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Recent questions tagged gate2024-da-memory-based

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GATE DA 2024 ANSWER KEY CHALLENGE
Hello,I wanted to discuss the answer key given for some of the questions in official website. The doubts are following1) It's about alpha beta pruning (Q25 in master ques...
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Memory Based GATE DA 2024 | Question: 1
Consider the probability density function \(f(x) = \lambda e^{-\lambda x}\) for \(x \geq 0\) and \(\lambda 0\). Determine the value of \(\lambda\) such that \(5E(x) = V(...
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Memory Based GATE DA 2024 | Question: 3
Evaluate the limit:\[\lim_{{x \to 0}} \frac{\ln \left(\left(x^2+1\right) \cos x\right)}{x^2}\]
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Memory Based GATE DA 2024 | Question: 4
Consider the matrix\[\mathrm{M} = \begin{bmatrix}1 & 2 & 3 \\3 & 1 & 3 \\4 & 3 & 6\end{bmatrix}\]Find the value of \(|\mathrm{M}^2 + 12M|\).
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Memory Based GATE DA 2024 | Question: 5
Consider a matrix \(M \in \mathbb{R}^{3 \times 3}\) and let \(U\) be a 2-dimensional subspace such that \(M\) is a projection onto \(U\). Which of the following statement...
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3 3 answers
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Memory Based GATE DA 2024 | Question: 6
 Consider the matrix\[\begin{bmatrix}2 & -1 \\3 & 1\end{bmatrix}\]What is the nature of the eigenvalues of the given matrix?Both eigenvalues are positive.One eigenvalue i...
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Memory Based GATE DA 2024 | Question: 7
Consider the function \(f(x) = \frac{1}{1+e^{-x}}\). Determine the derivative \(f^{\prime}(x)\) when \(f(x) = 0.4\).
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Memory Based GATE DA 2024 | Question: 8
In a family with three children, determine the probability of having two boys and one girl.
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2 2 answers
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Memory Based GATE DA 2024 | Question: 9
Three coins are tossed. Let $T$ be the event of getting at least two heads, and $S$ be the event of getting at least two tails. Determine the value of $\mathrm{P}(\mathrm...
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1 1 vote
2 2 answers
637
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Memory Based GATE DA 2024 | Question: 10
In a voting process with a total of 115,000 votes, 5,000 votes are deemed invalid. If 25\% of the valid votes are in favor of B and 10\% for C, what is the total number o...
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Memory Based GATE DA 2024 | Question: 11
Consider a dataset with a raw score \(x = 75\), a mean \(\mu = 70\), and a standard deviation \(\sigma = 5\). Calculate the Z-score using the formula \(z = \frac{x - \mu}...
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Memory Based GATE DA 2024 | Question: 12
Consider the following table:$$\begin{array}{cccc}& A & B & C \\Person 1 & 10,000 & 20,000 & 20,000 \\Person 2 & 20,000 & 15,000 & 15,000 \\& x \% & 15 \% & 15 \%\end{arr...
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Memory Based GATE DA 2024 | Question: 13
A fair six-sided die is thrown repeatedly. Find the expected number of throws until two consecutive throws show even numbers.
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Memory Based GATE DA 2024 | Question: 14
Consider two events $\mathrm{T}$ and $\mathrm{S}$. Let $\overline{\mathrm{T}}$ denote the complement of event $\mathrm{T}$. The probabilities associated with different ev...
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Memory Based GATE DA 2024 | Question: 15
Consider the joint probability density function given by:$$f(x, y)=\begin{cases}    2xy & \text{if } 0 < x < 2 \text{ and } 0 < y < x \\    0 & \text{otherwise}\end{cases...
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1 1 vote
2 2 answers
854
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Memory Based GATE DA 2024 | Question: 16
Consider a relation R:\[\begin{aligned}& R(U, V, W, X, Y, Z) \\& F=\left\{\begin{array}{l}    U \rightarrow V \\    U \rightarrow W \\    WX \rightarrow Y \\    WX \right...
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Memory Based GATE DA 2024 | Question: 18
Consider a directed acyclic graph (DAG) with vertices labeled as P, Q, R, S, T, U, and V. Which of the following sequences represents a possible topological sort of the g...
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Memory Based GATE DA 2024 | Question: 20
Consider the following Python code:S = x = [6, 3, 5, 4, 10]for i in range(2, len(x)):    S[i] =     if x[i - 1]
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Memory Based GATE DA 2024 | Question: 21
What does the following Python code do?\begin{verbatim}def fun(D, S_1, S_2):    if S_1 < S_2:        D[S_1], D[S_2] = D[S_2], D[S_1]        fun(D, S_1 + 1, S_2 - 1)\end{v...
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0 0 votes
1 1 answer
549
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Memory Based GATE DA 2024 | Question: 22
Given the array \( [4, 3, 2, 1, 5] \), which of the following sorting algorithms can successfully sort the array in exactly two passes?Bubble SortInsertion Sort Selection...
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1 1 vote
1 1 answer
738
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Memory Based GATE DA 2024 | Question: 24
Consider a doubly linked list with the following operations:- Insert First (\texttt{InsertFirst})\\- Insert Last (\texttt{InsertLast})\\- Remove First (\texttt{RemoveFirs...
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2 2 votes
1 1 answer
860
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Memory Based GATE DA 2024 | Question: 25
Consider the QuickSort algorithm with the last element chosen as the pivot. If the goal is to sort the given array \(a = [30, 40, 50, 60, 70, 80]\) in ascending order, ho...
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2 2 answers
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Memory Based GATE DA 2024 | Question: 26
Consider a set of 50 samples with an average of 40:\[\text{Samples average} = 40\]If a new value of 142 is added, what is the new average?
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Memory Based GATE DA 2024 | Question: 27
Consider performing Depth-First Search (DFS) on an undirected and unweighted graph $\bar{G}$ starting at vertex $S$. For any vertex $u$ in $G$, where $d[u]$ is the length...
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Memory Based GATE DA 2024 | Question: 28
Consider a function \(f\) with \(f^1(X^*) = 0\) and \(f^{1l}(X^*) 0\). Based on these conditions, determine the nature of the critical point \(X^*\) for the function \(f...
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1 1 vote
1 1 answer
625
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Memory Based GATE DA 2024 | Question: 29
Consider the vector \( u = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \end{bmatrix} \), and let \( M = uu^{\top} \). If \( \sigma_1, \sigma_2, \sigma_3, \ldots, \sigma_5 \) ar...
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2 2 votes
1 1 answer
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Memory Based GATE DA 2024 | Question: 30
Consider the function \( F(x) \) defined as follows:\[ F(x) = \left\{\begin{array}{cc}    -x & \text{if } x < -2 \\    ax^2 + bx + c & \text{if } x \in [-2, 2] \\    x & ...
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2 2 votes
2 2 answers
616
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Memory Based GATE DA 2024 | Question: 31
Consider the scenario where there was growth in dairy farms in a city, and coincidentally, there was a mutation in the gene of people in that locality, enabling them to d...
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1 1 vote
1 1 answer
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Memory Based GATE DA 2024 | Question: 32
Consider two admissible heuristic functions, \(h_1\) and \(h_2\). Determine which of the following combinations are admissible:\(\frac{h_1}{h_2}\) \(\left(h_2 0\right)\)...
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Memory Based GATE DA 2024 | Question: 33
Which of the following are tautologies? \(x \land \neg y \Rightarrow y \rightarrow x\)\(\neg x \land y \Rightarrow \neg x \rightarrow y\)\(x \land \neg y \Rightarrow \neg...
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