GATE CS 2025 Set 1 question paper: all 65 questions with answers and solutions

General Aptitude

10 questions, 15 marks

General AptitudeMCQ1 markEasy (estimate)
Q.1
Ravi had ______ younger brother who taught at ______ university. He was widely regarded as ______ honorable man. Select the option with the correct sequence of articles to fill...
Verbal Ability and Grammar
General AptitudeMCQ1 markEasy (estimate)
Q.2
The CEO's decision to downsize the workforce was considered myopic because it sacrificed long-term stability to accommodate short-term gains. Select the most appropriate option...
Verbal Ability and Grammar
General AptitudeMCQ1 markEasy (estimate)
Q.3
The average marks obtained by a class in an examination were calculated as $30.8$ . However, while checking the marks entered, the teacher found that the marks of one student wer...
Quantitative Aptitude
General AptitudeMCQ1 markEasy (estimate)
Q.4
Consider the relationships among P, Q, R, S, and T: P is the brother of Q. S is the daughter of Q. T is the sister of S. R is the mother of Q. The following statements are made...
Analytical and Logical Reasoning
General AptitudeMCQ1 markEasy (estimate)
Q.5
According to the map shown in the figure, which one of the following statements is correct? Note: The figure shown is representative. Campus map showing 1st Main Road running No...
Spatial Aptitude
General AptitudeMCQ2 marksEasy (estimate)
Q.6
"I put the brown paper in my pocket along with the chalks, and possibly other things. I suppose every one must have reflected how primeval and how poetical are the things that o...
Reading Comprehension and Verbal Deduction
General AptitudeMCQ2 marksEasy (estimate)
Q.7
In the diagram, the lines $QR$ and $S T$ are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point $P$ and line…
Quantitative Aptitude
General AptitudeMCQ2 marksEasy (estimate)
Q.8
A fair six-faced dice, with the faces labelled '1', '2', '3', '4', '5', and '6', is rolled thrice. What is the probability of rolling '6' exactly once?
Quantitative Aptitude
General AptitudeMCQ2 marksMedium (estimate)
Q.9
A square paper, shown in figure (I), is folded along the dotted lines as shown in the figures (II) and (III). Then a few cuts are made as shown in figure (IV). Which one of the...
Spatial Aptitude
General AptitudeMCQ2 marksEasy (estimate)
Q.10
A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential. If one wants to...
Quantitative Aptitude

Computer Science and Information Technology

55 questions, 85 marks

Computer Organization and ArchitectureMCQ1 markEasy (estimate)
Q.11
Suppose a program is running on a non-pipelined single processor computer system. The computer is connected to an external device that can interrupt the processor asynchronously...
I/O Interface, Interrupts and DMA
Compiler DesignMCQ1 markEasy (estimate)
Q.12
Which ONE of the following statements is FALSE regarding the symbol table?
Lexical Analysis
Compiler DesignMCQ1 markEasy (estimate)
Q.13
Which ONE of the following techniques used in compiler code optimization uses live variable analysis?
Intermediate Code Generation, Data Flow Analysis and Code Optimization
Operating SystemsMCQ1 markEasy (estimate)
Q.14
Consider a demand paging memory management system with 32-bit logical address, 20-bit physical address, and page size of 2048 bytes. Assuming that the memory is byte addressable...
Memory Management and Virtual Memory
DatabasesMCQ1 markEasy (estimate)
Q.15
A schedule of three database transactions $T_{1}$ , $T_{2}$ , and $T_{3}$ is shown. $R_{i} (A)$ and $W_{i} (A)$ denote read and write of data item $A$ by transaction $T_{i}$ , $i = 1, 2, 3$ . The...
Transactions, Serializability and Concurrency Control
Computer NetworksMCQ1 markEasy (estimate)
Q.16
Identify the ONE CORRECT matching between the OSI layers and their corresponding functionalities as shown. OSI Layers Functionalities (a) Network layer (I) Packet routing (b) Tr...
OSI/TCP-IP Layering, Physical Layer and Switching
Engineering MathematicsMCQ1 markEasy (estimate)
Q.17
$g (.)$ is a function from $A$ to $B$ , $f (.)$ is a function from $B$ to $C$ , and their composition defined as $f (g (.))$ is a mapping from $A$ to $C$ . If $f (.)$ and $f (g (.))$ are...
