Recent questions tagged numerical-answers / GATE Overflow for GATE CSE

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31

GATE CSE 2024 | Set 2 | Question: 24
Let $\text{P}$ be the partial order defined on the set $\{1,2,3,4\}$ as follows \[ P=\{(x, x) \mid x \in\{1,2,3,4\}\} \cup\{(1,2),(3,2),(3,4)\} \] The number of total orders on $\{1,2,3,4\}$ that contain $\text{P}$ is __________.

Let $\text{P}$ be the partial order defined on the set $\{1,2,3,4\}$ as follows\[P=\{(x, x) \mid x \in\{1,2,3,4\}\} \cup\{(1,2),(3,2),(3,4)\}\]The number of total orders ...

Arjun

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Arjun asked Feb 16

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32

GATE CSE 2024 | Set 2 | Question: 25
Let $\text{A}$ be an array containing integer values. The distance of $\text{A}$ is defined as the minimum number of elements in $\text{A}$ that must be replaced with another integer so that the resulting array is sorted in non-decreasing order. The distance of the array $[2,5,3,1,4,2,6]$ is ___________.

Let $\text{A}$ be an array containing integer values. The distance of $\text{A}$ is defined as the minimum number of elements in $\text{A}$ that must be replaced with ano...

Arjun

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Arjun asked Feb 16

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1 answer

33

GATE CSE 2024 | Set 2 | Question: 43
Consider a disk with the following specifications: rotation speed of $6000$ RPM, average seek time of $5$ milliseconds, $500$ sectors/track, $512$-byte sectors. A file has content stored in $3000$ sectors located randomly on the disk. Assuming ... total time (in seconds, rounded off to $2$ decimal places) to read the entire file from the disk is ______________.

Consider a disk with the following specifications: rotation speed of $6000$ RPM, average seek time of $5$ milliseconds, $500$ sectors/track, $512$-byte sectors. A file ha...

Arjun

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Arjun asked Feb 16

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34

GATE CSE 2024 | Set 2 | Question: 44
Consider a $\text{TCP}$ connection operating at a point of time with the congestion window of size $12$ $\text{MSS}$ (Maximum Segment Size), when a timeout occurs due to packet loss. Assuming that all the segments transmitted in the next ... Time) are acknowledged correctly, the congestion window size (in $MSS$) during the third $\text{RTT}$ will be __________.

Consider a $\text{TCP}$ connection operating at a point of time with the congestion window of size $12$ $\text{MSS}$ (Maximum Segment Size), when a timeout occurs due to ...

Arjun

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Arjun asked Feb 16

2 votes

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35

GATE CSE 2024 | Set 2 | Question: 45
Consider an Ethernet segment with a transmission speed of $10^{8} \mathrm{bits} / \mathrm{sec}$ and a maximum segment length of $500$ meters. If the speed of propagation of the signal in the medium is $2 \times 10^{8} \mathrm{~meters} / \mathrm{sec}$, then the minimum frame size (in bits) required for collision detection is ___________.

Consider an Ethernet segment with a transmission speed of $10^{8} \mathrm{bits} / \mathrm{sec}$ and a maximum segment length of $500$ meters. If the speed of propagation ...

Arjun

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Arjun asked Feb 16

1 votes

1 answer

36

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 ...

Arjun

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Arjun asked Feb 16

2 votes

1 answer

37

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...

Arjun

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Arjun asked Feb 16

2 votes

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38

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...

Arjun

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Arjun asked Feb 16

1 votes

1 answer

39

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

Arjun

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Arjun asked Feb 16

1 votes

3 answers

40

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 __________.

Arjun

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Arjun asked Feb 16

1 votes

1 answer

41

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...

Arjun

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Arjun asked Feb 16

1 votes

3 answers

42

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\}...

Arjun

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Arjun asked Feb 16

2 votes

2 answers

43

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...

Arjun

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Arjun asked Feb 16

6 votes

2 answers

44

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...

Arjun

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Arjun asked Feb 16

2 votes

1 answer

45

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...

Arjun

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Arjun asked Feb 16

0 votes

1 answer

46

GATE CSE 2024 | Set 1 | Question: 22
Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions $\text{(i)}$ from $A$ to $B$ and $\text{(ii)}$ from $A \times A$ to $A \cup B$. The number of possible values of $\text{|A|}$ is ___________.

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions $\text{(i)}$ from $A$ to $B$ and $\text{(ii)}$ from $A \times A$ to $A \cup B...

Arjun

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Arjun asked Feb 16

3 votes

1 answer

47

GATE CSE 2024 | Set 1 | Question: 23
Consider the operator precedence and associativity rules for the integer arithmetic operators given in the table below. Operator Precedence Associativity + Highest Left - High Right * Medium Right / Low Right The value of the expression $3+1+5 * 2 / 7+2-4-7-6 / 2$ as per the above rules is ________.

Consider the operator precedence and associativity rules for the integer arithmetic operators given in the table below.Operator PrecedenceAssociativity+Highest Left-HighR...

Arjun

2.4k views

Arjun asked Feb 16

2 votes

2 answers

48

GATE CSE 2024 | Set 1 | Question: 24
The number of spanning trees in a complete graph of $4$ vertices labelled $\text{A, B, C,}$ and $\text{D}$ is _________.

The number of spanning trees in a complete graph of $4$ vertices labelled $\text{A, B, C,}$ and $\text{D}$ is _________.

Arjun

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Arjun asked Feb 16

1 votes

1 answer

49

GATE CSE 2024 | Set 1 | Question: 25
Consider the following two relations, $R(A, B)$ and $S(A, C)$: $R$ $A$ $B$ $10$ $20$ $20$ $30$ $30$ $40$ $30$ $50$ $50$ $95$ $S$ $A$ $C$ $10$ $90$ $30$ $45$ $40$ $80$ The total number of tuples obtained by evaluating the following expression $\sigma_{B<C}\left(R \bowtie_{R . A=S . A} S\right)$ is ___________.

Consider the following two relations, $R(A, B)$ and $S(A, C)$:$R$$A$$B$$10$$20$$20$$30$$30$$40$$30$$50$$50$$95$$S$$A$$C$$10$$90$$30$$45$$40$$80$The total number of tuples...

Arjun

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Arjun asked Feb 16

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50

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

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Arjun asked Feb 16

0 votes

3 answers

51

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

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Arjun asked Feb 16

1 votes

2 answers

52

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

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Arjun asked Feb 16

1 votes

2 answers

53

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

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Arjun asked Feb 16

2 votes

2 answers

54

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

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Arjun asked Feb 16

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1 answer

55

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

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Arjun asked Feb 16

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56

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

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Arjun asked Feb 16

2 votes

3 answers

57

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

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Arjun asked Feb 16

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58

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

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Arjun asked Feb 16

2 votes

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59

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

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Arjun asked Feb 16

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3 answers

60

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

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Arjun asked Feb 16

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