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121
GATE DS&AI 2024 | Question: 25
Consider the $3 \times 3$ matrix $\boldsymbol{M}=\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6\end{array}\right]$. The determinant of $\left(\boldsymbol{M}^{2}+12 \boldsymbol{M}\right)$ is $\_\_\_\_\_\_\_\_\_$.
Arjun
asked
in
Others
Feb 16
by
Arjun
613
views
gate-ds-ai-2024
numerical-answers
0
votes
1
answer
122
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? $2$ $4$ $6$ $8$
Arjun
asked
in
Probability
Feb 16
by
Arjun
978
views
gate-ds-ai-2024
probability
0
votes
1
answer
123
GATE DS&AI 2024 | Question: 27
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function. Note: $\mathbb{R}$ denotes the set of real numbers. \[ f(x)=\left\{\begin{array}{cl} -x, & \text { if } x<-2 \\ a x^{2}+b x+c, & \text { if } x \in[-2,2] \\ x, & \text { if } x>2 \end ... differentiable? $a=\frac{1}{4}, b=0, c=1$ $a=\frac{1}{2}, b=0, c=0$ $a=0, b=0, c=0$ $a=1, b=1, c=-4$
Arjun
asked
in
Others
Feb 16
by
Arjun
768
views
gate-ds-ai-2024
0
votes
1
answer
124
GATE DS&AI 2024 | Question: 28
Consider the following Python code: def count(child_dict, i): if i not in child_dict.keys(): return 1 ans $=1$ for $j$ in child_dict[i]: ans $+=$ count (child_dict, j) return ans child_dict $=$ dict () child_dict $[0]=[1,2]$ child_dict $[1]=[3,4,5]$ ... $)$ ) Which ONE of the following is the output of this code? $6$ $1$ $8$ $9$
Arjun
asked
in
Programming in Python
Feb 16
by
Arjun
792
views
gate-ds-ai-2024
programming
0
votes
2
answers
125
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 $X=[6,3,5,4,10]$ ? $[1,1,2,3,4]$ $[1,1,2,3,3]$ $[1,1,2,1,2]$ $[1,1,2,1,5]$
Arjun
asked
in
Others
Feb 16
by
Arjun
609
views
gate-ds-ai-2024
0
votes
1
answer
126
GATE DS&AI 2024 | Question: 30
Let $F(n)$ denote the maximum number of comparisons made while searching for an entry in a sorted array of size $n$ using binary search. Which ONE of the following options is TRUE? $F(n)=F(\lfloor n / 2\rfloor)+1$ $F(n)=F(\lfloor n / 2\rfloor)+F(\lceil n / 2\rceil)$ $F(n)=F(\lfloor n / 2\rfloor)$ $F(n)=F(n-1)+1$
Arjun
asked
in
Algorithms
Feb 16
by
Arjun
790
views
gate-ds-ai-2024
algorithms
binary-search
0
votes
2
answers
127
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.
Arjun
asked
in
Programming in Python
Feb 16
by
Arjun
867
views
gate-ds-ai-2024
programming
0
votes
2
answers
128
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?
Arjun
asked
in
Others
Feb 16
by
Arjun
649
views
gate-ds-ai-2024
0
votes
1
answer
129
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. $p=36, q=24, r=24$ $p=24, q=24, r=36$ $p=18, q=36, r=24$ $p=36, q=36, r=36$
Arjun
asked
in
Others
Feb 16
by
Arjun
620
views
gate-ds-ai-2024
0
votes
1
answer
130
GATE DS&AI 2024 | Question: 34
Consider a state space where the start state is number $1$. The successor function for the state numbered $n$ returns two states numbered $n+1$ and $n+2$. Assume that the states in the unexpanded state list are expanded in the ascending order of ... than BFS. Both BFS and DFS expand equal number of states. Both BFS and DFS do not reach the goal state number $6$.