Sets, Relations, Functions, Partial Orders and Lattices
AlgorithmsMCQ1 markEasy (estimate)
Q.18
Let $G$ be any undirected graph with positive edge weights, and $T$ be a minimum spanning tree of $G$ . For any two vertices, $u$ and $v$ , let $d_{1} (u, v)$ and $d_{2} (u, v)$ be the...
Minimum Spanning Trees
Theory of ComputationMCQ1 markEasy (estimate)
Q.19
Consider the following context-free grammar $G$ , where $S$ , $A$ , and $B$ are the variables (non-terminals), $a$ and $b$ are the terminal symbols, $S$ is the start variable, and...
Context-Free Grammars, Pushdown Automata and CFLs
AlgorithmsMCQ1 markEasy (estimate)
Q.20
Consider the following recurrence relation: $T (n) = 2 T (n - 1) + n 2^{n} for n > 0, T (0) = 1.$ Which ONE of the following options is CORRECT?
Asymptotic Analysis and Time/Space Complexity
DatabasesMSQ1 markMedium (estimate)
Q.21
Consider the following $B^{+}$ tree with 5 nodes, in which a node can store at most 3 key values. The value $23$ is now inserted in the $B^{+}$ tree. Which of the following options(...
File Organization, B-Trees and B+ Trees Indexing
Computer NetworksMSQ1 markEasy (estimate)
Q.22
Consider the 3-way handshaking protocol for TCP connection establishment. Let the three packets exchanged during the connection establishment be denoted as P1, P2, and P3, in or...
Transport Layer: UDP, TCP Flow and Congestion Control, Sockets
Engineering MathematicsMSQ1 markEasy (estimate)
Q.23
Consider the given system of linear equations for variables $x$ and $y$ , where $k$ is a real-valued constant. Which of the following option(s) is/are CORRECT? $x + k y = 1$ …
Linear Algebra
Digital LogicMSQ1 markMedium (estimate)
Q.24
Let $X$ be a 3-variable Boolean function that produces output as '1' when at least two of the input variables are '1'. Which of the following statement(s) is/are CORRECT, where...
Boolean Algebra and Logic Minimization
Digital LogicMSQ1 markEasy (estimate)
Q.25
The number $- 6$ can be represented as $1010$ in 4-bit 2's complement representation. Which of the following is/are CORRECT 2's complement representation(s) of $- 6$ ?
Number Representations and Computer Arithmetic
Data StructuresMSQ1 markEasy (estimate)
Q.26
Which of the following statement(s) is/are TRUE for any binary search tree (BST) having $n$ distinct integers?
Binary Trees, Binary Search Trees and Balanced Trees
Computer Organization and ArchitectureMSQ1 markEasy (estimate)
Q.27
A partial data path of a processor is given in the figure, where RA, RB, and RZ are 32-bit registers. Which option(s) is/are CORRECT related to arithmetic operations using the d...
ALU, Datapath and Control Unit
Theory of ComputationMSQ1 markEasy (estimate)
Q.28
A regular language $L$ is accepted by a non-deterministic finite automaton (NFA) with $n$ states. Which of the following statement(s) is/are FALSE?
Regular Expressions, Finite Automata and Regular Languages
Operating SystemsNAT1 markEasy (estimate)
Q.29
Suppose in a multiprogramming environment, the following C program segment is executed. A process goes into I/O queue whenever an I/O related operation is performed. Assume that...
Processes, Threads and System Calls
Engineering MathematicsNAT1 markEasy (estimate)
Q.30
Let $S$ be the set of all ternary strings defined over the alphabet ${a, b, c}$ . Consider all strings in $S$ that contain at least one occurrence of two consecutive symbols, t...
Combinatorics, Counting, Recurrence Relations and Generating Functions
Engineering MathematicsNAT1 markEasy (estimate)
Q.31
Consider the given function $f (x)$ . $f (x) = {a x + b x^{3} + x^{2} + 1 for x < 1 for x \geq 1$ If the function is differentiable ever...
Calculus
Engineering MathematicsNAT1 markEasy (estimate)
Q.32
A box contains 5 coins: 4 regular coins and 1 fake coin. When a regular coin is tossed, the probability $P (head) = 0.5$ and for a fake coin, $P (head) = 1$ . You pic...
Probability and Statistics
AlgorithmsNAT1 markEasy (estimate)
Q.33
The pseudocode of a function fun() is given below: fun(int A[0,...,n-1]){ for i=0 to n-2 for j=0 to n-i-2 if (A[j]>A[j+1]) then swap A[j] and A[j+1] } Let $A [0, \dots, 29]$ be...
