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241
GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 21
The worst-case running times of Insertion sort, Merge sort and Quick sort respectively are $\Theta(n\operatorname{logn}), \Theta\left(n^{\wedge} 2\right), \Theta\left(n^{\wedge} 2\right)$ ... $\Theta\left(n^{\wedge} 2\right), \Theta\left(n^{\wedge} 2\right), \Theta(n\operatorname{logn})$
The worst-case running times of Insertion sort, Merge sort and Quick sort respectively are$\Theta(n\operatorname{logn}), \Theta\left(n^{\wedge} 2\right), \Theta\left(n^{\...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 22
Consider the following program. int func(int n ) { if (n<=1) return n; else return 3 * func(n-3) - 3 * func(n-2); end } The running time of the above function is $\Theta(\mathrm{n})$ $\Theta\left(n^{\wedge} 2\right)$ $\Theta\left(3^{\wedge} n\right)$ $\Theta\left(2^{\wedge} n\right)$
Consider the following program.int func(int n ) { if (n<=1) return n; else return 3 * func(n-3) - 3 * func(n-2); end }The running time of the above function is$\Theta(\ma...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 23
Which of the following correctly describes the recurrence relation for the standard binary search algorithm on a sorted array of $\mathrm{n}$ numbers where $\mathrm{c}$ ... $\mathrm{T}(\mathrm{n})=\mathrm{T}(\mathrm{n} / 2)+\mathrm{c}$
Which of the following correctly describes the recurrence relation for the standard binary search algorithm on a sorted array of $\mathrm{n}$ numbers where $\mathrm{c}$ i...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 24
Consider the following $\mathrm{C}$ program int func(int A[], int n, int m ) { int s= A[0]; for(int i = 1 ; i<= n - 1 ; i ++) total = m * s+ A[i]; return m; } Let $\text{Z}$ be an array of $10$ ... $\text{i}$ such that $0<=i<=9$; The value returned by func $(\text{Z}, 10,2)$ is __________.
Consider the following $\mathrm{C}$ programint func(int A[], int n, int m ) { int s= A[0]; for(int i = 1 ; i<= n – 1 ; i ++) total = m * s+ A[i]; return m; }Let $\text{...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 25
Two eigenvalues of $3 \times 3$ matrix $\mathbf{X}$ are $(1+i)$ and $2$. The determinant of the text matrix $\mathrm{X}$ is __________.
Two eigenvalues of $3 \times 3$ matrix $\mathbf{X}$ are $(1+i)$ and $2$. The determinant of the text matrix $\mathrm{X}$ is __________.
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 26
Given the following relation instances $\text{X}$ $\text{Y}$ $\text{Z}$ $1$ $4$ $2$ $1$ $5$ $3$ $1$ $4$ $3$ $1$ $5$ $2$ $3$ $2$ $1$ ... $\mathrm{Y} ->>\mathrm{X}$ $\mathrm{XZ}->\mathrm{Y}$ and $\mathrm{Y}->\mathrm{X}$
Given the following relation instances$\text{X}$$\text{Y}$$\text{Z}$$1$$4$$2$$1$$5$$3$$1$$4$$3$$1$$5$$2$$3$$2$$1$Which of the following conditions is/are TRUE?$\mathrm{XY...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 27
Consider the search space depicted in the Figure below. $\text{S}$ is the initial state. $\text{G1}$ and $\text{G2}$ are two states that satisfy the goal test. The cost of traversing from one state to another is depicted by the numerical ... $16$ $\text{G1}$ and $15$ $\text{G2}$ and $16$ $\mathrm{G}2$ and $15$
Consider the search space depicted in the Figure below. $\text{S}$ is the initial state. $\text{G1}$ and $\text{G2}$ are two states that satisfy the goal test. The cost o...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 28
Given a discrete $\text{K}$-class dataset containing $\text{N}$ points, where sample points are described using $\text{D}$ features with each feature capable of taking $\text{V}$ values, how many parameters need to be estimated for Naïve Bayes Classifier? $V^{D} K$ $K^{V^{D}}$ $\text{VDK}$ $\text{K(V + D)}$
Given a discrete $\text{K}$-class dataset containing $\text{N}$ points, where sample points are described using $\text{D}$ features with each feature capable of taking $\...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 29
$K\left(x, x^{\prime}\right)=f(x) g\left(x^{\prime}\right)+f\left(x^{\prime}\right) g(x)$, where $f$ and $g$ are real-valued functions $\left(\mathcal{R}^{D} \rightarrow \mathcal{R}\right)$ is not a valid kernel ... $f\left(x^{\prime}\right)+g\left(x^{\prime}\right)$
$K\left(x, x^{\prime}\right)=f(x) g\left(x^{\prime}\right)+f\left(x^{\prime}\right) g(x)$, where $f$ and $g$ are real-valued functions $\left(\mathcal{R}^{D} \rightarrow ...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 30
For perfectly spherical $2\text{D}$ data centered at the origin, which of the following the pairs of vectors are possible pairs of principal components? $(1,0)$ and $(0,1)$ $(0,-1)$ and $(-1,0)$ $(1,1)$ and $(1,-1)$ $(-1,1)$ and $(-1,-1)$ $\text{i}$ $\text{i and iii}$ $\text{i, ii, and iii}$ $\text{i, ii, iii and iv}$
For perfectly spherical $2\text{D}$ data centered at the origin, which of the following the pairs of vectors are possible pairs of principal components?$(1,0)$ and $(0,1)...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 31
Consider the game tree shown below. The value below each node is the output of the utility function. The subtrees rooted at which of these nodes will be pruned because of alpha-beta pruning? $\text{m and j}$ $\text{r and j}$ $\text{h and p}$ no nodes are pruned
Consider the game tree shown below. The value below each node is the output of the utility function. The subtrees rooted at which of these nodes will be pruned because of...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 32
Consider the Bayes Net containing four Boolean random variables $\text{(A, B, C, D)}$, with the following convention: $A=$ True $\Rightarrow A=a$, and $A=$ False $\Rightarrow A=$ $\neg a$; and similarly for the other variables. The conditional ...
