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1
UGC NET CSE | December 2019 | Part 2 | Question: 41
When using Dijkstra's algorithm to find shortest path in a graph, which of the following statement is not true? It can find shortest path within the same graph data structure Every time a new node is visited, we choose the ... Shortest path always passes through least number of vertices The graph needs to have a non-negative weight on every edge
answered
in
Others
Aug 13, 2021
888
views
ugcnetcse-dec2019-paper2
2
votes
2
GATE CSE 2004 | Question: 78
Two $n$ bit binary strings, $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to $d$ is $\dfrac{^{n}C_{d}}{2^{n}}$ $\dfrac{^{n}C_{d}}{2^{d}}$ $\dfrac{d}{2^{n}}$ $\dfrac{1}{2^{d}}$
answered
in
Probability
Aug 31, 2020
7.3k
views
gatecse-2004
probability
normal
uniform-distribution
0
votes
3
GATE CSE 2005 | Question: 52
A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is: $\frac{1}{2^n}$ $1 - \frac{1}{n}$ $\frac{1}{n!}$ $1 - \frac{1}{2^n}$
answered
in
Probability
Aug 31, 2020
8.5k
views
gatecse-2005
probability
binomial-distribution
easy
0
votes
4
GATE CSE 2001 | Question: 2.1
How many $4$-digit even numbers have all $4$ digits distinct? $2240$ $2296$ $2620$ $4536$
answered
in
Combinatory
Aug 26, 2020
12.7k
views
gatecse-2001
combinatory
normal
0
votes
5
ISRO2009-56
A simple graph ( a graph without parallel edge or loops) with $n$ vertices and $k$ components can have at most $n$ edges $n-k$ edges $(n-k) (n-k+1)$ edges $(n-k) (n-k+1)/2$ edges
answered
in
Graph Theory
Aug 26, 2020
3.4k
views
isro2009
graph-theory
graph-connectivity
0
votes
6
GATE CSE 2019 | Question: 30
Consider three $4$-variable functions $f_1, f_2$, and $f_3$, which are expressed in sum-of-minterms as $f_1=\Sigma(0,2,5,8,14),$ $f_2=\Sigma(2,3,6,8,14,15),$ $f_3=\Sigma (2,7,11,14)$ For the following circuit with one AND gate and one XOR gate the output function $f$ can be ... as: $\Sigma(7,8,11)$ $\Sigma (2,7,8,11,14)$ $\Sigma (2,14)$ $\Sigma (0,2,3,5,6,7,8,11,14,15)$
answered
in
Digital Logic
Aug 22, 2020
14.3k
views
gatecse-2019
digital-logic
k-map
digital-circuits
2-marks
2
votes
7
GATE IT 2006 | Question: 21
Consider the following first order logic formula in which $R$ is a binary relation symbol. $∀x∀y (R(x, y) \implies R(y, x))$ The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable
answered
in
Mathematical Logic
Aug 18, 2020
13.4k
views
gateit-2006
mathematical-logic
normal
first-order-logic
0
votes
8
relations and functions
answered
in
Mathematical Logic
Aug 15, 2020
379
views
0
votes
9
relations and functions
A binary relation R on Z × Z is defined as follows: (a, b) R (c, d) iff a = c or b = d Consider the following propositions: 1. R is reflexive. 2. R is symmetric. 3. R is antisymmetric. Which one of the above statements is True?
answered
in
Mathematical Logic
Aug 15, 2020
638
views
3
votes
10
GATE CSE 2004 | Question: 26
The number of different $n \times n $ symmetric matrices with each element being either 0 or 1 is: (Note: $\text{power} \left(2, X\right)$ is same as $2^X$) $\text{power} \left(2, n\right)$ $\text{power} \left(2, n^2\right)$ $\text{power} \left(2,\frac{ \left(n^2+ n \right) }{2}\right)$ $\text{power} \left(2, \frac{\left(n^2 - n\right)}{2}\right)$
answered
in
Linear Algebra
Aug 10, 2020
12.5k
views
gatecse-2004
linear-algebra
normal
matrix
0
votes
11
GATE CSE 2015 Set 3 | Question: 53
Language $L_1$ is polynomial time reducible to language $L_2$. Language $L_3$ is polynomial time reducible to language $L_2$, which in turn polynomial time reducible to language $L_4$. Which of the following is/are true? $\text{ if } L_4 \in P, \text{ then } L_2 \in P$ ... $\text{ if } L_4 \in P, \text{ then } L_3 \in P$ II only III only I and IV only I only
answered
in
Theory of Computation
Aug 9, 2020
9.1k
views
gatecse-2015-set3
theory-of-computation
decidability
normal
1
vote
12
GATE CSE 2018 | Question: 15
Two people, $P$ and $Q$, decide to independently roll two identical dice, each with $6$ faces, numbered $1$ to $6$. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a ... and that all trials are independent. The probability (rounded to $3$ decimal places) that one of them wins on the third trial is ____
answered
in
Probability
Aug 9, 2020
10.9k
views
gatecse-2018
probability
normal
numerical-answers
1-mark
2
votes
13
GATE CSE 2008 | Question: 21
The minimum number of equal length subintervals needed to approximate $\int_1^2 xe^x\,dx$ to an accuracy of at least $\frac{1}{3}\times10^{-6}$ using the trapezoidal rule is 1000e 1000 100e 100
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in
Numerical Methods
Aug 1, 2020
3.0k
views
gatecse-2008
normal
numerical-methods
trapezoidal-rule
non-gate
0
votes
14
GATE CSE 1988 | Question: 1i
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.
