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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.
Consider the following Python function:def $\operatorname{fun}(D, s 1, s 2)$ :if $\mathrm{s} 1<\mathrm{s} 2$ :$\mathrm{D}[\mathrm{s} 1], \mathrm{D}[\mathrm...
Arjun
858
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Arjun
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Feb 16
Programming in Python
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programming
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122
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?
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...
Arjun
636
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Arjun
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Feb 16
Others
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123
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. $p=36, q=24, r=24$ $p=24, q=24, r=36$ $p=18, q=36, r=24$ $p=36, q=36, r=36$
Consider the two neural networks (NNs) shown in Figures $1$ and $2$, with $R e L U$ activation $(\text{ReLU}(z)=\max \{0, z\}, \forall z \in \text{R})$....
Arjun
625
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Arjun
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Feb 16
Others
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124
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 $6$.
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 $n+2$. ...
Arjun
787
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Arjun
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Feb 16
Others
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125
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
Consider the following sorting algorithms:Bubble sortInsertion sortSelection sortWhich ONE among the following choices of sorting algorithms sorts the numbers in the arra...
Arjun
796
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Arjun
asked
Feb 16
Algorithms
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algorithms
sorting
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126
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? $V W \rightarrow Y Z$ $W X \rightarrow Y Z$ $V W \rightarrow U$ $V W \rightarrow Y$
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 \...
Arjun
783
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Arjun
asked
Feb 16
Databases
gate-ds-ai-2024
databases
database-normalization
multiple-selects
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127
GATE DS&AI 2024 | Question: 37
Select all choices that are subspaces of $\mathbb{R}^{3}$. Note: $\mathbb{R}$ ...
Select all choices that are subspaces of $\mathbb{R}^{3}$.Note: $\mathbb{R}$ denotes the set of real numbers.$\left\{\mathbf{x}=\left[\begin{array}{l}x_{1} \\ x_{2} \\ x_...
Arjun
817
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Arjun
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Feb 16
Others
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128
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.
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}, \tex...
Arjun
784
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Arjun
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Feb 16
Others
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129
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. $M^{2}=M$ $M^{3}=M$
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 t...
Arjun
711
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Arjun
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Feb 16
Others
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130
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 $f$
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}-\fr...
Arjun
707
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Arjun
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Feb 16
Others
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131
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? $\text{P Q R S T U V}$ $\text{P R Q V SUT}$ $\text{P Q R S V U T}$ $\text{P R Q S V T U}$
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...
Arjun
664
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Arjun
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Feb 16
Algorithms
gate-ds-ai-2024
algorithms
topological-sort
directed-acyclic-graph
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132
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? $L \leq I+1$ $H+1 \leq N \leq 2^{H+1}-1$ $H \leq I \leq 2^{H}-1$ $H \leq L \leq 2^{H-1}$
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...
Arjun
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Feb 16
Others
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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.
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 ...
Arjun
702
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Arjun
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Feb 16
Others
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134
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"? $s 1 \wedge s 3$ $s 1 \wedge s 2$ $s 2 \wedge s 3$ $s 3 \wedge s 4$
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.Cons...
Arjun
883
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Arjun
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Feb 16
Others
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135
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.
An OTT company is maintaining a large disk-based relational database of different movies with the following schema:\[\begin{array}{l}\text { Movie (ID, ...
Arjun
803
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Arjun
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Feb 16
Others
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136
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).
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...
Arjun
791
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Arjun
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Feb 16
Others
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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).
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}...
Arjun
601
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Arjun
asked
Feb 16
Probability
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probability
random-variable
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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).
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})=...
Arjun
632
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Arjun
asked
Feb 16
Probability
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numerical-answers
probability
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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 $\_\_\_\_\_\_\_\_\_$
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 { otherwi...
