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121
GATE CSE 2024 | Set 2 | Question: 46
A functional dependency $F: X \rightarrow Y$ is termed as a useful functional dependency if and only if it satisfies all the following three conditions: $\text{X}$ is not the empty set. $\text{Y}$ is not the empty set. Intersection ... set. For a relation $\text{R}$ with $4$ attributes, the total number of possible useful functional dependencies is __________.
A functional dependency $F: X \rightarrow Y$ is termed as a useful functional dependency if and only if it satisfies all the following three conditions:$\text{X}$ is not ...
1.6k
views
asked
Feb 16
Databases
gatecse2024-set2
numerical-answers
databases
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2
votes
1
answer
122
GATE CSE 2024 | Set 2 | Question: 47
A processor with $16$ general purpose registers uses a $32$-bit instruction format. The instruction format consists of an opcode field, an addressing mode field, two register operand fields, and a $16$-bit scalar field. If $8$ addressing modes are to be supported, the maximum number of unique opcodes possible for every addressing mode is ___________.
A processor with $16$ general purpose registers uses a $32$-bit instruction format. The instruction format consists of an opcode field, an addressing mode field, two regi...
1.5k
views
asked
Feb 16
CO and Architecture
gatecse2024-set2
numerical-answers
co-and-architecture
+
–
2
votes
0
answers
123
GATE CSE 2024 | Set 2 | Question: 48
A non-pipelined instruction execution unit operating at $2 \mathrm{GHz}$ takes an average of $6$ cycles to execute an instruction of a program $\text{P}$. The unit is then redesigned to operate on a $5$ ... hazards. The speedup (rounded off to one decimal place) obtained by the pipelined design over the non-pipelined design is ____________.
A non-pipelined instruction execution unit operating at $2 \mathrm{GHz}$ takes an average of $6$ cycles to execute an instruction of a program $\text{P}$. The unit is the...
1.5k
views
asked
Feb 16
CO and Architecture
gatecse2024-set2
numerical-answers
co-and-architecture
pipelining
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1
votes
1
answer
124
GATE CSE 2024 | Set 2 | Question: 49
The number of distinct minimum-weight spanning trees of the following graph is
The number of distinct minimum-weight spanning trees of the following graph is
1.6k
views
asked
Feb 16
Algorithms
gatecse2024-set2
numerical-answers
algorithms
minimum-spanning-tree
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1
votes
2
answers
125
GATE CSE 2024 | Set 2 | Question: 50
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is __________.
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is __________.
1.7k
views
asked
Feb 16
Graph Theory
gatecse2024-set2
graph-theory
numerical-answers
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1
votes
1
answer
126
GATE CSE 2024 | Set 2 | Question: 51
A processor uses a $32$-bit instruction format and supports byte-addressable memory access. The $\text{ISA}$ of the processor has $150$ distinct instructions. The instructions are equally divided into two types, namely $\text{R}$ ... the number of bits used to encode the immediate value/address field. The value of $\text{X+2Y+Z}$ is __________.
A processor uses a $32$-bit instruction format and supports byte-addressable memory access. The $\text{ISA}$ of the processor has $150$ distinct instructions. The instruc...
1.6k
views
asked
Feb 16
CO and Architecture
gatecse2024-set2
numerical-answers
co-and-architecture
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1
votes
3
answers
127
GATE CSE 2024 | Set 2 | Question: 52
Let $L_{1}$ be the language represented by the regular expression $b^{*} a b^{*}\left(a b^{*} a b^{*}\right)^{*}$ and $L_{2}=\left\{w \in(a+b)^{*}|| w \mid \leq 4\right\}$, where $|w|$ denotes the length of string $w$. The number of strings in $L_{2}$ which are also in $L_{1}$ is _________.
Let $L_{1}$ be the language represented by the regular expression $b^{*} a b^{*}\left(a b^{*} a b^{*}\right)^{*}$ and $L_{2}=\left\{w \in(a+b)^{*}|| w \mid \leq 4\right\}...
1.7k
views
asked
Feb 16
Theory of Computation
gatecse2024-set2
numerical-answers
theory-of-computation
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2
votes
2
answers
128
GATE CSE 2024 | Set 2 | Question: 53
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \times Z_{4}$ that are their own inverses is ___________.
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \ti...
1.8k
views
asked
Feb 16
Set Theory & Algebra
gatecse2024-set2
numerical-answers
set-theory&algebra
group-theory
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5
votes
2
answers
129
GATE CSE 2024 | Set 2 | Question: 54
Consider a $32$-bit system with $4 \mathrm{~KB}$ page size and page table entries of size $4$ bytes each. Assume $1 \mathrm{~KB}=2^{10}$ bytes. The OS uses a $2$-level page table for memory management, with the page table containing ... the maximum number of pages across the two levels of the page table of the process. The value of $\text{X+Y}$ is ___________.
Consider a $32$-bit system with $4 \mathrm{~KB}$ page size and page table entries of size $4$ bytes each. Assume $1 \mathrm{~KB}=2^{10}$ bytes. The OS uses a $2$-level pa...
2.2k
views
asked
Feb 16
Operating System
gatecse2024-set2
numerical-answers
operating-system
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2
votes
1
answer
130
GATE CSE 2024 | Set 2 | Question: 55
Consider the following augmented grammar, which is to be parsed with a $\text{SLR}$ parser. The set of terminals is $\{a, b, c, d, \#, @\}$ \[ \begin{array}{l} S^{\prime} \rightarrow S \\ S \rightarrow S S|A a| b A c|B c| b ... $\operatorname{GOTO}\left(I_{0}, S\right)$ is __________.
