Questions by Arjun / GATE Overflow for GATE CSE

1 votes

1 answer

21

GATE DS&AI 2024 | Question: 11
Consider performing uniform hashing on an open address hash table with load factor $\alpha=\frac{n}{m}<1$, where $n$ elements are stored in the table with $m$ slots. The expected number of probes in an unsuccessful search is at most $\frac{1}{1-\alpha}$. Inserting ... $\frac{1}{1-\alpha}$ $1+\frac{\alpha}{2}$ $\frac{1}{1+\alpha}$

Consider performing uniform hashing on an open address hash table with load factor $\alpha=\frac{n}{m}<1$, where $n$ elements are stored in the table wi...

787 views

asked Feb 16

0 votes

1 answer

22

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 $u^{*} \in \mathbb{R}^{d}$, ... $S_{B} S_{W} u^{*}=\lambda u^{*}$ $u^{* T} u^{*}=\lambda^{2}$

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-c...

496 views

asked Feb 16

0 votes

1 answer

23

GATE DS&AI 2024 | Question: 13
Let $h_{1}$ and $h_{2}$ be two admissible heuristics used in $A^{*}$ search. Which ONE of the following expressions is always an admissible heuristic? $h_{1}+h_{2}$ $h_{1} \times h_{2}$ $h_{1} / h_{2},\left(h_{2} \neq 0\right)$ $\left|h_{1}-h_{2}\right|$

Let $h_{1}$ and $h_{2}$ be two admissible heuristics used in $A^{*}$ search.Which ONE of the following expressions is always an admissible heuristic?$h_...

893 views

asked Feb 16

0 votes

2 answers

24

GATE DS&AI 2024 | Question: 14
Consider five random variables $U, V, W, X$, and $Y$ whose joint distribution satisfies: \[ P(U, V, W, X, Y)=P(U) P(V) P(W \mid U, V) P(X \mid W) P(Y \mid W) \] Which ONE of the following statements is FALSE? ... $U$ given $W$ $U$ and $V$ are conditionally independent given $W$ $Y$ and $X$ are conditionally independent given $W$

Consider five random variables $U, V, W, X$, and $Y$ whose joint distribution satisfies:\[P(U, V, W, X, Y)=P(U) P(V) P(W \mid U, V) P(X \mid W) P(Y \mid...

886 views

asked Feb 16

0 votes

1 answer

25

GATE DS&AI 2024 | Question: 15
Consider the following statement: In adversarial search, $\alpha-\beta$ pruning can be applied to game trees of any depth where $\alpha$ is the (m) value choice we have formed so far at any choice point along the path for the MAX player and $\beta$ is the (n ... $(\mathbf{m})=$ highest,$(\mathbf{n})=$ lowest $(\mathbf{m})=$ lowest, $(\mathbf{n})=$ lowest

Consider the following statement:In adversarial search, $\alpha-\beta$ pruning can be applied to game trees of any depth where $\alpha$ is the (m) value choic...

694 views

asked Feb 16

0 votes

1 answer

26

GATE DS&AI 2024 | Question: 16
Consider a database that includes the following relations: Defender(name, rating, side, goals) Forward(name, rating, assists, goals) Team(name, club, price) Which ONE of the following relational algebra expressions checks that every name occurring in Team appears in ... $\left.)\right) \backslash \Pi_{\text {name }}($ Team $)=\phi$

Consider a database that includes the following relations:Defender(name, rating, side, goals)Forward(name, rating, assists, goals)Team(name, club, price)Wh...

910 views

asked Feb 16

0 votes

1 answer

27

GATE DS&AI 2024 | Question: 17
Let the minimum, maximum, mean and standard deviation values for the attribute income of data scientists be ₹$46000$, ₹ $170000$, ₹ $96000$, and ₹ $21000$, respectively. The $z$-score normalized income value of ₹ $106000$ is closest to which ONE of the following options? $0.217$ $0.476$ $0.623$ $2.304$

Let the minimum, maximum, mean and standard deviation values for the attribute income of data scientists be ₹$46000$, ₹ $170000$, ₹ $96000$, and ₹ ...