Consider the Bayes Net containing four Boolean random variables $\text{(A, B, C, D)}$, with the following convention: $A=$ True $\Rightarrow A=a$, and $A=$ False $\Righta...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 33
$\mathrm{X}$ is a uniformly distributed random variable from $0$ to $1$ $ f(x)= \begin{cases}1, & 0 \leq x \leq 1 \\ 0, & \text { otherwise }\end{cases} $ The variance of $\mathrm{X}$ is $\frac{1}{2}$ $\frac{1}{3}$ $\frac{1}{4}$ $\frac{1}{12}$
$\mathrm{X}$ is a uniformly distributed random variable from $0$ to $1$$$f(x)= \begin{cases}1, & 0 \leq x \leq 1 \\ 0, & \text { otherwise }\end{cases}$$The variance of $...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 34
The function $f(x)=1+2 x+3 x^{2}+\cdots+2026 x^{2025}$. Which of the following statement is true? $f(x)$ has global minimum $f(x)$ has global maximum $f(x)$ does not have global minimum None of the above
The function $f(x)=1+2 x+3 x^{2}+\cdots+2026 x^{2025}$. Which of the following statement is true?$f(x)$ has global minimum$f(x)$ has global maximum$f(x)$ does not have gl...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 35
Given a smooth sufficiently differentiable function, the following statements are given (P) A concave function can have a global minimum (Q) All convex functions have a global minimum $\text{P}$ and $\text{Q}$ are true $\text{P}$ is ... $\text{P}$ is false and $\text{Q}$ is true $\text{P}$ and $\text{Q}$ are false
Given a smooth sufficiently differentiable function, the following statements are given(P) A concave function can have a global minimum(Q) All convex functions have a glo...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 36
Consider the following joint distribution of random variables $\mathrm{X}$ and $\mathrm{Y}$ ... $\mathrm{X}$ is $1$. The mean of $\mathrm{Y}$ is $0.5$.
Consider the following joint distribution of random variables $\mathrm{X}$ and $\mathrm{Y}$: $f(x, y)=\left\{\begin{array}{cl}\frac{x\left(1+3 y^2\right)}{4}, & 0 \leq x ...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 37
For matrix $H=\left[\begin{array}{cc}3 & -1 \\ -1 & 3\end{array}\right]$, one of the eigenvectors is $\left[\begin{array}{l}-1 \\ -1\end{array}\right]$ ... $\left[\begin{array}{l}0 \\ 1\end{array}\right]$.
For matrix $H=\left[\begin{array}{cc}3 & -1 \\ -1 & 3\end{array}\right]$, one of the eigenvectors is $\left[\begin{array}{l}-1 \\ -1\end{array}\right]$. Then, the other e...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 38
Given a matrix $\mathbf{A}_{\mathrm{mxn}}$. The following statements are made regarding the matrix $\text{A}$. $\mathrm{P}$. The column space is orthogonal to the row space $\mathrm{Q}$. The column space is orthogonal to the left null ... $\text{R}$ $\text{Q}$ and $\text{R}$ $\text{P}$ and $\text{T}$
Given a matrix $\mathbf{A}_{\mathrm{mxn}}$. The following statements are made regarding the matrix $\text{A}$.$\mathrm{P}$. The column space is orthogonal to the row spac...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 39
Consider a matrix $\left[\begin{array}{lll}0 & 1 & 0 \\ a & 2 & d \\ b & 3 & c\end{array}\right]$. The matrix cannot have rank. $0$ $1$ $2$ $3$
Consider a matrix $\left[\begin{array}{lll}0 & 1 & 0 \\ a & 2 & d \\ b & 3 & c\end{array}\right]$. The matrix cannot have rank.$0$$1$$2$$3$
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 40
A file with $100,000$ records is indexed with $\mathrm{B}+$ tree. If the size of a memory block is $2 \mathrm{~K}$ bytes, the size of a key is $4$ bytes, the size of a pointer is $4$ bytes, what ... the nodes, only keys are stored. The sizes of the pointers are same, irrespective of they point to a node of a record.
A file with $100,000$ records is indexed with $\mathrm{B}+$ tree. If the size of a memory block is $2 \mathrm{~K}$ bytes, the size of a key is $4$ bytes, the size of a po...
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