQ2 marksHard (estimate)
Q.49
Let $A$ be any $n \times m$ matrix, where $m > n$ . Which of the following statements is/are TRUE about the system of linear equations $A x = 0$ ?
Linear Algebra
Theory of ComputationMSQ2 marksMedium (estimate)
Q.50
Consider the 5-state DFA $M$ accepting the language $L (M) \subset (0 + 1)^{*}$ shown below. For any string $w \in (0 + 1)^{*}$ let $n_{0} (w)$ be the number of $0$ 's in $w$ and…
Regular Expressions, Finite Automata and Regular Languages
Engineering MathematicsMSQ2 marksMedium (estimate)
Q.51
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let $G$ be any graph with $n$ vertices and chromatic number $k$ . Whic...
Graph Theory
Engineering MathematicsMSQ2 marksEasy (estimate)
Q.52
Consider the operators $⋄$ and $□$ defined by $a ⋄ b = a + 2 b, a □ b = ab$ , for positive integers. Which of the following statements is/are TRUE?
Monoids and Groups
Computer Organization and ArchitectureMSQ2 marksEasy (estimate)
Q.53
Consider two set-associative cache memory architectures: WBC, which uses the write back policy, and WTC, which uses the write through policy. Both of them use the LRU (Least Rec...
Memory Hierarchy: Cache, Main Memory and Secondary Storage
Computer Organization and ArchitectureNAT2 marksEasy (estimate)
Q.54
Consider a 512 GB hard disk with 32 storage surfaces. There are 4096 sectors per track and each sector holds 1024 bytes of data. The number of cylinders in the hard disk is ____...
Memory Hierarchy: Cache, Main Memory and Secondary Storage · File Systems, I/O and Disk Scheduling
Computer Organization and ArchitectureNAT2 marksMedium (estimate)
Q.55
The baseline execution time of a program on a 2 GHz single core machine is 100 nanoseconds (ns). The code corresponding to 90% of the execution time can be fully parallelized. T...
Instruction Pipelining and Hazards · Calculus
Computer Organization and ArchitectureNAT2 marksEasy (estimate)
Q.56
A given program has 25% load/store instructions. Suppose the ideal CPI (cycles per instruction) without any memory stalls is 2. The program exhibits 2% miss rate on instruction...
Memory Hierarchy: Cache, Main Memory and Secondary Storage · Instruction Pipelining and Hazards
Operating SystemsNAT2 marksEasy (estimate)
Q.57
Consider the following code snippet using the fork() and wait() system calls. Assume that the code compiles and runs correctly, and that the system calls run successfully wi...
Processes, Threads and System Calls
Computer NetworksNAT2 marksEasy (estimate)
Q.58
Consider the entries shown below in the forwarding table of an IP router. Each entry consists of an IP prefix and the corresponding next hop router for packets whose destination...
IPv4/IPv6 Addressing, Subnetting, CIDR, ARP, ICMP and NAT
Theory of ComputationNAT2 marksEasy (estimate)
Q.59
Let $G = (V, Σ, S, P)$ be a context-free grammar in Chomsky Normal Form with $Σ = {a, b, c}$ and $V$ containing 10 variable symbols including the start symbol $S$ . T...
Context-Free Grammars, Pushdown Automata and CFLs
AlgorithmsNAT2 marksEasy (estimate)
Q.60
The number of edges present in the forest generated by the DFS traversal of an undirected graph $G$ with 100 vertices is 40. The number of connected components in $G$ is _________
Graph Traversals, Topological Sort and Connectivity
Theory of ComputationNAT2 marksMedium (estimate)
Q.61
Consider the following two regular expressions over the alphabet ${0, 1}$ : $r = 0^{*} + 1^{*}$ $s = 0 1^{*} + 1 0^{*}$ The total number of strings of length less than or equal to 5,...
Regular Expressions, Finite Automata and Regular Languages
Operating SystemsNAT2 marksEasy (estimate)
Q.62
Consider a memory management system that uses a page size of 2 KB. Assume that both the physical and virtual addresses start from 0. Assume that the pages 0, 1, 2, and 3 are sto...
Memory Management and Virtual Memory
Engineering MathematicsNAT2 marksEasy (estimate)
Q.63
A bag contains 10 red balls and 15 blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to 3 decima...
Probability and Statistics
Digital LogicNAT2 marksEasy (estimate)
Q.64
Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. X1 and X2 are inputs of M1. X3 and X4 are inputs of M2. A, B, and C are s...
Combinational Circuits
Computer NetworksNAT2 marksMedium (estimate)
Q.65
Consider sending an IP datagram of size 1420 bytes (including 20 bytes of IP header) from a sender to a receiver over a path of two links with a router between them. The first l...
IPv4/IPv6 Addressing, Subnetting, CIDR, ARP, ICMP and NAT