Answers by gatecse / GATE Overflow for GATE CSE

1 votes

61

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 29
Which of the following relations on the set $A = \{1,2,3,4\}$ is reflexive? $\{(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)\}$ $\{(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)\}$ $\{(2, 4),(4, 2)\}$ $\{(1, 2),(2, 3),(3, 4)\}$

Which of the following relations on the set $A = \{1,2,3,4\}$ is reflexive?$\{(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)\}$$\{(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), ...

76 views

answered Feb 8, 2021

3 votes

62

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 30
The number of relations on the set $S = \{0,1\}$ that contain the pair $(0,1)$ _________

The number of relations on the set $S = \{0,1\}$ that contain the pair $(0,1)$ _________

347 views

answered Feb 8, 2021

5 votes

63

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 31
Consider the set $A = \{a, \{p,q\},\{v\}\}.$ $B,C \subseteq 2^A$ such that $B = \{\{a\},\{\{v\}\},\{a,\{v\}\}\}.$ Which of the following can be $C$ such that $B$ and $C$ form a valid partition of $2^A?$ $\{\phi,a,\{p,q\},\{\{p,q\},\{v\}\}\}$ ... $\{\phi,\{\{p,q\}\},\{\{p,q\},\{v\}\},\{a,\{p,q\}\},\{a, \{p,q\},\{v\}\}\}$

Consider the set $A = \{a, \{p,q\},\{v\}\}.$ $B,C \subseteq 2^A$ such that $B = \{\{a\},\{\{v\}\},\{a,\{v\}\}\}.$ Which of the following can be $C$ such that $B$ and $C$...

200 views

answered Feb 8, 2021

2 votes

64

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 32
Consider the relation $R(A,B,C,D),$ on which the following set of functional dependencies hold. $F:\{A \rightarrow B,B\rightarrow C, C \rightarrow D\}$ $G:\{A \rightarrow B, B \rightarrow C, A \rightarrow D\}$ Which of the following ... ? (Mark all the appropriate options) $F$ covers $G$ $G$ covers $F$ $F \equiv G$ $F \not\equiv G$

Consider the relation $R(A,B,C,D),$ on which the following set of functional dependencies hold.$F:\{A \rightarrow B,B\rightarrow C, C \rightarrow D\}$ $G:\{A \rightarrow ...

160 views

answered Feb 8, 2021

4 votes

65

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 33
A multiple choice test is having $100$ questions and $5$ options per question. How many different ways can the test be completed? $6^{100}$ $100^5$ $5^{100}$ None of these

A multiple choice test is having $100$ questions and $5$ options per question. How many different ways can the test be completed?$6^{100}$$100^5$$5^{100}$None of these

339 views

answered Feb 8, 2021

5 votes

66

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 34
A variation of an inode is called a linode (short for little node). Assume the size of a disk block is $4K$ bytes and a disk block can contain $2K$ disk block addresses. A linode has the following structure: entries ... double indirect block pointer The maximum size of a file (rounded to the nearest GB) using a linode will be _________

A variation of an inode is called a linode (short for little node). Assume the size of a disk block is $4K$ bytes and a disk block can contain $2K$ disk block addresses. ...

371 views

answered Feb 8, 2021

2 votes

67

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 35
A system uses FIFO policy for system replacement. It has $3$ page frames with no pages loaded to begin with. The system first accesses $200$ distinct pages in some order and then accesses the same $200$ pages but now in the reverse order. The number of page faults will be ________

A system uses FIFO policy for system replacement. It has $3$ page frames with no pages loaded to begin with. The system first accesses $200$ distinct pages in some order ...

152 views

answered Feb 8, 2021

8 votes

68

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 36
Consider a hard disk with $16$ recording surfaces $(0-15)$ having $32768$ cylinders $(0-32767)$ and each cylinder contains $32$ sectors $(0-31)$. Data storage capacity in each sector is $4096$ bytes. Data are organized ... . The cylinder number of the last sector of the file, if it is stored in a contiguous manner will be __________

Consider a hard disk with $16$ recording surfaces $(0-15)$ having $32768$ cylinders $(0-32767)$ and each cylinder contains $32$ sectors $(0-31)$. Data storage capacity in...