Searching and Sorting Algorithms
Programming in CNAT1 markEasy (estimate)
Q.34
#include <stdio.h> void foo(int *p, int x){ *p=x; } int main(){ int *z; int a = 20, b = 25; z = &a; foo(z,b); printf("%d",a); return 0; } The output of the given C program is __...
Pointers, Arrays and Strings
Data StructuresNAT1 markEasy (estimate)
Q.35
The height of any rooted tree is defined as the maximum number of edges in the path from the root node to any leaf node. Suppose a Min-Heap $T$ stores 32 keys. The height of $T$ ...
Binary Heaps and Priority Queues
Computer Organization and ArchitectureMCQ2 marksEasy (estimate)
Q.36
Consider a memory system with 1M bytes of main memory and 16K bytes of cache memory. Assume that the processor generates 20-bit memory address, and the cache block size is 16 by...
Memory Hierarchy: Cache, Main Memory and Secondary Storage
Computer Organization and ArchitectureMCQ2 marksEasy (estimate)
Q.37
A processor has 64 general-purpose registers and 50 distinct instruction types. An instruction is encoded in 32-bits. What is the maximum number of bits that can be used to stor...
Machine Instructions and Addressing Modes
Operating SystemsMCQ2 marksMedium (estimate)
Q.38
A computer has two processors, $M_{1}$ and $M_{2}$ . Four processes $P_{1}, P_{2}, P_{3}, P_{4}$ with CPU bursts of 20, 16, 25, and 10 milliseconds, respectively, arrive at the same time and...
CPU Scheduling
DatabasesMCQ2 marksEasy (estimate)
Q.39
Consider two relations describing $teams$ and $players$ in a sports league: $teams (tid, tname)$ : $tid, tname$ are...
Relational Algebra and Tuple Relational Calculus
Computer NetworksMCQ2 marksEasy (estimate)
Q.40
A packet with the destination IP address 145.36.109.70 arrives at a router whose routing table is shown. Which interface will the packet be forwarded to? Subnet Address Subnet...
IPv4/IPv6 Addressing, Subnetting, CIDR, ARP, ICMP and NAT
Engineering MathematicsMCQ2 marksEasy (estimate)
Q.41
Let $A$ be a $2 \times 2$ matrix as given. $A = [11 1 - 1]$ What are the eigenvalues of the matrix $A^{13}$ ?
Linear Algebra
Digital LogicMCQ2 marksEasy (estimate)
Q.42
Consider the following four variable Boolean function in sum-of-product form $F (b_{3}, b_{2}, b_{1}, b_{0}) = \sum (0, 2, 4, 8, 10, 11, 12) .$ where the value of the function is compute...
Boolean Algebra and Logic Minimization
AlgorithmsMCQ2 marksMedium (estimate)
Q.43
Let $G (V, E)$ be an undirected and unweighted graph with 100 vertices. Let $d (u, v)$ denote the number of edges in a shortest path between vertices $u$ and $v$ in $V$ . Let the m...
Graph Traversals, Topological Sort and Connectivity
Theory of ComputationMCQ2 marksMedium (estimate)
Q.44
Consider the following two languages over the alphabet ${a, b}$ : $L_{1} = {α β α ∣ α \in {a, b}^{+} AND β \in {a, b}^{+}}$ …
Regular Expressions, Finite Automata and Regular Languages
Theory of ComputationMCQ2 marksMedium (estimate)
Q.45
Consider the following two languages over the alphabet ${a, b, c}$ , where $m$ and $n$ are natural numbers. $L_{1} = {a^{m} b^{m} c^{m + n} ∣ m, n \geq 1}$ …
Context-Free Grammars, Pushdown Automata and CFLs
Compiler DesignMSQ2 marksEasy (estimate)
Q.46
Which of the following statement(s) is/are TRUE while computing First and Follow during top down parsing by a compiler?
Parsing and Syntax Analysis (LL and LR)
DatabasesMSQ2 marksEasy (estimate)
Q.47
Consider a relational schema $team (name, city, owner)$ , with functional dependencies…
Functional Dependencies and Normalization
Engineering MathematicsMSQ2 marksMedium (estimate)
Q.48
Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: "Everyone has exactly one mother"? The meanings of the predicates used...
