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121
GATE CSE 2019 | Question: 35
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z | w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ denotes ... of all integers Which of the above sets satisfy $\varphi$? $S_1$ and $S_2$ $S_1$ and $S_3$ $S_2$ and $S_3$ $S_1, S_2$ and $S_3$
Consider the first order predicate formula $\varphi$:$\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w x) \wedge (\forall z \:...
Arjun
19.8k
views
Arjun
asked
Feb 7, 2019
Mathematical Logic
gatecse-2019
engineering-mathematics
discrete-mathematics
mathematical-logic
first-order-logic
2-marks
+
–
15
votes
10
answers
122
GATE CSE 2018 | Question: GA-7
If $pqr \ne 0$ and $p^{-x}=\dfrac{1}{q},q^{-y}=\dfrac{1}{r},r^{-z}=\dfrac{1}{p},$ what is the value of the product $xyz$ ? $-1$ $\dfrac{1}{pqr}$ $1$ $pqr$
If $pqr \ne 0$ and $p^{-x}=\dfrac{1}{q},q^{-y}=\dfrac{1}{r},r^{-z}=\dfrac{1}{p},$ what is the value of the product $xyz$ ?$-1$$\dfrac{1}{pqr}$$1$$pqr$
gatecse
7.3k
views
gatecse
asked
Feb 14, 2018
Quantitative Aptitude
gatecse-2018
quantitative-aptitude
ratio-proportions
2-marks
logarithms
+
–
15
votes
10
answers
123
GATE CSE 2018 | Question: GA-5
$\text{ What is the missing number in the following sequence?}$ $2,\,12,\,60,\,240,\,720,\,1440,\,\underline{\;\;\;\;\;\;\;\;},0$ $2880$ $1440$ $720$ $0$
$\text{ What is the missing number in the following sequence?}$$$2,\,12,\,60,\,240,\,720,\,1440,\,\underline{\;\;\;\;\;\;\;\;},0$$$2880$$1440$$720$$0$
gatecse
5.6k
views
gatecse
asked
Feb 14, 2018
Quantitative Aptitude
gatecse-2018
quantitative-aptitude
sequence-series
easy
1-mark
+
–
62
votes
10
answers
124
GATE CSE 2017 Set 1 | Question: 54
A cache memory unit with capacity of $N$ words and block size of $B$ words is to be designed. If it is designed as a direct mapped cache, the length of the $\textsf{TAG}$ field is $10$ bits. If the cache unit is now designed as a $16$-way set-associative cache, the length of the $\textsf{TAG}$ field is ____________ bits.
A cache memory unit with capacity of $N$ words and block size of $B$ words is to be designed. If it is designed as a direct mapped cache, the length of the $\textsf{TAG}$...
Arjun
19.5k
views
Arjun
asked
Feb 14, 2017
CO and Architecture
gatecse-2017-set1
co-and-architecture
cache-memory
normal
numerical-answers
+
–
56
votes
10
answers
125
GATE CSE 2017 Set 1 | Question: 48
Let $A$ be an array of $31$ numbers consisting of a sequence of $0$'s followed by a sequence of $1$'s. The problem is to find the smallest index $i$ such that $A\left [i \right ]$ is $1$ by probing the minimum number of locations in $A$. The worst case number of probes performed by an optimal algorithm is ____________.
Let $A$ be an array of $31$ numbers consisting of a sequence of $0$'s followed by a sequence of $1$'s. The problem is to find the smallest index $i$ such that $A\left [i ...
Arjun
21.5k
views
Arjun
asked
Feb 14, 2017
Algorithms
gatecse-2017-set1
algorithms
normal
numerical-answers
searching
+
–
48
votes
10
answers
126
GATE CSE 2017 Set 1 | Question: 29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \r...
Arjun
10.5k
views
Arjun
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set1
mathematical-logic
propositional-logic
+
–
33
votes
10
answers
127
GATE CSE 2017 Set 1 | Question: 6
Let $T$ be a binary search tree with $15$ nodes. The minimum and maximum possible heights of $T$ are: Note: The height of a tree with a single node is $0$. $4$ and $15$ respectively. $3$ and $14$ respectively. $4$ and $14$ respectively. $3$ and $15$ respectively.