675 views

answered Feb 8, 2021

6 votes

69

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 37
Cylinder a disk queue with requests for $\text{I/O}$ to blocks on cylinders $191, 18, 11, 61, 137, 41, 2.$ The C-LOOK scheduling algorithm is used. The head is initially at cylinder number $100$, moving ... numbered from $0$ to $199$. The total head movement (in number of cylinders) incurred while servicing these requests is ________

Cylinder a disk queue with requests for $\text{I/O}$ to blocks on cylinders $191, 18, 11, 61, 137, 41, 2.$ The C-LOOK scheduling algorithm is used. The head is initially ...

379 views

answered Feb 8, 2021

16 votes

70

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 38
How many triangles can be formed with vertices on a $3 \times3 $ grid of squares? $516$ $548$ $536$ None of these

How many triangles can be formed with vertices on a $3 \times3 $ grid of squares?$516$$548$$536$None of these

743 views

answered Feb 8, 2021

9 votes

71

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 39
Consider the following C program: #include<stdio.h> #include<unistd.h> #define N 8 void fun1() { printf("%s", "hello"); } int main() { void fun1(); for(int i=0; i<N; i+=2) { fork(); fun1(); fflush(stdout); } } The total number of characters printed by the above program once executed is _________

Consider the following C program:#include<stdio.h #include<unistd.h #define N 8 void fun1() { printf("%s", "hello"); } int main() { void fun1(); for(int i=0; i<N; i+=2) {...

788 views

answered Feb 8, 2021

11 votes

72

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 40
Consider the following C program: #include<stdio.h> int (*foo(int (*f)(int,int))) (int, int) { return f+1; } int fun1(int x,int y) { return x+y; } int fun2(int x,int y) { return x*y; } int main() { int (*fun_ptr[2])(int ... ; } What will be the output when the above program is executed? $4\;\; 5$ $20\;\; 9$ $9\;\; 20$ None of these

Consider the following C program:#include<stdio.h int (*foo(int (*f)(int,int))) (int, int) { return f+1; } int fun1(int x,int y) { return x+y; } int fun2(int x,int y) { r...

547 views

answered Feb 8, 2021

10 votes

73

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 41
In a system to store a file a hash table is created for each word. The alphanumeric value is their alphabetical order. For example, alphanumeric value for $a$ is $1$. The word is placed in hash table while reading from left to ... the total number of anagrams of the word "ISOMER" is $n$, then the value of $n-p$ is ________

In a system to store a file a hash table is created for each word. The alphanumeric value is their alphabetical order. For example, alphanumeric value for $a$ is $1$. The...

664 views

answered Feb 8, 2021

12 votes

74

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 42
The time complexity of the following C snippet is: int gate_2020(int n) { for(int i=1; i <= n; i++) { for(int j=i ; j<=i*i ; j++) if(j%i==0) { for(int k=0; k < j; k++) printf("gate2020"); } } } $\Theta(n^3)$ $\Theta (n^2)$ $\Theta(n^4)$ $\Theta(n^5)$

The time complexity of the following C snippet is:int gate_2020(int n) { for(int i=1; i <= n; i++) { for(int j=i ; j<=i*i ; j++) if(j%i==0) { for(int k=0; k < j; k++) pri...

594 views

answered Feb 8, 2021

2 votes

75

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 43
Suppose we are given an algorithm $'X'$ that find the median in time $\Theta(n^2)$, where $n$ is the number of inputs. Now consider a QuickSort implementation where we first find median using the above algorithm $'X'$, then use this median as pivot. What ... QuickSort? $\Theta(n^2)$ $\Theta(n \log n)$ $O(n \log n)$ $\Theta(n^2 \log n)$

Suppose we are given an algorithm $’X’$ that find the median in time $\Theta(n^2)$, where $n$ is the number of inputs. Now consider a QuickSort implementation where w...

