Recent questions tagged gatecse2024-set1 / GATE Overflow for GATE CSE

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31

GATE CSE 2024 | Set 1 | Question: 27
Consider the following syntax-directed definition $\text{(SDD)}$. $S \rightarrow D H T U$ $ \left\{S.v a l = D.val + H.val + T.val + U.val\right\};$ $D \rightarrow ^{"} \mathrm{M}^{"} D_1$ ... the following options is the $\text{CORRECT}$ value computed by the $\text{SDD}$ (in the attribute $S.val$)? $45$ $50$ $55$ $65$

Consider the following syntax-directed definition $\text{(SDD)}$.$S \rightarrow D H T U$$ \left\{S.v a l = D.val + H.val + T.val + U.val\right\};$$D \rightarrow ^{"} \...

Arjun

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Arjun asked Feb 16

2 votes

1 answer

32

GATE CSE 2024 | Set 1 | Question: 31
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? $82,90,101$ $82,11,93$ $131,11,93$ $131,111,90$

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?$...

Arjun

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Arjun asked Feb 16

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2 answers

33

GATE CSE 2024 | Set 1 | Question: 33
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 values of $k$ is $53$ $52$ $27$ $1$

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 pos...

Arjun

2.8k views

Arjun asked Feb 16

2 votes

3 answers

34

GATE CSE 2024 | Set 1 | Question: 34
The symbol $\rightarrow$ indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE? $(X, Y) \rightarrow(Z, W)$ implies $X \rightarrow(Z, W)$ $(X, Y) \rightarrow(Z, W)$ ... $(X, W) \rightarrow Z$ $(X \rightarrow Y$ and $Y \rightarrow Z)$ implies $X \rightarrow Z$

The symbol $\rightarrow$ indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?$(X, Y) \rightarrow(Z, W)$...

Arjun

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Arjun asked Feb 16

4 votes

2 answers

35

GATE CSE 2024 | Set 1 | Question: 35
Let $G$ be a directed graph and $T$ a depth first search $\text{(DFS)}$ spanning tree in $G$ that is rooted at a vertex $v$. Suppose $T$ is also a breadth first search $\text{(BFS)}$ tree in $G$, rooted at $v$. Which of the following ... the tree $T$ There are no forward-edge in $G$ with respect to the tree $T$ The only edges in $G$ are the edges in $T$

Let $G$ be a directed graph and $T$ a depth first search $\text{(DFS)}$ spanning tree in $G$ that is rooted at a vertex $v$. Suppose $T$ is also a breadth fir...

Arjun

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Arjun asked Feb 16

1 votes

1 answer

36

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

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Arjun asked Feb 16

1 votes

2 answers

37

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

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Arjun asked Feb 16

2 votes

2 answers

38

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

2.5k views

Arjun asked Feb 16

13 votes

4 answers

39

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

4.0k views

Arjun asked Feb 16

1 votes

1 answer

40

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

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Arjun asked Feb 16

0 votes

1 answer

41

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

2.3k views

Arjun asked Feb 16

3 votes

2 answers

42

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

2.0k views

Arjun asked Feb 16

2 votes

2 answers

43

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

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Arjun asked Feb 16

0 votes

2 answers

44

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

2.4k views

Arjun asked Feb 16

0 votes

3 answers

45

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

46

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

3.0k views

Arjun asked Feb 16

2 votes

2 answers

47

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

48

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

0 votes

1 answer

49

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

1.5k views

Arjun asked Feb 16

1 votes

2 answers

50

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

2.1k views

Arjun asked Feb 16

2 votes

3 answers

51

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

2.2k views

Arjun asked Feb 16

1 votes

3 answers

52

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

2.9k views

Arjun asked Feb 16

2 votes

2 answers

53

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

2.5k views

Arjun asked Feb 16

2 votes

3 answers

54

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

2.5k views

Arjun asked Feb 16

0 votes

1 answer

55

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

3.0k views

Arjun asked Feb 16

3 votes

1 answer

56

GATE CSE 2024 | Set 1 | GA: 1
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [dry $\rightarrow$ arid $\rightarrow$ parched] is analogous to [diet $\rightarrow$ fast $\rightarrow$ ________ ]. Which one of the given options is appropriate to fill the blank? starve reject feast deny

If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words[dry $\rightarrow$ arid $\rightarrow$ parched] is analogous to [diet $\rightarrow...

Arjun

4.6k views

Arjun asked Feb 16

2 votes

1 answer

57

GATE CSE 2024 | Set 1 | GA: 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 $\frac{x}{y}$ depends on $x y$ depends only on $x$ and not on $y$ depends only on $y$ and not on $x$ is a constant

If two distinct non-zero real variables $x$ and $y$ are such that $(x+y)$ is proportional to $(x-y)$ then the value of $\frac{x}{y}$depends on $x y$depends only ...

Arjun

3.6k views

Arjun asked Feb 16

5 votes

1 answer

58

GATE CSE 2024 | Set 1 | GA: 3
Consider the following sample of numbers: $9,18,11,14,15,17,10,69,11,13$ The median of the sample is $13.5$ $14$ $11$ $18.7$

Consider the following sample of numbers:$9,18,11,14,15,17,10,69,11,13$The median of the sample is$13.5$$14$$11$$18.7$

Arjun

3.3k views

Arjun asked Feb 16

4 votes

3 answers

59

GATE CSE 2024 | Set 1 | GA: 4
The number of coins of ₹$1$, ₹$5$, and ₹$10$ denominations that a person has are in the ratio $5:3:13$. Of the total amount, the percentage of money in ₹$5$ coins is $21 \%$ $14 \frac{2}{7} \%$ $10 \%$ $30 \%$

The number of coins of ₹$1$, ₹$5$, and ₹$10$ denominations that a person has are in the ratio $5:3:13$. Of the total amount, the percentage of money in ...

Arjun

3.8k views

Arjun asked Feb 16

3 votes

2 answers

60

GATE CSE 2024 | Set 1 | GA: 5
For positive non-zero real variables $p$ and $q$, if $\log \left(p^2+q^2\right)=\log p+\log q+2 \log 3,$ then, the value of $\frac{p^4+q^4}{p^2 q^2}$ is $79$ $81$ $9$ $83$

For positive non-zero real variables $p$ and $q$, if$\log \left(p^2+q^2\right)=\log p+\log q+2 \log 3,$then, the value of $\frac{p^4+q^4}{p^2 q^2}$ is$79$$81$$9$$83$

Arjun

3.7k views

Arjun asked Feb 16

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