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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 following 1) It's about alpha beta pruning (Q25 in master question paper, 1 mark). The answer should be (m) = lowest, (n) = ... other people think ? I am planning to challenge these two questions but I feel that 2nd one will not be accepted by GATE.

redshellspy asked in Unknown Category Feb 24

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2 votes

1 answer

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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 \(5E(x) = V(x)\).

GO Classes asked in Probability Feb 4

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1 vote

1 answer

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Memory Based GATE DA 2024 | Question: 2
How many unique four-digit numbers can be created using the digits 1, 3, 4, and 6, with each digit appearing only once, such that the resulting number is divisible by 3?

GO Classes asked in Quantitative Aptitude Feb 4

297 views

1 vote

2 answers

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Memory Based GATE DA 2024 | Question: 3
Evaluate the limit: \[ \lim_{{x \to 0}} \frac{\ln \left(\left(x^2+1\right) \cos x\right)}{x^2} \]

GO Classes asked in Calculus Feb 4

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2 votes

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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 \(|\mathrm{M}^2 + 12M|\).

GO Classes asked in Linear Algebra Feb 4

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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 statements are true? \(M^3 = M\) \(M^2 = M\) The nullspace of \(M\) is 1-dimensional. The nullspace of \(M\) is 2-dimensional.

GO Classes asked in Linear Algebra Feb 4

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2 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 is negative. Eigenvalues are complex conjugate pairs. None of the above.

GO Classes asked in Linear Algebra Feb 4

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1 answer

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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 \(f(x) = 0.4\).

GO Classes asked in Calculus Feb 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.

GO Classes asked in Quantitative Aptitude Feb 4

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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 $\mathrm{P}(\mathrm{T} \cap \mathrm{S})$.

GO Classes asked in Quantitative Aptitude Feb 4

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1 answer

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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 of votes combined for options B and C?

GO Classes asked in Quantitative Aptitude Feb 4

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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 \(z = \frac{x - \mu}{\sigma}\).

GO Classes asked in Probability Feb 4

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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{array} $ After a year, if Person 1's mutual fund value is 500 more than Person 2's, determine the value of \(x\).

GO Classes asked in Quantitative Aptitude Feb 4

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2 answers

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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.

GO Classes asked in Probability Feb 4

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1 answer

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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 events are given as follows: $\mathrm{P}({\mathrm{T}})=0.4$ ... $\mathrm{P}(\mathrm{T}|\mathrm{S})$.

GO Classes asked in Probability Feb 4

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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} $ \noindent Determine the conditional expectation $E(Y | X = 1.5)$.

GO Classes asked in Probability Feb 4

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1 answer

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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 \rightarrow Z \\ V \rightarrow X \end ... be deduced. Which of the following options is correct? $VW \rightarrow U$ $VW \rightarrow Y$ $VW \rightarrow YZ$ $WX \rightarrow YZ$

GO Classes asked in Databases Feb 4

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Memory Based GATE DA 2024 | Question: 17
Consider the following SQL query: \[ \begin{aligned} &\text{SELECT * FROM Raider, Team} \\ &\text{WHERE Raider.id = Team.id} \\ &\text{AND City = 'Jaipur'} \\ &\text{AND Raid_points \textgreater 200; ... {aligned} \] Determine the number of rows returned by the SQL query, given the conditions specified for the City and Raid points.

GO Classes asked in Databases Feb 4

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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 graph? PRQVSUT PQRSVUT PQRSTUV PRQSVUT

GO Classes asked in Algorithms Feb 4

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1 vote

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Memory Based GATE DA 2024 | Question: 19
Consider the function \(f(n)\), which represents the maximum number of comparisons in binary search on a sorted array of size \(n\). Which of the following recursive relationships correctly defines \(f(n)\)? \(f(n) = f\left(\lfloor \frac{n}{2} \rfloor\right) ... \rfloor\right)\) \(f(n) = f\left(\lfloor \frac{n}{2} \rfloor\right) + 1\) None of the above

GO Classes asked in Algorithms Feb 4

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Memory Based GATE DA 2024 | Question: 20
Consider the following Python code: S[1] = [1] x = [6, 3, 5, 4, 10] for i in range(2, len(x)): S[i] = [1] if x[i - 1]

GO Classes asked in Programming Feb 4

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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{verbatim}

GO Classes asked in Programming Feb 4

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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 Sort Insertion Sort Selection Sort Merge Sort

GO Classes asked in Algorithms Feb 4

146 views

2 votes

2 answers

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Memory Based GATE DA 2024 | Question: 23
Consider a binary tree. Among the following traversal combinations, which of them can uniquely construct the tree? Inorder + Preorder Preorder + Postorder Only Inorder Inorder + Postorder

GO Classes asked in DS Feb 4

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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{RemoveFirst}) \\ - Remove Last (\texttt{RemoveLast}) The following operations are ... \ & a = \text{RemoveLast} \end{aligned} \] What is the value of \(a\) after these operations?

GO Classes asked in DS Feb 4

166 views

1 vote

1 answer

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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, how many swaps will occur during the execution of the algorithm?

GO Classes asked in Algorithms Feb 4

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1 answer

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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?

GO Classes asked in Quantitative Aptitude Feb 4

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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 of the shortest path from $S$ to $u$, let $(u \geqslant v)$ be an edge in ... $v$, then in the above DFS, the edge $(u, v)$ becomes: A forward edge A back edge A cross edge A tree edge

GO Classes asked in Algorithms Feb 4

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1 vote

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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 \(f(X)\). \(X^*\) is a local maximum \(X^*\) is a local minimum \(X^*\) is a global maximum \(X^*\) is a global minimum

GO Classes asked in Calculus Feb 4

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1 answer

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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 \( \sigma_1, \sigma_2, \sigma_3, \ldots, \sigma_5 \) are the singular values of \( M \), what is the value of \( \sum_{i=1}^5 \sigma_i \)?

GO Classes asked in Linear Algebra Feb 4

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