725 views

asked Feb 16

0 votes

1 answer

28

GATE DS&AI 2024 | Question: 18
Consider the following tree traversals on a full binary tree: Preorder Inorder Postorder Which of the following traversal options is/are sufficient to uniquely reconstruct the full binary tree? $\text{(i) and (ii)}$ $\text{(ii) and (iii)}$ $\text{(i) and (iii)}$ $\text{(ii) only}$

Consider the following tree traversals on a full binary tree:PreorderInorderPostorderWhich of the following traversal options is/are sufficient to uniqu...

1.1k views

asked Feb 16

0 votes

1 answer

29

GATE DS&AI 2024 | Question: 19
Let $x$ and $y$ be two propositions. Which of the following statements is a tautology /are tautologies? $(\neg x \wedge y) \Rightarrow(y \Rightarrow x)$ $(x \wedge \neg y) \Rightarrow(\neg x \Rightarrow y)$ $(\neg x \wedge y) \Rightarrow(\neg x \Rightarrow y)$ $(x \wedge \neg y) \Rightarrow(y \Rightarrow x)$

Let $x$ and $y$ be two propositions. Which of the following statements is a tautology /are tautologies?$(\neg x \wedge y) \Rightarrow(y \Rightarrow x)$$...

800 views

asked Feb 16

0 votes

3 answers

30

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|} \hline 60 & 70 & 80 & 90 & 100 \\ \hline \end{array} The minimum number of swaps performed during this Quicksort is $\_\_\_\_\_\_\_\_$.

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|...

1.2k views

asked Feb 16

0 votes

2 answers

31

GATE DS&AI 2024 | Question: 21
Consider the following two tables named Raider and Team in a relational database maintained by a Kabaddi league. The attribute ID in table Team references the primary key of the Raider table, ID. Raider ID Name Raids RaidPoints $1$ Arjun $200$ $250$ $2$ ... Jaipur" AND RaidPoints > 200; The number of rows returned by this query is $\_\_\_\_\_\_\_\_$.

Consider the following two tables named Raider and Team in a relational database maintained by a Kabaddi league. The attribute ID in table Team references the primary key...

881 views

asked Feb 16

0 votes

1 answer

32

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 $e$ at the end of D. removeFirst () - Remove and return the first element of $D$. removeLast () ... $\mathbf{a} \leftarrow$ removeLast () The value of $\mathbf{a}$ is $\_\_\_\_\_\_\_\_$.

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 $e$ ...

717 views

asked Feb 16

0 votes

1 answer

33

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.

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...

713 views

asked Feb 16

0 votes

2 answers

34

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 $\_\_\_\_\_\_\_\_$.

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 $\_\_\_\_\_\_\_\_$.

777 views

asked Feb 16

0 votes

1 answer

35

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 $\_\_\_\_\_\_\_\_\_$.

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}^{...

644 views

asked Feb 16

1 votes

1 answer

36

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? $2$ $4$ $6$ $8$

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 t...

1.1k views

asked Feb 16

0 votes

1 answer

37

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? $a=\frac{1}{4}, b=0, c=1$ $a=\frac{1}{2}, b=0, c=0$ $a=0, b=0, c=0$ $a=1, b=1, c=-4$

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 { i...

790 views

asked Feb 16

0 votes

1 answer

38

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? $6$ $1$ $8$ $9$

Consider the following Python code:def count(child_dict, i):if i not in child_dict.keys():return 1ans $=1$for $j$ in child_dict[i]:ans $+=$ count (child_dict,...

832 views

asked Feb 16

0 votes

2 answers

39

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 $X=[6,3,5,4,10]$ ? $[1,1,2,3,4]$ $[1,1,2,3,3]$ $[1,1,2,1,2]$ $[1,1,2,1,5]$

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$...

650 views

asked Feb 16

0 votes

1 answer

40

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? $F(n)=F(\lfloor n / 2\rfloor)+1$ $F(n)=F(\lfloor n / 2\rfloor)+F(\lceil n / 2\rceil)$ $F(n)=F(\lfloor n / 2\rfloor)$ $F(n)=F(n-1)+1$

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 fo...

873 views

asked Feb 16

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author	user:martin
title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true