Consider the following augmented grammar, which is to be parsed with a $\text{SLR}$ parser. The set of terminals is $\{a, b, c, d, \#, @\}$\[\begin{array}{l}S^{\prime} \r...
2.3k
views
asked
Feb 16
Compiler Design
gatecse2024-set2
numerical-answers
compiler-design
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2
votes
2
answers
131
GATE CSE 2024 | Set 1 | Question: 1
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x)=\max \left\{x, x^3\right\}, x \in \mathbb{R}$, where $\mathbb{R}$ is the set of all real numbers. The set of all points where $f(x)$ is NOT differentiable is $\{-1,1,2\}$ $\{-2,-1,1\}$ $\{0,1\}$ $\{-1,0,1\}$
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x)=\max \left\{x, x^3\right\}, x \in \mathbb{R}$, where $\mathbb{R}$ is the set of all real numbers....
3.3k
views
asked
Feb 16
Calculus
gatecse2024-set1
calculus
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3
votes
8
answers
132
GATE CSE 2024 | Set 1 | Question: 2
The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is $-1$ $0$ $1$ $2$
The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is$-1$$0$$1$$2$
2.7k
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asked
Feb 16
Linear Algebra
gatecse2024-set1
linear-algebra
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3
votes
5
answers
133
GATE CSE 2024 | Set 1 | Question: 3
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 $B$=$11010$. Which one of the following operations will result in either an arithmetic overflow or an arithmetic underflow? $A+B$ $A-B$ $B-A$ $2 * B$
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 $A$=$01010$...
3.4k
views
asked
Feb 16
Digital Logic
gatecse2024-set1
digital-logic
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0
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1
answer
134
GATE CSE 2024 | Set 1 | Question: 4
Consider a permutation sampled uniformly at random from the set of all permutations of $\{1,2,3, \cdots, n\}$ for some $n \geq 4$. Let $X$ be the event that $1$ occurs before $2$ in the permutation, and $Y$ the event that $3$ occurs before ... The events $X$ and $Y$ are independent Either event $X$ or $Y$ must occur Event $X$ is more likely than event $Y$
Consider a permutation sampled uniformly at random from the set of all permutations of $\{1,2,3, \cdots, n\}$ for some $n \geq 4$. Let $X$ be the event that $1$ occurs be...
2.2k
views
asked
Feb 16
Probability
gatecse2024-set1
probability
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0
votes
2
answers
135
GATE CSE 2024 | Set 1 | Question: 5
Which one of the following statements is FALSE? In the cycle stealing mode of DMA, one word of data is transferred between an I/O device and main memory in a stolen cycle For bulk data transfer, the burst mode of ... driven I/O mechanism The CPU can start executing an interrupt service routine faster with vectored interrupts than with non-vectored interrupts
Which one of the following statements is FALSE?In the cycle stealing mode of DMA, one word of data is transferred between an I/O device and main memory in a s...
2.0k
views
asked
Feb 16
CO and Architecture
gatecse2024-set1
co-and-architecture
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3
votes
2
answers
136
GATE CSE 2024 | Set 1 | Question: 6
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-level index page with multiple embedded image objects. Assume that all caches (e.g., DNS cache, browser cache) are ... $\text{(ii), (iv), (i), (iii)}$ $\text{(iv), (ii), (i), (iii)}$
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...
2.3k
views
asked
Feb 16
Computer Networks
gatecse2024-set1
computer-networks
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–
1
votes
1
answer
137
GATE CSE 2024 | Set 1 | Question: 7
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 through the array and comparing each element of the array only with its adjacent elements. The ... $\Omega(N)$ but not $\mathrm{O}(N)$ neither $\mathrm{O}(N)$ nor $\Omega(N)$
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...
3.0k
views
asked
Feb 16
Algorithms
gatecse2024-set1
algorithms
time-complexity
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3
votes
3
answers
138
GATE CSE 2024 | Set 1 | Question: 8
Consider the following $\mathrm{C}$ 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 following ... The program prints $9$ as output The program prints $10$ as output The program gets stuck in an infinite loop The program prints $6$ as output
Consider the following $\mathrm{C}$ 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 ...
5.6k
views
asked
Feb 16
Programming in C
gatecse2024-set1
programming
programming-in-c
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1
votes
3
answers
139
GATE CSE 2024 | Set 1 | Question: 9
Consider the following $\mathrm{C}$ program: #include <stdio.h> void fX () { void fX () ; char a; int main() { if ((a=g e t c h a r()) ! = '\n') fX}() ; fX(); return 0 ; if (a ! ... program will not terminate The program will terminate with no output The program will terminate with $4321$ as output The program will terminate with $1234$ as output
Consider the following $\mathrm{C}$ program:#include <stdio.h void fX () {void fX () ; char a;int main() { if ((a=g e t c h a r()) ! = '\n')fX}() ; fX();return 0 ; if ...
2.7k
views
asked
Feb 16
Programming in C
gatecse2024-set1
programming
programming-in-c
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1
votes
2
answers
140
GATE CSE 2024 | Set 1 | Question: 10
Let $\mathrm{S}$ be the specification: "Instructors teach courses. Students register for courses. Courses are allocated classrooms. Instructors guide students." Which one of the following $\mathrm{ER}$ diagrams CORRECTLY represents $\mathrm{S}$? $\text{(i)}$ $\text{(ii)}$ $\text{(iii)}$ $\text{(iv)}$
Let $\mathrm{S}$ be the specification: "Instructors teach courses. Students register for courses. Courses are allocated classrooms. Instructors guide students." Which one...
1.9k
views
asked
Feb 16
Databases
gatecse2024-set1
databases
er-diagram
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