Let $T$ be a binary search tree with $15$ nodes. The minimum and maximum possible heights of $T$ are:Note: The height of a tree with a single node is $0$.$4$ and $15$ res...
Arjun
16.6k
views
Arjun
asked
Feb 14, 2017
DS
gatecse-2017-set1
data-structures
binary-search-tree
easy
+
–
57
votes
10
answers
128
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
Let $p, q, r$ denote the statements ”It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleas...
khushtak
12.0k
views
khushtak
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set2
mathematical-logic
propositional-logic
+
–
73
votes
10
answers
129
GATE CSE 2010 | Question: 53
A hash table of length $10$ uses open addressing with hash function $h(k) = k \: \mod \: 10$, and linear probing. After inserting $6$ ... of the key values using the same hash function and linear probing will result in the hash table shown above? $10$ $20$ $30$ $40$
A hash table of length $10$ uses open addressing with hash function $h(k) = k \: \mod \: 10$, and linear probing. After inserting $6$ values into an empty hash table, the...
go_editor
26.9k
views
go_editor
asked
Apr 21, 2016
DS
data-structures
hashing
normal
gatecse-2010
+
–
66
votes
10
answers
130
GATE CSE 2016 Set 1 | Question: 27
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Sandeep Singh
28.2k
views
Sandeep Singh
asked
Feb 12, 2016
Combinatory
gatecse-2016-set1
combinatory
recurrence-relation
normal
numerical-answers
+
–
49
votes
10
answers
131
GATE CSE 2016 Set 1 | Question: 05
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______
Sandeep Singh
14.5k
views
Sandeep Singh
asked
Feb 12, 2016
Linear Algebra
gatecse-2016-set1
linear-algebra
eigen-value
numerical-answers
normal
+
–
44
votes
10
answers
132
GATE CSE 2016 Set 2 | Question: 29
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
Akash Kanase
17.5k
views
Akash Kanase
asked
Feb 12, 2016
Combinatory
gatecse-2016-set2
modular-arithmetic
normal
numerical-answers
+
–
51
votes
10
answers
133
GATE CSE 2016 Set 2 | Question: 49
Consider a non-negative counting semaphore $S$. The operation $P(S)$ decrements $S$, and $V(S)$ increments $S$. During an execution, $20$ $P(S)$ operations and $12$ $V(S)$ operations are issued in some order. The largest initial value of $S$ for which at least one $P(S)$ operation will remain blocked is _______
Consider a non-negative counting semaphore $S$. The operation $P(S)$ decrements $S$, and $V(S)$ increments $S$. During an execution, $20$ $P(S)$ operations and $12$ $V(S)...
Akash Kanase
15.6k
views
Akash Kanase
asked
Feb 12, 2016
Operating System
gatecse-2016-set2
operating-system
semaphore
normal
numerical-answers
+
–
46
votes
10
answers
134
GATE CSE 2016 Set 2 | Question: 05
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than $100$ hours given that it is of Type $1$ is $0.7$, and given that it is of Type $2$ is $0.4$. The probability that an LED bulb chosen uniformly at random lasts more than $100$ hours is _________.
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than $100$ hours given that it is of Type $1$ is ...
Akash Kanase
9.4k
views
Akash Kanase
asked
Feb 12, 2016
Probability
gatecse-2016-set2
probability
conditional-probability
normal
numerical-answers
+
–
54
votes
10
answers
135
GATE CSE 2016 Set 2 | Question: 08
Let, $x_{1} ⊕ x_{2} ⊕ x_{3} ⊕ x_{4}= 0$ where $x_{1}, x_{2}, x_{3}, x_{4}$ are Boolean variables, and $⊕$ is the XOR operator. Which one of the following must always be TRUE? $x_{1}x_{2}x_{3}x_{4} = 0$ $x_{1}x_{3} + x_{2} = 0$ $\bar{x}_{1} ⊕ \bar{x}_{3} = \bar{x}_{2} ⊕ \bar{x}_{4}$ $x_{1} + x_{2} + x_{3} + x_{4} = 0$
Let, $x_{1} ⊕ x_{2} ⊕ x_{3} ⊕ x_{4}= 0$ where $x_{1}, x_{2}, x_{3}, x_{4}$ are Boolean variables, and $⊕$ is the XOR operator.Which one of the following must alwa...
