Previous GATE Questions / GATE Overflow for GATE CSE

1 votes

1 answer

101

GATE CSE 2024 | Set 1 | Question: 36
Consider the following read-write schedule $\text{S}$ over three transactions $T_{1}, T_{2}$, and $T_{3}$ ... to $\text{S}$? $T_{1} T_{2} T_{3}$ $T_{1} T_{3} T_{2}$ $T_{3} T_{2} T_{1}$ $T_{3} T_{1} T_{2}$

Consider the following read-write schedule $\text{S}$ over three transactions $T_{1}, T_{2}$, and $T_{3}$, where the subscripts in the schedule indicate trans...

Arjun

2.3k views

Arjun asked Feb 16

0 votes

2 answers

102

GATE CSE 2024 | Set 1 | Question: 37
Consider a Boolean expression given by $\text{F(X, Y, Z)}=\sum(3,5,6,7)$. Which of the following statements is/are CORRECT? $\text{F(X, Y, Z)}=\Pi(0,1,2,4)$ $\text{F(X, Y, Z)=X Y+Y Z+X Z}$ $\text{F(X, Y, Z)}$ is independent of input $\text{Y}$ $\text{F(X, Y, Z)}$ is independent of input $\text{X}$

Consider a Boolean expression given by $\text{F(X, Y, Z)}=\sum(3,5,6,7)$.Which of the following statements is/are CORRECT?$\text{F(X, Y, Z)}=\Pi(0,1,2,4)$ $\text{F(X, Y, ...

Arjun

2.0k views

Arjun asked Feb 16

2 votes

2 answers

103

GATE CSE 2024 | Set 1 | Question: 38
Consider the following $\mathrm{C}$ ... the return value is less than $2^{10}$ If the inputs are $x=10, y=20$, then the return value is greater than $2^{20}$

Consider the following $\mathrm{C}$ 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 stateme...

Arjun

2.2k views

Arjun asked Feb 16

12 votes

3 answers

104

GATE CSE 2024 | Set 1 | Question: 39
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 $Ax=0$? There exist at least $m-n$ linearly independent solutions to this system There exist $m-n$ ... solution in which at least $m-n$ variables are $0$ There exists a solution in which at least $n$ variables are non-zero

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 $Ax=0$?There exist at least $m-n...

Arjun

3.3k views

Arjun asked Feb 16

1 votes

1 answer

105

GATE CSE 2024 | Set 1 | Question: 40
Consider the $5$ -state $\text{DFA}$. $M$ 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 $0^{\prime} s$ in $w$ and $n_1(w)$ be the number of 1 's in $w$. ... $4$ are distinguishable in $M$ States $2$ and $5$ are distinguishable in $M$ Any string $w$ with $n_0(w)=n_1(w)$ is in $L(M)$

Consider the $5$ -state $\text{DFA}$. $M$ 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^{\...

Arjun

2.5k views

Arjun asked Feb 16

0 votes

1 answer

106

GATE CSE 2024 | Set 1 | Question: 41
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 $k$. Which of the following statements is/are always TRUE? $G$ contains a complete subgraph with ... $n/k$ $G$ contains at least $k(k-1) / 2$ edges $G$ contains a vertex of degree at least $k$

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 nu...

Arjun

2.1k views

Arjun asked Feb 16

3 votes

2 answers

107

GATE CSE 2024 | Set 1 | Question: 42
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE? Operator $\diamond$ ... $\square$ obeys the distributive law Operator $\square$ over the operator $\diamond$ obeys the distributive law

Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE?Ope...

Arjun

1.8k views

Arjun asked Feb 16

1 votes

2 answers

108

GATE CSE 2024 | Set 1 | Question: 43
Consider two set-associative cache memory architectures: $\text{WBC}$, which uses the write back policy, and $\text{WTC}$, which uses the write through policy. Both of them use the $\text{LRU}$ (Least Recently Used) block ... write miss in $\text{WTC}$ always writes the victim cache block to main memory before loading the missed block to the cache

Consider two set-associative cache memory architectures: $\text{WBC}$, which uses the write back policy, and $\text{WTC}$, which uses the write through policy...

Arjun

2.2k views

Arjun asked Feb 16

0 votes

2 answers

109

GATE CSE 2024 | Set 1 | Question: 44
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 _________.

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 ha...

Arjun

1.7k views

Arjun asked Feb 16

0 votes

3 answers

110

GATE CSE 2024 | Set 1 | Question: 45
The baseline execution time of a program on a $2 \mathrm{GHz}$ single core machine is $100$ nanoseconds ( $n s)$. The code corresponding to $90 \%$ of the execution time can be fully parallelized. The overhead for using an ... the parallelized code for an equal amount of time. The number of cores that minimize the execution time of the program is __________.

The baseline execution time of a program on a $2 \mathrm{GHz}$ single core machine is $100$ nanoseconds ( $n s)$. The code corresponding to $90 \%$ of the execution time ...

Arjun

1.8k views

Arjun asked Feb 16

1 votes

2 answers

111

GATE CSE 2024 | Set 1 | Question: 46
A given program has $25 \%$ load/store instructions. Suppose the ideal $\text{CPI}$ (cycles per instruction) without any memory stalls is $2$. The program exhibits $2 \%$ miss rate on instruction cache and $8 \%$ miss rate on data ... rounded off to two decimal places) achieved with a perfect cache (i.e., with NO data or instruction cache misses) is __________.