383 views

answered Feb 8, 2021

1 votes

76

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 44
A sorting algorithm is said to be stable if two objects with equal keys appear in the same order in sorted output as they appear in the input unsorted array. We have a list of $2$-dimensional points $(a,b)$ where $a$ represents $ x'$ coordinate and $b$ represents $ y'$ ... $(7,8) (9,6) (8,5) (3,5) (8,2) (7,2)$

A sorting algorithm is said to be stable if two objects with equal keys appear in the same order in sorted output as they appear in the input unsorted array.We have a lis...

124 views

answered Feb 8, 2021

2 votes

77

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 45
Consider the following C program: #include <stdio.h> int foo(int A[], int n, int s) { for (int i = 0; i < n - 2; i++) for (int j = i + 1; j < n - 1; j++) for (int k = j + 1; k < n; k++) ... $\Theta(n^k)$ where $n$ is the number of elements in the array passed to it (second argument), then $x+ k = $ ________

Consider the following C program:#include <stdio.h int foo(int A[], int n, int s) { for (int i = 0; i < n - 2; i++) for (int j = i + 1; j < n - 1; j++) for (int k = j + 1...

395 views

answered Feb 8, 2021

4 votes

78

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 46
While searching the key value $4$ in a binary search tree, key values $1,2,3,6,8,9,10$ and $11$ are traversed not necessarily in the order given. How many different orders are possible in which these key values can occur on the search path from the root to the node containing value $4$?

While searching the key value $4$ in a binary search tree, key values $1,2,3,6,8,9,10$ and $11$ are traversed not necessarily in the order given. How many different order...

499 views

answered Feb 8, 2021

3 votes

79

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 47
Consider a C function print() which takes a root of binary search tree and a positive number $ k'$ as arguments as given below: struct node { int data; struct node *left, *right; }; int count = 0; void ... represents root of the following Binary Search Tree? (You can assume the binary search tree to be terminated properly by NULLs)

Consider a C function print() which takes a root of binary search tree and a positive number $‘k’$ as arguments as given below:struct node { int data; struct node *le...

342 views

answered Feb 8, 2021

2 votes

80

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 48
Stations $X$ and $Y$ are connected through a line of bandwidth $128$ kbps. Station $X$ uses $32$ byte packets to transmit messages to $Y$ using a sliding window protocol. The propagation delay between $X$ ... to maximize the line utilization? Assume that the acknowledgement frame is of negligible size and processing delay may be ignored.

Stations $X$ and $Y$ are connected through a line of bandwidth $128$ kbps. Station $X$ uses $32$ byte packets to transmit messages to $Y$ using a sliding window protocol....

285 views

answered Feb 8, 2021

9 votes

81

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 49
Consider the following SQL query over the Staff, Branch relations given below with Primary Keys being underlined: $\text{Staff:} \underline{\text{ID}}, \text{Name}, \text{position}, \text{branchNo}$ ... b on s.branchNo = b.branchNo AND (s.position = 'Manager' AND b.city = 'New Delhi');

Consider the following SQL query over the Staff, Branch relations given below with Primary Keys being underlined:$\text{Staff:} \underline{\text{ID}}, \text{Name}, \text{...

561 views

answered Feb 8, 2021

7 votes

82

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 50
Consider the C code fragment given below: #define N 1000 double a[N][N], d=0; .... for (j = 0; j < N; j++) for (i = 0; i < N; i++) d += a[i][j]; The elements of $a$ are $8$ bytes ... a[i][j]; Determine the percentage reduction in cache misses assuming an 8 KB direct-mapped data cache with 64-byte blocks. (Up to one decimal place)

Consider the C code fragment given below:#define N 1000 double a[N][N], d=0; .... for (j = 0; j < N; j++) for (i = 0; i < N; i++) d += a[i][j];The elements of $a$ are $8$...

