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Answers by ankitgupta.1729
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1
GATE DS&AI 2024 | Question: 54
Given the following Bayesian Network consisting of four Bernoulli random variables and the associated conditional probability tables: \begin{array}{|c|c|} \hline & P(\cdot) \\ \hline U=0 & 0.5 \\ \hline U=1 & 0.5 \\ \hline \end{array} \begin{array}{|c|c|c|} \ ... The value of $P(U=1, V=1, W=1, Z=1)= \_\_\_\_\_\_\_$ (rounded off to three decimal places).
answered
in
Others
Feb 19
1.0k
views
gate-ds-ai-2024
numerical-answers
0
votes
2
GATE DS&AI 2024 | Question: 32
Consider the table below, where the $(i, j)^{t h}$ element of the table is the distance between points $x_{i}$ and $x_{j}$. Single linkage clustering is performed on data points, $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$. \begin{array} ... & 3 & 5 & 1 & 0 \\ \hline \end{array} Which ONE of the following is the correct representation of the clusters produced?
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in
Others
Feb 17
655
views
gate-ds-ai-2024
0
votes
3
GATE DS&AI 2024 | Question: 52
Details of ten international cricket games between two teams "Green" and "Blue" are given in Table $\mathrm{C}$. This table consists of matches played on different pitches, across formats along with their winners. The attribute Pitch can take one of two values: spin-friendly ( ... $S$ $O$ Green $8$ $F$ $T$ Blue $9$ $F$ $O$ Blue $10$ $S$ $O$ Green
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in
Others
Feb 17
774
views
gate-ds-ai-2024
numerical-answers
1
vote
4
GATE DS&AI 2024 | GA Question: 9
Three different views of a dice are shown in the figure below. The piece of paper that can be folded to make this dice is
answered
in
Spatial Aptitude
Feb 17
1.2k
views
gate-ds-ai-2024
spatial-aptitude
figure-rotation
1
vote
5
GATE DS&AI 2024 | Question: 29
Consider the function computes $(X)$ whose pseudocode is given below: computes $(X)$ $S[1] \leftarrow 1$ for $i \leftarrow 2$ to length $(X)$ $S[i] \leftarrow 1$ if $X[i-1] \leq X[i]$ $S[i] \leftarrow S[i]+S[i-1]$ end if end for return $S$ Which ONE of the following values is ... for $X=[6,3,5,4,10]$ ? $[1,1,2,3,4]$ $[1,1,2,3,3]$ $[1,1,2,1,2]$ $[1,1,2,1,5]$
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in
Others
Feb 17
612
views
gate-ds-ai-2024
3
votes
6
GATE DS&AI 2024 | Question: 31
Consider the following Python function: def $\operatorname{fun}(D, s 1, s 2)$ : if $\mathrm{s} 1<\mathrm{s} 2$ ... both inclusive. It swaps the elements in $\mathrm{D}$ at indices $\mathrm{s} 1$ and $\mathrm{s} 2$, and leaves the remaining elements unchanged.
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in
Programming in Python
Feb 17
870
views
gate-ds-ai-2024
programming
0
votes
7
GATE DS&AI 2024 | Question: 12
For any binary classification dataset, let $S_{B} \in \mathbb{R}^{d \times d}$ and $S_{W} \in \mathbb{R}^{d \times d}$ be the between-class and within-class scatter (covariance) matrices, respectively. The Fisher linear discriminant is defined by $u^{*} \in \mathbb{R}^{d}$, ... $S_{B} S_{W} u^{*}=\lambda u^{*}$ $u^{* T} u^{*}=\lambda^{2}$
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in
Others
Feb 17
464
views
gate-ds-ai-2024
2
votes
8
GATE DS&AI 2024 | Question: 55
Two fair coins are tossed independently. $X$ is a random variable that takes a value of $1$ if both tosses are heads and $0$ otherwise. $Y$ is a random variable that takes a value of $1$ if at least one of the tosses is heads and $0$ otherwise. The value of the covariance of $X$ and $Y$ is $\_\_\_\_\_\_\_$ (rounded off to three decimal places).
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in
Others
Feb 16
1.7k
views
gate-ds-ai-2024
numerical-answers
1
vote
9
GATE DS&AI 2024 | Question: 39
Let $\mathbb{R}$ be the set of real numbers, $U$ be a subspace of $\mathbb{R}^{3}$ and $\text{M} \in \mathbb{R}^{3 \times 3}$ be the matrix corresponding to the projection on to the subspace $U$. Which of the following statements is/are TRUE? If $U$ is a ... of $\mathbb{R}^{3}$, then the null space of $\text{M}$ is a $1$-dimensional subspace. $M^{2}=M$ $M^{3}=M$
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in
Others
Feb 16
725
views
gate-ds-ai-2024
1
vote
10
GATE CSE 2024 | Set 2 | Question: 7
Let $\text{A}$ be the adjacency matrix of a simple undirected graph $\text{G}$. Suppose $\text{A}$ is its own inverse. Which one of the following statements is always TRUE? $\text{G}$ is a cycle $\text{G}$ is a perfect matching $\text{G}$ is a complete graph There is no such graph $\text{G}$
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in
Graph Theory
Feb 16
2.5k
views
gatecse2024-set2
graph-theory
1
vote
11
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 ___________.
