Recent questions in Engineering Mathematics / GATE Overflow for GATE CSE

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61

Memory Based GATE DA 2024 | Question: 7
Consider the function $f(x) = \frac{1}{1+e^{-x}}$. Determine the derivative $f^{\prime}(x)$ when $f(x) = 0.4$.

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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GO Classes asked Feb 4

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62

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 $z = \frac{x - \mu}{\sigma}$.

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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GO Classes asked Feb 4

1 votes

2 answers

63

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.

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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GO Classes asked Feb 4

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1 answer

64

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: $\mathrm{P}({\mathrm{T}})=0.4$ ... $\mathrm{P}(\mathrm{T}|\mathrm{S})$.

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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GO Classes asked Feb 4

1 votes

0 answers

65

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 $E(Y | X = 1.5)$.

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}\e...

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GO Classes asked Feb 4

1 votes

0 answers

66

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

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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GO Classes asked Feb 4

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1 answer

67

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 $?

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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GO Classes asked Feb 4

1 votes

1 answer

68

Memory Based GATE DA 2024 | Question: 30
Consider the function $ F(x) $ defined as follows: \[ F(x) = \left\{ \begin{array}{cc} -x & \text{if } x < -2 \\ ax^2 + bx + c & \text{if } x \in [-2, 2] \\ x & \text{if } x > 2 \end{ ... \] \noindent Determine the values of $ a, b, $ and $ c $ such that $ F(x) $ is continuous and differentiable over its entire domain.

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] \\...

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GO Classes asked Feb 4

2 votes

2 answers

69

Memory Based GATE DA 2024 | Question: 33
Which of the following are tautologies? $x \land \neg y \Rightarrow y \rightarrow x$ $\neg x \land y \Rightarrow \neg x \rightarrow y$ $x \land \neg y \Rightarrow \neg x \rightarrow y$ $\neg x \land y \Rightarrow y \rightarrow x$

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 \ne...

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GO Classes asked Feb 4

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70

Memory Based GATE DA 2024 | Question: 35
Conditional probability \[ \begin{aligned} & \mathrm{P}(\mathrm{U}, \mathrm{V}, \mathrm{W}, \mathrm{X}, \mathrm{Y}) & = \mathrm{P}(\mathrm{U}) \cdot \mathrm{P}(\mathrm{V}) \cdot \mathrm{P}(\mathrm{W} / \mathrm{U}, \mathrm{V}) \cdot \mathrm{P}(\mathrm{X} / \mathrm{W}) \cdot \mathrm{P}(\mathrm{Y} / \mathrm{W}) \end{aligned} \]

Conditional probability\[\begin{aligned} & \mathrm{P}(\mathrm{U}, \mathrm{V}, \mathrm{W}, \mathrm{X}, \mathrm{Y}) & = \mathrm{P}(\mathrm{U}) \cdot \mathrm{P...

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GO Classes asked Feb 4

0 votes

1 answer

71

Memory Based GATE DA 2024 | Question: 41
Consider two random variables, $x$ and $y$, defined as follows: \[ x = \begin{cases} 1 & \text{if HH } \\ 0 & \text{otherwise} \end{cases} \] \[ y = \begin{cases} 1 & \text{if at least one head} \\ 0 & \text{otherwise} \end{cases} \] What is the covariance between $x$ and $y?$

Consider two random variables, $x$ and $y$, defined as follows:\[x =\begin{cases}1 & \text{if HH } \\0 & \text{otherwise}\end{cases}\]\[y =\begin{cases}1 & \text{if at le...

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GO Classes asked Feb 4

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1 answer

72

Memory Based GATE DA 2024 | Question: 42
Consider two random variables, (x) and (y), each following a uniform distribution. Specifically, (x) is uniformly distributed over the interval ([1, 3]), and (y) is uniformly distributed over the interval ([2, 4]). What will be $P(x \geq y)$

Consider two random variables, (x) and (y), each following a uniform distribution. Specifically, (x) is uniformly distributed over the interval ([1, 3]), and (y) is uni...

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GO Classes asked Feb 4

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73

Memory Based GATE DA 2024 | Question: 44
Consider the statements below related to probability distributions: \textbf{(S1):} For a Poisson distribution, the mean and variance are equal. \textbf{(S2):} For a standard normal distribution, the mean is 0, and the variance is 1. Which of the following ... true. S1 is true, but S2 is false. S1 is false, but S2 is true. Both S1 and S2 are false.

Consider the statements below related to probability distributions:\textbf{(S1):} For a Poisson distribution, the mean and variance are equal.\textbf{(S2):} For a standar...

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GO Classes asked Feb 4

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0 answers

74

Memory Based GATE DA 2024 | Question: 52
Consider the function $f(x) = \frac{x^4}{4} - \frac{2x^3}{3} - \frac{3x^2}{2}$. Which of the following statements about the critical points of $f(x)$ are correct? Local minima at $x = 0$ Local maxima at $x = 0$ Local minima at $x = 3$ Local minima at $x = -1$

Consider the function $f(x) = \frac{x^4}{4} - \frac{2x^3}{3} - \frac{3x^2}{2}$.Which of the following statements about the critical points of $f(x)$ are correct?Local...

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GO Classes asked Feb 4

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1 answer

75

Memory Based GATE DA 2024 | Question: 53
Consider the following scenarios involving linear algebra: For a $3 \times 3$ matrix, if some vector p has a unique solution, can there exist another vector q with an infinite solution? For a $3 \times 3$ matrix, if some vector p ... 2 \times 3\) matrix, if some vector p has a unique solution, can there exist another vector q with an infinite solution?

Consider the following scenarios involving linear algebra:For a $3 \times 3$ matrix, if some vector p has a unique solution, can there exist another vector q with an in...

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GO Classes asked Feb 4

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76

Memory Based GATE DA 2024 | Question: 57
First-order logic question: All balls are round except rugby balls.

First-order logic question: All balls are round except rugby balls.

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GO Classes asked Feb 4

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77

Memory Based GATE DA 2024 | Question: 60
Linear Algebra Question: Four options were given related to subspace R3. Something like this : A. $ \alpha \cdot x + \beta \cdot y $ B. $ \alpha^2 \cdot x + \beta^2 \cdot y $ C. $f(x) = 4x_1 + 2x_3 + 3x_3 $ D.

Linear Algebra Question: Four options were given related to subspace R3.Something like this :A. $ \alpha \cdot x + \beta \cdot y $B. \( \alpha^2 \cdot x + \beta^2 \cdot...

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GO Classes asked Feb 4

1 votes

0 answers

78

Memory Based GATE DA 2024 | Question: 64
Minimum Number of colors in concentric circles.

Minimum Number of colors in concentric circles.

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GO Classes asked Feb 4

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79

madeeasy
plz explain option c

plz explain option c

nihal_chourasiya

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nihal_chourasiya asked Feb 1

1 votes

1 answer

80

#self doubt
In the above figure, how many topological sorts are possible, I tried the following method, if we include 5 _ _ _ _ _ for 5 space 5c3 for (2,3,1) then 2 position is 4,0 so a total of 10 if we do like 4 5 _ _ _ _ then only ... GFG the total possible sorts are 13 can someone why this difference is coming ? https://www.geeksforgeeks.org/all-topological-sorts-of-a-directed-acyclic-graph/

In the above figure, how many topological sorts are possible,I tried the following method,if we include 5 _ _ _ _ _ for 5 space 5c3 for (2,3,1) then 2 position is 4,0 so ...

Dknights

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Dknights asked Jan 31

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