Arjun
asked
in
Others
Feb 16
by
Arjun
792
views
gate-ds-ai-2024
0
votes
1
answer
131
GATE DS&AI 2024 | Question: 35
Consider the following sorting algorithms: Bubble sort Insertion sort Selection sort Which ONE among the following choices of sorting algorithms sorts the numbers in the array $[4,3,2,1,5]$ in increasing order after exactly two passes over the array? $\text{(i)}$ only $\text{(iii)}$ only $\text{(i)}$ and $\text{(iii)}$ only $\text{(ii)}$ and $\text{(iii)}$ only
Arjun
asked
in
Algorithms
Feb 16
by
Arjun
796
views
gate-ds-ai-2024
algorithms
sorting
0
votes
1
answer
132
GATE DS&AI 2024 | Question: 36
Given the relational schema $R=(U, V, W, X, Y, Z)$ and the set of functional dependencies: \[ \{U \rightarrow V, U \rightarrow W, W X \rightarrow Y, W X \rightarrow Z, V \rightarrow X\} \] Which of the following functional dependencies can be derived from the above set? $V W \rightarrow Y Z$ $W X \rightarrow Y Z$ $V W \rightarrow U$ $V W \rightarrow Y$
Arjun
asked
in
Databases
Feb 16
by
Arjun
784
views
gate-ds-ai-2024
databases
database-normalization
multiple-selects
1
vote
1
answer
133
GATE DS&AI 2024 | Question: 37
Select all choices that are subspaces of $\mathbb{R}^{3}$. Note: $\mathbb{R}$ ...
Arjun
asked
in
Others
Feb 16
by
Arjun
820
views
gate-ds-ai-2024
0
votes
1
answer
134
GATE DS&AI 2024 | Question: 38
Which of the following statements is/are TRUE? Note: $\mathbb{R}$ denotes the set of real numbers. There exist $\text{M} \in \mathbb{R}^{3 \times 3}, \text{p} \in \mathbb{R}^{3}$, and $\text{q} \in \mathbb{R}^{3}$ ... $\text{Mx}=\text{p}$ has a unique solution and $\text{M x}=\text{q}$ has no solutions.
Arjun
asked
in
Others
Feb 16
by
Arjun
796
views
gate-ds-ai-2024
0
votes
1
answer
135
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. $M^{2}=M$ $M^{3}=M$
Arjun
asked
in
Others
Feb 16
by
Arjun
722
views
gate-ds-ai-2024
0
votes
2
answers
136
GATE DS&AI 2024 | Question: 40
Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ where $\mathbb{R}$ is the set of all real numbers. \[ f(x)=\frac{x^{4}}{4}-\frac{2 x^{3}}{3}-\frac{3 x^{2}}{2}+1 \] Which of the following statements is/are TRUE? $x=0$ is a local maximum of $f$ $x=3$ is a local minimum of $f$ $x=-1$ is a local maximum of $f$ $x=0$ is a local minimum of $f$
Arjun
asked
in
Others
Feb 16
by
Arjun
713
views
gate-ds-ai-2024
0
votes
1
answer
137
GATE DS&AI 2024 | Question: 41
Consider the directed acyclic graph (DAG) below: Which of the following is/are valid vertex orderings that can be obtained from a topological sort of the DAG? $\text{P Q R S T U V}$ $\text{P R Q V SUT}$ $\text{P Q R S V U T}$ $\text{P R Q S V T U}$
Arjun
asked
in
Algorithms
Feb 16
by
Arjun
672
views
gate-ds-ai-2024
algorithms
topological-sort
directed-acyclic-graph
0
votes
2
answers
138
GATE DS&AI 2024 | Question: 42
Let $H, I, L$, and $N$ represent height, number of internal nodes, number of leaf nodes, and the total number of nodes respectively in a rooted binary tree. Which of the following statements is/are always TRUE? $L \leq I+1$ $H+1 \leq N \leq 2^{H+1}-1$ $H \leq I \leq 2^{H}-1$ $H \leq L \leq 2^{H-1}$
Arjun
asked
in
Others
Feb 16
by
Arjun
839
views
gate-ds-ai-2024
0
votes
1
answer
139
GATE DS&AI 2024 | Question: 43
Consider the following figures representing datasets consisting of two-dimensional features with two classes denoted by circles and squares. Which of the following is/are TRUE? $\text{(i)}$ is linearly separable. $\text{(ii)}$ is linearly separable. $\text{(iii)}$ is linearly separable. $\text{(iv)}$ is linearly separable.