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in
Set Theory & Algebra
Feb 16
1.8k
views
gatecse2024-set2
numerical-answers
set-theory&algebra
group-theory
0
votes
12
GATE DS&AI 2024 | Question: 53
Given the two-dimensional dataset consisting of $5$ data points from two classes (circles and squares) and assume that the Euclidean distance is used to measure the distance between two points. The minimum odd value of $k$ in $k$-nearest neighbor algorithm for which the diamond $(\diamond)$ shaped data point is assigned the label square is $\_\_\_\_\_\_\_$.
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in
Others
Feb 16
969
views
gate-ds-ai-2024
numerical-answers
0
votes
13
GATE DS&AI 2024 | Question: 33
Consider the two neural networks (NNs) shown in Figures $1$ and $2$, with $R e L U$ activation $(\text{ReLU}(z)=\max \{0, z\}, \forall z \in \text{R})$. The connections and their corresponding weights are shown in the Figures. The biases at every neuron are set to $0$. ... real numbers. $p=36, q=24, r=24$ $p=24, q=24, r=36$ $p=18, q=36, r=24$ $p=36, q=36, r=36$
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in
Others
Feb 16
621
views
gate-ds-ai-2024
0
votes
14
GATE DS&AI 2024 | Question: 46
Let $X$ be a random variable uniformly distributed in the interval $[1,3]$ and $Y$ be a random variable uniformly distributed in the interval $[2, 4]$. If $X$ and $Y$ are independent of each other, the probability $P(X \geq Y)$ is $\_\_\_\_\_\_\_\_$ (rounded off to three decimal places).
answered
in
Others
Feb 16
796
views
gate-ds-ai-2024
numerical-answers
2
votes
15
GATE DS&AI 2024 | Question: 23
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be the function $f(x)=\frac{1}{1+e^{-x}}$. The value of the derivative of $f$ at $x$ where $f(x)=0.4$ is $\_\_\_\_\_\_\_$. (rounded off to two decimal places). Note: $\mathbb{R}$ denotes the set of real numbers.
answered
in
Others
Feb 16
678
views
gate-ds-ai-2024
numerical-answers
0
votes
16
GATE DS&AI 2024 | Question: 49
Consider a joint probability density function of two random variables $X$ and $Y$ \[ f_{X, Y}(x, y)=\left\{\begin{array}{rll}2 x y, & 0<x<2, & 0<y<x \\ 0, & \text { otherwise } & \end{array}\right. \] Then, $E[Y \mid X=1.5]$ is $\_\_\_\_\_\_\_\_\_$
answered
in
Others
Feb 16
936
views
gate-ds-ai-2024
numerical-answers
1
vote
17
GATE DS&AI 2024 | Question: 10
Given a dataset with $K$ binary-valued attributes (where $K>2$ ) for a two-class classification task, the number of parameters to be estimated for learning a naïve Bayes classifier is $2^{K}+1$ $2 K+1$ $2^{K+1}+1$ $K^{2}+1$
answered
in
Others
Feb 16
797
views
gate-ds-ai-2024
1
vote
18
GATE DS&AI 2024 | Question: 7
Consider the dataset with six datapoints: $\left\{\left(\text{x}_{1}, \text{y}_{1}\right),\left(\text{x}_{2}, \text{y}_{2}\right), \ldots,\left(\text{x}_{6}, \text{y}_{6}\right)\right\}$ ... $\left\{x_{4}, x_{5}\right\}$ $\left\{x_{1}, x_{2}, x_{3}, x_{4}\right\}$
answered
in
Others
Feb 16
640
views
gate-ds-ai-2024
1
vote
19
GATE DS&AI 2024 | Question: 51
Let $\text{u}=\left[\begin{array}{l}1 \\ 2 \\ 3 \\ 4 \\ 5\end{array}\right]$, and let $\sigma_{1}, \sigma_{2}, \sigma_{3}, \sigma_{4}, \sigma_{5}$ be the singular values of the matrix $\text{M}=\text{u} \text{u}^{\text{T}}$ (where $\text{u}^{\text{T}}$ is the transpose of $\text{u}$ ). The value of $\sum_{i=1}^{5} \sigma_{i}$ is $\_\_\_\_\_\_\_\_\_$
answered
in
Others
Feb 16
922
views
gate-ds-ai-2024
numerical-answers
0
votes
20
GATE DS&AI 2024 | Question: 26
A fair six-sided die (with faces numbered $1,2,3,4,5,6$ ) is repeatedly thrown independently. What is the expected number of times the die is thrown until two consecutive throws of even numbers are seen? $2$ $4$ $6$ $8$
answered
in
Probability
Feb 16
986
views
gate-ds-ai-2024
probability
1
vote
21
GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 53