A given program has $25 \%$ load/store instructions. Suppose the ideal $\text{CPI}$ (cycles per instruction) without any memory stalls is $2$. The program exhibits $2 \%$...

Arjun

2.6k views

Arjun asked Feb 16

1 votes

2 answers

112

GATE CSE 2024 | Set 1 | Question: 47
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 without any errors. int x=3; while (x>0){ fork (); printf("hello"); wait (NULL) ; X-- ; } The total number of times the printf statement is executed is __________.

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 successful...

Arjun

2.5k views

Arjun asked Feb 16

2 votes

2 answers

113

GATE CSE 2024 | Set 1 | Question: 48
Consider the entries shown below in the forwarding table of an $\text{IP}$ router. Each entry consists of an $\text{IP}$ prefix and the corresponding next hop router for packets whose destination $\text{IP}$ address matches the prefix. The notation " ... and $10.1.1.205$. The number of packets forwarded via the next hop router $\mathrm{R} 2$ is __________.

Consider the entries shown below in the forwarding table of an $\text{IP}$ router. Each entry consists of an $\text{IP}$ prefix and the corresponding next hop router for ...

Arjun

2.2k views

Arjun asked Feb 16

0 votes

1 answer

114

GATE CSE 2024 | Set 1 | Question: 49
Let $G=(V, \Sigma, S, P)$ be a context-free grammar in Chomsky Normal Form with $\Sigma=\{a, b, c\}$ and $V$ containing $10$ variable symbols including the start symbol $S$. The string $w=a^{30} b^{30} c^{30}$ is derivable from $S$. The number of steps (application of rules) in the derivation $S \rightarrow^* w$ is __________.

Let $G=(V, \Sigma, S, P)$ be a context-free grammar in Chomsky Normal Form with $\Sigma=\{a, b, c\}$ and $V$ containing $10$ variable symbols including the start symbol $...

Arjun

1.3k views

Arjun asked Feb 16

1 votes

2 answers

115

GATE CSE 2024 | Set 1 | Question: 50
The number of edges present in the forest generated by the $\text{DFS}$ traversal of an undirected graph $G$ with $100$ vertices is $40$. The number of connected components in $G$ is __________.

The number of edges present in the forest generated by the $\text{DFS}$ traversal of an undirected graph $G$ with $100$ vertices is $40$. The number of connected componen...

Arjun

1.9k views

Arjun asked Feb 16

2 votes

3 answers

116

GATE CSE 2024 | Set 1 | Question: 51
Consider the following two regular expressions over the alphabet $\{0,1\}$ : $r= 0^{*}+1^{*}$ $s = 01^{*} + 10^{*}$ The total number of strings of length less than or equal to $5$, which are neither in $r$ nor in $s$, is ________.

Consider the following two regular expressions over the alphabet $\{0,1\}$ :$r= 0^{*}+1^{*}$$s = 01^{*} + 10^{*}$The total number of strings of length less than or equal ...

Arjun

1.8k views

Arjun asked Feb 16

1 votes

3 answers

117

GATE CSE 2024 | Set 1 | Question: 52
Consider a memory management system that uses a page size of $2 \mathrm{~KB}$. Assume that both the physical and virtual addresses start from $0$. Assume that the pages $0,1,2$, and $3$ ... $0$, respectively. The physical address (in decimal format) corresponding to the virtual address $2500$ (in decimal format) is ___________.

Consider a memory management system that uses a page size of $2 \mathrm{~KB}$. Assume that both the physical and virtual addresses start from $0$. Assume that the pages $...

Arjun

2.4k views

Arjun asked Feb 16

2 votes

2 answers

118

GATE CSE 2024 | Set 1 | Question: 53
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 $3$ decimal places) that both balls drawn are red is ___________.

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 ...

Arjun

2.2k views

Arjun asked Feb 16

1 votes

3 answers

119

GATE CSE 2024 | Set 1 | Question: 54
Consider a digital logic circuit consisting of three $2$-to-$1$ multiplexers $\text{M1, M2}$, and $\text{M3}$ as shown below. $\mathrm{X} 1$ and $\mathrm{X} 2$ are inputs of $\mathrm{M} 1$. $\text{X3}$ and $\text{X4}$ are inputs ... the number of combinations of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ that give the output $\mathbf{Y}=\mathbf{1}$ is ____________.

Consider a digital logic circuit consisting of three $2$-to-$1$ multiplexers $\text{M1, M2}$, and $\text{M3}$ as shown below. $\mathrm{X} 1$ and $\mathrm{X} 2$ are inputs...

Arjun

2.1k views

Arjun asked Feb 16

0 votes

1 answer

120

GATE CSE 2024 | Set 1 | Question: 55
Consider sending an $\text{IP}$ datagram of size $1420$ bytes (including $20$ bytes of $\text{IP}$ ... ) has an $\text{MTU}$ size of $360$ bytes. The number of fragments that would be delivered at the receiver is ____________.

Consider sending an $\text{IP}$ datagram of size $1420$ bytes (including $20$ bytes of $\text{IP}$ header) from a sender to a receiver over a path of two links with a rou...

Arjun

2.5k views

Arjun asked Feb 16

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