Propositional and First-Order Logic
Engineering MathematicsMSQ2 marksEasy (estimate)
Q.49
$A = {0, 1, 2, 3, \dots}$ is the set of non-negative integers. Let $F$ be the set of functions from $A$ to itself. For any two functions, $f_{1}, f_{2} \in F$ , we define…
Monoids and Groups
Theory of ComputationMSQ2 marksMedium (estimate)
Q.50
Consider the following deterministic finite automaton (DFA) defined over the alphabet, $Σ = {a, b}$ . Identify which of the following language(s) is/are accepted by the gi...
Regular Expressions, Finite Automata and Regular Languages
Operating SystemsNAT2 marksMedium (estimate)
Q.51
A disk of size 512M bytes is divided into blocks of 64K bytes. A file is stored in the disk using linked allocation. In linked allocation, each data block reserves 4 bytes to st...
File Systems, I/O and Disk Scheduling
Compiler DesignNAT2 marksEasy (estimate)
Q.52
Refer to the given 3-address code sequence. This code sequence is split into basic blocks. The number of basic blocks is ________. (Answer in integer) 1001: i = 1 1002: j = 1 10...
Intermediate Code Generation, Data Flow Analysis and Code Optimization
Computer Organization and ArchitectureNAT2 marksEasy (estimate)
Q.53
A computer has a memory hierarchy consisting of two-level cache (L1 and L2) and a main memory. If the processor needs to access data from memory, it first looks into L1 cache. I...
Memory Hierarchy: Cache, Main Memory and Secondary Storage
Operating SystemsNAT2 marksMedium (estimate)
Q.54
In optimal page replacement algorithm, information about all future page references is available to the operating system (OS). A modification of the optimal page replacement alg...
Memory Management and Virtual Memory
DatabasesNAT2 marksEasy (estimate)
Q.55
Consider the following database tables of a sports league. player(pid,pname,age) coach(cid,cname) team(tid,tname,city,cid) members(pid,tid) An instance of the table and...
SQL Queries and Integrity Constraints
Computer NetworksNAT2 marksEasy (estimate)
Q.56
Suppose a 5-bit message is transmitted from a source to a destination through a noisy channel. The probability that a bit of the message gets flipped during transmission is…
Data Link Layer: Framing, Error Detection and Sliding Window
Computer NetworksNAT2 marksMedium (estimate)
Q.57
Suppose a message of size 15000 bytes is transmitted from a source to a destination using IPv4 protocol via two routers as shown in the figure. Each router has a defined maximum...
IPv4/IPv6 Addressing, Subnetting, CIDR, ARP, ICMP and NAT
Engineering MathematicsNAT2 marksEasy (estimate)
Q.58
Consider a probability distribution given by the density function $P (x)$ .…
Probability and Statistics
Digital LogicNAT2 marksMedium (estimate)
Q.59
Consider a finite state machine (FSM) with one input $X$ and one output $f$ , represented by the given state transition table. The minimum number of states required to realize th...
Sequential Circuits, Counters and Registers
Digital LogicNAT2 marksMedium (estimate)
Q.60
Consider the given sequential circuit designed using D-Flip-flops. The circuit is initialized with some value (initial state). The number of distinct states the circuit will go...
Sequential Circuits, Counters and Registers
Programming in CNAT2 marksEasy (estimate)
Q.61
#include <stdio.h> int foo(int S[],int size){ if(size == 0) return 0; if(size == 1) return 1; if(S[0] != S[1]) return 1+foo(S+1,size-1); return foo(S+1,size-1); } int main(){ in...
Pointers, Arrays and Strings
Data StructuresNAT2 marksMedium (estimate)
Q.62
Let LIST be a datatype for an implementation of linked list defined as follows: typedef struct list { int data; struct list *next; } LIST; Suppose a program has created two li...
Arrays and Linked Lists
Programming in CNAT2 marksEasy (estimate)
Q.63
Consider the following C program: #include <stdio.h> int gate (int n) { int d, t, newnum, turn; newnum = turn = 0; t=1; while (n>=t) t *= 10; t /=10; while (t>0) { d = n/t; n =...
Data Types, Operators and Control Flow
AlgorithmsNAT2 marksMedium (estimate)
Q.64
The maximum value of $x$ such that the edge between the nodes B and C is included in every minimum spanning tree of the given graph is _________ . (answer in integer) An undirec...
Minimum Spanning Trees
Data StructuresNAT2 marksMedium (estimate)
Q.65
In a double hashing scheme, $h_{1} (k) = k mod 11$ and $h_{2} (k) = 1 + (k mod 7)$ are the auxiliary hash functions. The size $m$ of the hash table is $11$ . The hash function for...
Hash Tables and Collision Resolution