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Recent questions tagged gate-ds-ai-2024

13 13 votes
6 answers 6 answers
10.5k
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GATE DS&AI 2024 | Question: 20
Consider sorting the following array of integers in ascending order using an inplace Quicksort algorithm that uses the last element as the pivot.\begin{array}{|l|l|l|l|l|...
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9 9 votes
4 4 answers
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GATE DS&AI 2024 | Question: 22
The fundamental operations in a double-ended queue $D$ are: insertFirst (e) - Insert a new element $e$ at the beginning of $D$. insertLast (e) - Insert a new element $e$ ...
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5 5 votes
2 2 answers
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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 $\_\_\_\_\_\_\_$. (roun...
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2 2 votes
3 3 answers
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GATE DS&AI 2024 | Question: 24
The sample average of $50$ data points is $40$. The updated sample average after including a new data point taking the value of $142$ is $\_\_\_\_\_\_\_\_$.
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38 38 votes
11 answers 11 answers
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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}^{...
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28 28 votes
8 answers 8 answers
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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 consecu...
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13 13 votes
2 2 answers
4.4k
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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&lt-2...
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8 8 votes
2 2 answers
5.9k
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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) retur...
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4 4 votes
2 2 answers
3.9k
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GATE DS&AI 2024 | Question: 29
​​​​​Consider the function computes $(X)$ whose pseudocode is given below:computes $(X)$$S \leftarrow 1$for $i \leftarrow 2$ to length $(X)$$S[i] \leftarrow 1$if $X[i-1]...
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23 23 votes
4 4 answers
9.1k
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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 op...
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6 6 votes
4 4 answers
5.8k
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GATE DS&AI 2024 | Question: 31
​​​​​Consider the following Python function:def fun(D, s1, s2): if s1 < s2: D[s1], D[s2] = D[s2], D[s1] fun(D, s1+1, s2-1)What does this Python function fun ( ) do? Selec...
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3 3 votes
3 3 answers
4.6k
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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...
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4 4 votes
2 2 answers
5.5k
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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 connect...
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18 18 votes
8 8 answers
6.8k
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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 tha...
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13 13 votes
4 4 answers
7.3k
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GATE DS&AI 2024 | Question: 35
Consider the following sorting algorithms:Bubble sortInsertion sortSelection sortWhich ONE among the following choices of sorting algorithms sorts the numbers in the arra...
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21 21 votes
3 3 answers
6.0k
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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...
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8 8 votes
5 5 answers
7.1k
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GATE DS&AI 2024 | Question: 37
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_...
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12 12 votes
3 3 answers
4.7k
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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 \ma...
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6 6 votes
2 2 answers
4.4k
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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 proj...
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6 6 votes
3 3 answers
2.6k
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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}...
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11 11 votes
5 5 answers
5.0k
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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{...
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19 19 votes
3 3 answers
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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 ...
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3 3 votes
3 3 answers
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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...
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7 7 votes
3 3 answers
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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 f...
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20 20 votes
5 answers 5 answers
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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, CustomerRati...
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19 19 votes
5 5 answers
8.9k
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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...
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12 12 votes
3 answers 3 answers
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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}...
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7 7 votes
6 answers 6 answers
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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})=...
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8 8 votes
2 2 answers
6.3k
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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 { otherwi...
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7 7 votes
2 2 answers
5.0k
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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 dista...
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