403 views

answered Feb 8, 2021

2 votes

83

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 51
Consider the following minimal state finite automata: Which of the following binary strings is/are accepted by the given automata? $10010$ $100010001$ $111010101$ $10010000$

Consider the following minimal state finite automata:Which of the following binary strings is/are accepted by the given automata?$10010$$100010001$$111010101$$10010000$

78 views

answered Feb 8, 2021

1 votes

84

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 52
The following pushdown automata (PDA) recognizes the language $L = \{wcw^{R} \mid w \in \{a,b\}^{\ast}\}$ $(w_R$ being the reverse of $w)$ and is accepting by empty stack (denoted by $\varepsilon$ in the transitions). Which ... $\langle q_1, (a,b,\varepsilon) \rangle$ $\langle q_1, (b,a,\varepsilon) \rangle$

The following pushdown automata (PDA) recognizes the language $L = \{wcw^{R} \mid w \in \{a,b\}^{\ast}\}$ $(w_R$ being the reverse of $w)$ and is accepting by empty stack...

269 views

answered Feb 8, 2021

3 votes

85

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 53
A logic circuit implements the following Boolean function: $F = ABC + AC'D'$ It is found that the circuit input combination $A=D=1$ can never occur. The simplified expression for $F$ using the proper don't-care conditions is $F = AC'+AB $ $F = BC$ $F = BC+C'$ $F = A'B + CD'$

A logic circuit implements the following Boolean function:$F = ABC + AC'D'$It is found that the circuit input combination $A=D=1$ can never occur. The simplified expressi...

369 views

answered Feb 8, 2021

9 votes

86

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 54
The implicants being chosen for a circuit implementation are marked in the following four Karnaugh-maps all representing the same function $f$. In which of them, a static-$1$ hazard is possible? (Mark all the appropriate choices)

The implicants being chosen for a circuit implementation are marked in the following four Karnaugh-maps all representing the same function $f$. In which of them, a static...

527 views

answered Feb 8, 2021

3 votes

87

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 55
Which of the following languages is/are not recursively enumerable? Here, $\langle M \rangle$ denotes an encoding of Turing machine $M.$ (Mark all the appropriate choices) $L = \{\langle M \rangle\mid L(M) \text{ is empty}\}$ ... $L = \{\langle M \rangle\mid L(M) \text{ has at most 2021 strings}\}$

Which of the following languages is/are not recursively enumerable? Here, $\langle M \rangle$ denotes an encoding of Turing machine $M.$ (Mark all the appropriate choices...

476 views

answered Feb 8, 2021

4 votes

88

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 56
A channel has a bit rate of $72$ kbps and one-way propagation delay of $36$ milliseconds. The channel uses stop and wait protocol and the transmission time of the acknowledgement frame is negligible. To get a channel efficiency of at least $85\%,$ the minimum frame size in bytes should be ________

A channel has a bit rate of $72$ kbps and one-way propagation delay of $36$ milliseconds. The channel uses stop and wait protocol and the transmission time of the acknowl...

279 views

answered Feb 8, 2021

10 votes

89

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 57
A slotted ALOHA network transmits $250$-bit frames using a shared channel with a $750$ kbps bandwidth. The throughput (in frames per second) if the system (all stations together) produces $180$ frames per second(round off to $2$ decimal places) will be _________

A slotted ALOHA network transmits $250$-bit frames using a shared channel with a $750$ kbps bandwidth. The throughput (in frames per second) if the system (all stations t...

699 views

answered Feb 8, 2021

5 votes

90

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 58
Several friends are planning a road trip. If Biden goes on the road trip, then Neilia goes on the road trip. If Neilia does not go on the road trip, then Trump does not go on the road trip. Which of the following statements must ... trip, then Neilia goes on the road trip. If Biden goes on the road trip, then Trump goes on the road trip.

Several friends are planning a road trip. If Biden goes on the road trip, then Neilia goes on the road trip. If Neilia does not go on the road trip, then Trump does not g...

281 views

answered Feb 8, 2021

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