Arjun
937
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Arjun
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Feb 16
Others
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numerical-answers
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140
GATE DS&AI 2024 | Question: 50
Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
Evaluate the following limit:\[\lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
Arjun
762
views
Arjun
asked
Feb 16
Calculus
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numerical-answers
limits
engineering-mathematics
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141
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 $\_\_\_\_\_\_\_\_\_$
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 ...
Arjun
904
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Arjun
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Feb 16
Others
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numerical-answers
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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
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 pitche...
Arjun
756
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Arjun
asked
Feb 16
Others
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numerical-answers
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143
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 $\_\_\_\_\_\_\_$.
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 dista...
Arjun
962
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Arjun
asked
Feb 16
Others
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numerical-answers
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144
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).
Given the following Bayesian Network consisting of four Bernoulli random variables and the associated conditional probability tables:\begin{array}{|c|c|}\hline & P(\cdot)...
Arjun
1.0k
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Arjun
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Feb 16
Others
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numerical-answers
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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).
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 take...
Arjun
1.7k
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Arjun
asked
Feb 16
Others
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numerical-answers
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146
GATE CSE 2024 | Set 2 | GA Question: 1
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [walk $\rightarrow$ jog $\rightarrow$ sprint] is analogous to [bothered $\rightarrow$ ________$\rightarrow$ daunted]. Which one of the given options is appropriate to fill the blank? phased phrased fazed fused
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [walk $\rightarrow$ jog $\rightarrow$ sprint] is analogous to [bo...
Arjun
4.9k
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Arjun
asked
Feb 16
Verbal Aptitude
gatecse2024-set2
verbal-aptitude
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147
GATE CSE 2024 | Set 2 | GA Question: 2
Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. They also decide to work independently. After trying all possible combination ... work. How many attempts does each wizard make before coming to this conclusion, independently? $24$ $48$ $16$ $12$
Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. ...
Arjun
3.6k
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Arjun
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Feb 16
Quantitative Aptitude
gatecse2024-set2
quantitative-aptitude
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GATE CSE 2024 | Set 2 | GA Question: 4
For positive non-zero real variables $x$ and $y$, if \[ \ln \left(\frac{x+y}{2}\right)=\frac{1}{2}[\ln (x)+\ln (y)] \] then, the value of $\frac{x}{y}+\frac{y}{x}$ is $1$ $1 / 2$ $2$ $4$
For positive non-zero real variables $x$ and $y$, if\[\ln \left(\frac{x+y}{2}\right)=\frac{1}{2}[\ln (x)+\ln (y)]\]then, the value of $\frac{x}{y}+\frac{y}{x}$ is$1$$1 / ...
Arjun
2.5k
views
Arjun
asked
Feb 16
Quantitative Aptitude
gatecse2024-set2
quantitative-aptitude
logarithms
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149
GATE CSE 2024 | Set 2 | GA Question: 6
Sequence the following sentences in a coherent passage. $\text{P}$: This fortuitous geological event generated a colossal amount of energy and heat that resulted in the rocks rising to an average height of $4 \mathrm{~km}$ across the contact zone ... Plate collided with the massive Eurasian Plate. $\text{QPSR}$ $\text{QSPR}$ $\text{SPRQ}$ $\text{SRPQ}$
Sequence the following sentences in a coherent passage.$\text{P}$: This fortuitous geological event generated a colossal amount of energy and heat that res...
Arjun
2.5k
views
Arjun
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Feb 16
Verbal Aptitude
gatecse2024-set2
verbal-aptitude
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150
GATE CSE 2024 | Set 2 | GA Question: 7
A person sold two different items at the same price. He made $10 \%$ profit in one item, and $10 \%$ loss in the other item. In selling these two items, the person made a total of $1 \%$ profit $2 \%$ profit $1 \%$ loss $2 \%$ loss
A person sold two different items at the same price. He made $10 \%$ profit in one item, and $10 \%$ loss in the other item. In selling these two items,...
Arjun
2.6k
views
Arjun
asked
Feb 16
Quantitative Aptitude
gatecse2024-set2
quantitative-aptitude
profit-loss
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