Arjun
asked
in
Others
Feb 16
by
Arjun
719
views
gate-ds-ai-2024
0
votes
1
answer
140
GATE DS&AI 2024 | Question: 44
Let game(ball, rugby) be true if the ball is used in rugby and false otherwise. Let shape(ball, round) be true if the ball is round and false otherwise. Consider the following logical sentences: s1: $\forall$ ball $\neg$ game(ball, rugby) $\Rightarrow$ shape(ball, round) ... used in rugby"? $s 1 \wedge s 3$ $s 1 \wedge s 2$ $s 2 \wedge s 3$ $s 3 \wedge s 4$
Arjun
asked
in
Others
Feb 16
by
Arjun
890
views
gate-ds-ai-2024
0
votes
1
answer
141
GATE DS&AI 2024 | Question: 45
An OTT company is maintaining a large disk-based relational database of different movies with the following schema: \[ \begin{array}{l} \text { Movie (ID, CustomerRating) } \\ \text { Genre (ID, Name) } \\ \text { Movie_Genre ... attributes. Hash index on Movie.CustomerRating and $\mathrm{B}^{+}$tree on the remaining attributes. Hash index on all the attributes.
Arjun
asked
in
Others
Feb 16
by
Arjun
806
views
gate-ds-ai-2024
0
votes
1
answer
142
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).
Arjun
asked
in
Others
Feb 16
by
Arjun
795
views
gate-ds-ai-2024
numerical-answers
0
votes
1
answer
143
GATE DS&AI 2024 | Question: 47
Let $X$ be a random variable exponentially distributed with parameter $\lambda>0$. The probability density function of $X$ is given by: \[ f_{X}(x)=\left\{\begin{array}{ll} \lambda e^{-\lambda x}, \quad x \geq 0 \\ 0, & \text { otherwise } \end ... variance of $X$, respectively, the value of $\lambda$ is $\_\_\_\_\_\_\_\_$ (rounded off to one decimal place).
Arjun
asked
in
Probability
Feb 16
by
Arjun
599
views
gate-ds-ai-2024
numerical-answers
probability
random-variable
0
votes
1
answer
144
GATE DS&AI 2024 | Question: 48
Consider two events $T$ and $S$. Let $\bar{T}$ denote the complement of the event $T$. The probability associated with different events are given as follows: \[ P(\bar{T})=0.6, \quad P(S \mid T)=0.3, \quad P(S \mid \bar{T})=0.6 \] Then, $P(T \mid S)$ is $\_\_\_\_\_\_\_\_$ (rounded off to two decimal places).
Arjun
asked
in
Probability
Feb 16
by
Arjun
639
views
gate-ds-ai-2024
numerical-answers
probability
0
votes
1
answer
145
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 $\_\_\_\_\_\_\_\_\_$
Arjun
asked
in
Others
Feb 16
by
Arjun
936
views
gate-ds-ai-2024
numerical-answers
1
vote
1
answer
146
GATE DS&AI 2024 | Question: 50
Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
Arjun
asked
in
Calculus
Feb 16
by
Arjun
769
views
gate-ds-ai-2024
numerical-answers
limits
engineering-mathematics
0
votes
1
answer
147
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 $\_\_\_\_\_\_\_\_\_$
Arjun
asked
in
Others
Feb 16
by
Arjun
921
views
gate-ds-ai-2024
numerical-answers
0
votes
1
answer
148
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
Arjun
asked
in
Others
Feb 16
by
Arjun
773
views
gate-ds-ai-2024
numerical-answers
0
votes
1
answer
149
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 $\_\_\_\_\_\_\_$.
Arjun
asked
in
Others
Feb 16
by
Arjun
963
views
gate-ds-ai-2024
numerical-answers
0
votes
2
answers
150
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).
Arjun
asked
in
Others
Feb 16
by
Arjun
1.0k
views
gate-ds-ai-2024
numerical-answers
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