answered
in
Numerical Methods
Jul 31, 2020
554
views
gate1988
numerical-methods
out-of-gate-syllabus
1
vote
15
GATE IT 2007 | Question: 66
Consider the following two transactions$: T1$ and $T2.$ ...
answered
in
Databases
Jul 23, 2020
17.9k
views
gateit-2007
databases
transaction-and-concurrency
normal
0
votes
16
GATE IT 2005 | Question: 34
Let $n =$ $p^{2}q$, where $p$ and $q$ are distinct prime numbers. How many numbers m satisfy $1 ≤ m ≤ n$ and $gcd$ $(m, n) = 1?$ Note that $gcd$ $(m, n)$ is the greatest common divisor of $m$ and $n$. $p(q - 1)$ $pq$ $\left ( p^{2}-1 \right ) (q - 1)$ $p(p - 1) (q - 1)$
answered
in
Set Theory & Algebra
Jul 20, 2020
8.1k
views
gateit-2005
set-theory&algebra
normal
number-theory
2
votes
17
GATE CSE 2006 | Question: 21
For each element in a set of size $2n$, an unbiased coin is tossed. The $2n$ coin tosses are independent. An element is chosen if the corresponding coin toss was a head. The probability that exactly $n$ elements are chosen is $\frac{^{2n}\mathrm{C}_n}{4^n}$ $\frac{^{2n}\mathrm{C}_n}{2^n}$ $\frac{1}{^{2n}\mathrm{C}_n}$ $\frac{1}{2}$
answered
in
Probability
Jul 20, 2020
8.1k
views
gatecse-2006
probability
binomial-distribution
normal
1
vote
18
GATE CSE 2008 | Question: 78
Let $x_n$ denote the number of binary strings of length $n$ that contain no consecutive $0$s. Which of the following recurrences does $x_n$ satisfy? $x_n = 2x_{n-1}$ $x_n = x_{\lfloor n/2 \rfloor} + 1$ $x_n = x_{\lfloor n/2 \rfloor} + n$ $x_n = x_{n-1} + x_{n-2}$
answered
in
Algorithms
Jul 18, 2020
8.4k
views
gatecse-2008
algorithms
recurrence-relation
normal
3
votes
19
GATE 1995
If the disk is rotating at 3600rpm, determine the effective data transfer rate which is defined as the number of bytes transferred per second between disk and memory. (Given the size of track = 512 bytes)?
answered
in
CO and Architecture
Jul 17, 2020
3.5k
views
co-and-architecture
disk
3
votes
20
GATE CSE 2003 | Question: 34
$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be placed in the bags if each bag must contain at least $k$ ... $\left( \begin{array}{c} m - kn + n + k - 2 \\ n - k \end{array} \right)$
answered
in
Combinatory
Jul 13, 2020
11.3k
views
gatecse-2003
combinatory
balls-in-bins
normal
1
vote
21
GATE CSE 2016 Set 2 | Question: 33
Consider a $3 \ \text{GHz}$ (gigahertz) processor with a three stage pipeline and stage latencies $\large\tau_1,\tau_2$ and $\large\tau_3$ such that $\large\tau_1 =\dfrac{3 \tau_2}{4}=2\tau_3$. If the longest pipeline stage is split into two pipeline stages of equal latency , the new frequency is __________ $\text{GHz}$, ignoring delays in the pipeline registers.