Let $S^{2}$ be the variance of a random sample of size $n>1$ from a normal population with an unknown mean $\mu$ and an unknown finite variance $\sigma^{2}<\infty$. Consider the following statements: $\text{(I)}$ $S^{2}$ is ... $\text{(I)}$ and $\text{(II)}$ Neither $\text{(I)}$ nor $\text{(II)}$
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in
Others
Jan 5
1.2k
views
gateda-sample-paper-2024
2
votes
22
TIFR CSE 2022 | Part A | Question: 6
Let $f$ be a polynomial of degree $n \geq 3$ all of whose roots are non-positive real numbers. Suppose that $f(1)=1$. What is the maximum possible value of $f^{\prime}(1)?$ $1$ $n$ $n+1$ $\frac{n(n+1)}{2}$ $f^{\prime}(1)$ can be arbitrarily large given only the constraints in the question
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in
Calculus
Sep 29, 2023
687
views
tifr2022
calculus
maxima-minima
2
votes
23
GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
answered
in
Combinatory
Aug 2, 2023
7.8k
views
gatecse-2023
combinatory
recurrence-relation
1-mark
5
votes
24
GATE CSE 2023 | Question: 19
Let $f$ and $g$ be functions of natural numbers given by $f(n)=n$ and $g(n)=n^{2}.$ Which of the following statements is/are $\text{TRUE}?$ $f \in O(g)$ $f \in \Omega(g)$ $f \in o(g)$ $f \in \Theta(g)$
answered
in
Algorithms
May 24, 2023
9.5k
views
gatecse-2023
algorithms
asymptotic-notation
multiple-selects
1-mark
0
votes
25
Find the value of [v]e wherev is a vector space and e is a list of polynomials
answered
in
Mathematical Logic
May 18, 2023
243
views
linear-algebra
16
votes
26
GATE CSE 2023 | Question: 16
Geetha has a conjecture about integers, which is of the form \[ \forall x(P(x) \Longrightarrow \exists y Q(x, y)), \] where $P$ is a statement about integers, and $Q$ is a statement about pairs of integers. Which of the following (one or more) option(s) would imply ... $\exists y \forall x(P(x) \Longrightarrow Q(x, y))$ $\exists x(P(x) \wedge \exists y Q(x, y))$
answered
in
Mathematical Logic
Feb 18, 2023
11.0k
views
gatecse-2023
mathematical-logic
first-order-logic
multiple-selects
1-mark
8
votes
27
GATE CSE 2023 | Question: 21
The value of the definite integral \[ \int_{-3}^{3} \int_{-2}^{2} \int_{-1}^{1}\left(4 x^{2} y-z^{3}\right) \mathrm{d} z \mathrm{~d} y \mathrm{~d} x \] is _________. (Rounded off to the nearest integer)
answered
in
Calculus
Feb 16, 2023
8.5k
views
gatecse-2023
calculus
definite-integral
numerical-answers
1-mark
14
votes
28
GATE CSE 2023 | Question: 39
Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as \[ a_{1} \sim a_{2} \text { if } f\left(a_{1}\right)=f\left(a_{2}\right), \] ... is NOT well-defined. $F$ is an onto (or surjective) function. $F$ is a one-to-one (or injective) function. $F$ is a bijective function.
answered
in
Set Theory & Algebra
Feb 16, 2023
5.7k
views
gatecse-2023
set-theory&algebra
equivalence-class
multiple-selects
2-marks
12
votes
29
GATE CSE 2023 | Question: 41
Let $X$ be a set and $2^{X}$ denote the powerset of $X$. Define a binary operation $\Delta$ on $2^{X}$ as follows: \[ A \Delta B=(A-B) \cup(B-A) \text {. } \] Let $H=\left(2^{X}, \Delta\right)$. Which of the following statements about $H$ is/are correct? ... $A \in 2^{X},$ the inverse of $A$ is the complement of $A$. For every $A \in 2^{X},$ the inverse of $A$ is $A$.
answered
in
Set Theory & Algebra
Feb 15, 2023
5.5k
views
gatecse-2023
set-theory&algebra
group-theory
multiple-selects
2-marks
18
votes
30
GATE CSE 2023 | Question: 34
A Boolean digital circuit is composed using two $4$-input multiplexers $\text{(M1 and M2)}$ and one $2$-input multiplexer $\text{(M3)}$ as shown in the figure. $\text{X0-X7}$ are the inputs of the multiplexers $\text{M1 and M2}$ and could be connected to either $0$ or $1.$ The select lines of the ... $(1,1,0,0,1,1,0,1)$ $(1,1,0,1,1,1,0,0)$ $(0,0,1,1,0,1,1,1)$
answered
in
Digital Logic
Feb 15, 2023
9.2k
views
gatecse-2023
digital-logic
combinational-circuit
multiplexer
2-marks
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