Akash Kanase
13.4k
views
Akash Kanase
asked
Feb 12, 2016
Digital Logic
gatecse-2016-set2
digital-logic
boolean-algebra
normal
+
–
11
votes
10
answers
136
ISRO2015-38
Suppose two jobs, each of which needs $10$ minutes of CPU time, start simultaneously. Assume $50\%$ I/O wait time. How long will it take for both to complete, if they run sequentially? 10 20 30 40
Suppose two jobs, each of which needs $10$ minutes of CPU time, start simultaneously. Assume $50\%$ I/O wait time. How long will it take for both to complete, if they run...
ajit
11.1k
views
ajit
asked
Oct 12, 2015
Operating System
process-scheduling
isro2015
+
–
47
votes
10
answers
137
GATE CSE 2015 Set 3 | Question: 28
Consider a network connecting two systems located $8000$ $\text{Km}$ apart. The bandwidth of the network is $500 \times 10^6$ $\text{bits}$ per second. The propagation speed of the media is $4 \times 10^6$ $\text{meters}$ per ... . Assume that processing delays at nodes are negligible. Then, the minimum size in bits of the sequence number field has to be ______.
Consider a network connecting two systems located $8000$ $\text{Km}$ apart. The bandwidth of the network is $500 \times 10^6$ $\text{bits}$ per second. The propagation sp...
go_editor
14.3k
views
go_editor
asked
Feb 15, 2015
Computer Networks
gatecse-2015-set3
computer-networks
sliding-window
normal
numerical-answers
+
–
51
votes
10
answers
138
GATE CSE 2015 Set 1 | Question: 45
Let $G = (V, E)$ be a simple undirected graph, and $s$ be a particular vertex in it called the source. For $x \in V$, let $d(x)$ denote the shortest distance in $G$ from $s$ to $x$. A breadth first search (BFS) is performed starting at $s$. Let $T$ be the ... that is not in $T$, then which one of the following CANNOT be the value of $d(u) - d(v)$? $-1$ $0$ $1$ $2$
Let $G = (V, E)$ be a simple undirected graph, and $s$ be a particular vertex in it called the source. For $x \in V$, let $d(x)$ denote the shortest distance in $G$ from ...
makhdoom ghaya
18.0k
views
makhdoom ghaya
asked
Feb 13, 2015
Algorithms
gatecse-2015-set1
algorithms
graph-algorithms
normal
graph-search
+
–
49
votes
10
answers
139
GATE CSE 2015 Set 2 | Question: 23
A system has $6$ identical resources and $N$ processes competing for them. Each process can request at most $2$ requests. Which one of the following values of $N$ could lead to a deadlock? $1$ $2$ $3$ $4$
A system has $6$ identical resources and $N$ processes competing for them. Each process can request at most $2$ requests. Which one of the following values of $N$ could l...
go_editor
33.8k
views
go_editor
asked
Feb 12, 2015
Operating System
gatecse-2015-set2
operating-system
resource-allocation
easy
+
–
69
votes
10
answers
140
GATE IT 2005 | Question: 73
On a TCP connection, current congestion window size is Congestion Window = $4$ KB. The window size advertised by the receiver is Advertise Window = $6$ KB. The last byte sent by the sender is LastByteSent = $10240$ and the last byte acknowledged by ... LastByteAcked = $8192$. The current window size at the sender is: $2048$ bytes $4096$ bytes $6144$ bytes $8192$ bytes
On a TCP connection, current congestion window size is Congestion Window = $4$ KB. The window size advertised by the receiver is Advertise Window = $6$ KB. The last byte ...
Ishrat Jahan
25.9k
views
Ishrat Jahan
asked
Nov 3, 2014
Computer Networks
gateit-2005
computer-networks
congestion-control
normal
+
–
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