answered
in
CO and Architecture
Jul 13, 2020
19.1k
views
gatecse-2016-set2
co-and-architecture
pipelining
normal
numerical-answers
0
votes
22
GATE CSE 2005 | Question: 65
Consider a three word machine instruction $\text{ADD} A[R_0], @B$ The first operand (destination) $ A[R_0] $ uses indexed addressing mode with $R_0$ as the index register. The second operand (source) $ @B $ uses indirect addressing mode. $A$ and $B$ ... (first operand). The number of memory cycles needed during the execution cycle of the instruction is: $3$ $4$ $5$ $6$
answered
in
CO and Architecture
Jul 13, 2020
34.3k
views
gatecse-2005
co-and-architecture
addressing-modes
normal
0
votes
23
GATE CSE 2004 | Question: 68
A hard disk with a transfer rate of $10$ Mbytes/second is constantly transferring data to memory using DMA. The processor runs at $600$ MHz, and takes $300$ and $900$ ... percentage of processor time consumed for the transfer operation? $5.0 \%$ $1.0\%$ $0.5\%$ $0.1\%$
answered
in
CO and Architecture
Jul 12, 2020
27.0k
views
gatecse-2004
dma
normal
co-and-architecture
0
votes
24
GATE CSE 2001 | Question: 2.13
Consider the following data path of a simple non-pipelined CPU. The registers $A, B$, $A_{1},A_{2}, \textsf{MDR},$ the $\textsf{bus}$ and the $\textsf{ALU}$ are $8$-$bit$ wide. $\textsf{SP}$ and $\textsf{MAR}$ are $16$-$bit$ registers. The ... $\textsf{CPU}$ clock cycles are required to execute the "push r" instruction? $2$ $3$ $4$ $5$
answered
in
CO and Architecture
Jul 12, 2020
21.2k
views
gatecse-2001
co-and-architecture
data-path
machine-instruction
normal
0
votes
25
GATE CSE 2005 | Question: 80
Consider the following data path of a $\text{CPU}.$ The $\text{ALU},$ the bus and all the registers in the data path are of identical size. All operations including incrementation of the $\text{PC}$ and the $\text{GPRs}$ are to be carried out in ... $2$ $3$ $4$ $5$
answered
in
CO and Architecture
Jul 12, 2020
24.2k
views
co-and-architecture
normal
gatecse-2005
data-path
machine-instruction
0
votes
26
GATE CSE 2004 | Question: 81
Let $G_1=(V,E_1)$ and $G_2 =(V,E_2)$ be connected graphs on the same vertex set $V$ with more than two vertices. If $G_1 \cap G_2= (V,E_1\cap E_2)$ is not a connected graph, then the graph $G_1\cup G_2=(V,E_1\cup E_2)$ cannot have a cut vertex must have a cycle must have a cut-edge (bridge) has chromatic number strictly greater than those of $G_1$ and $G_2$
answered
in
Algorithms
Jul 9, 2020
11.7k
views
gatecse-2004
algorithms
graph-algorithms
normal
1
vote
27
GATE CSE 2019 | Question: 46
Let $T$ be a full binary tree with $8$ leaves. (A full binary tree has every level full.) Suppose two leaves $a$ and $b$ of $T$ are chosen uniformly and independently at random. The expected value of the distance between $a$ and $b$ in $T$ (ie., the number of edges in the unique path between $a$ and $b$) is (rounded off to $2$ decimal places) _________.
answered
in
DS
Jul 8, 2020
30.6k
views
gatecse-2019
numerical-answers
data-structures
binary-tree
2-marks
0
votes
28
GATE CSE 2006 | Question: 51, ISRO2016-34
Consider the following recurrence: $ T(n)=2T\left ( \sqrt{n}\right )+1,$ $T(1)=1$ Which one of the following is true? $ T(n)=\Theta (\log\log n)$ $ T(n)=\Theta (\log n)$ $ T(n)=\Theta (\sqrt{n})$ $ T(n)=\Theta (n)$
answered
in
Algorithms
Jul 6, 2020
27.8k
views
algorithms
recurrence-relation
isro2016
gatecse-2006
0
votes
29
GATE CSE 2006 | Question: 17
An element in an array $X$ is called a leader if it is greater than all elements to the right of it in $X$. The best algorithm to find all leaders in an array solves it in linear time using a left to right pass of the array solves it in linear time using ... pass of the array solves it using divide and conquer in time $\Theta (n\log n)$ solves it in time $\Theta( n^2)$
answered
in
Algorithms
Jul 5, 2020
17.8k
views
gatecse-2006
algorithms
normal
algorithm-design
0
votes
30
GATE CSE 2019 | Question: 50
What is the minimum number of $2$-input NOR gates required to implement a $4$ -variable function expressed in sum-of-minterms form as $f=\Sigma(0,2,5,7, 8, 10, 13, 15)?$ Assume that all the inputs and their complements are available. Answer: _______
answered
in
Digital Logic
Jul 2, 2020
30.2k
views
gatecse-2019
numerical-answers
digital-logic
canonical-normal-form
2-marks
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