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Recent questions in Engineering Mathematics
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61
Memory Based GATE DA 2024 | Question: 33
Which of the following are tautologies? \(x \land \neg y \Rightarrow y \rightarrow x\) \(\neg x \land y \Rightarrow \neg x \rightarrow y\) \(x \land \neg y \Rightarrow \neg x \rightarrow y\) \(\neg x \land y \Rightarrow y \rightarrow x\)
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gate2024-da-memory-based
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0
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62
Memory Based GATE DA 2024 | Question: 35
Conditional probability \[ \begin{aligned} & \mathrm{P}(\mathrm{U}, \mathrm{V}, \mathrm{W}, \mathrm{X}, \mathrm{Y}) & = \mathrm{P}(\mathrm{U}) \cdot \mathrm{P}(\mathrm{V}) \cdot \mathrm{P}(\mathrm{W} / \mathrm{U}, \mathrm{V}) \cdot \mathrm{P}(\mathrm{X} / \mathrm{W}) \cdot \mathrm{P}(\mathrm{Y} / \mathrm{W}) \end{aligned} \]
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0
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0
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63
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 $y?$
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probability
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0
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1
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64
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 $P(x \geq y)$
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224
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gate2024-da-memory-based
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probability
random-variable
uniform-distribution
numerical-answers
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0
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65
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.
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probability
poisson-distribution
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0
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0
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66
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 \(x = -1\)
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calculus
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0
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1
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67
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?
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68
Memory Based GATE DA 2024 | Question: 57
First-order logic question: All balls are round except rugby balls.
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69
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.
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70
Memory Based GATE DA 2024 | Question: 64
Minimum Number of colors in concentric circles.
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71
madeeasy
plz explain option c
nihal_chourasiya
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Feb 1
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nihal_chourasiya
92
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engineering-mathematics
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1
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72
#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/
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Jan 31
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discrete-mathematics
0
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73
#self doubt
Can someone please explain the following case of combination I means identical D means different DOIB with boxes being empty and non empty As in this question the given value in question itself i am not able to interpret. https://gateoverflow.in/420251/go-classes-test-series-2024-mock-gate-test-12-question-17
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Jan 28
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7
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2
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74
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 11
Let $f(x)$ be a real-valued function all of whose derivatives exist. Recall that a point $x_0$ in the domain is called an inflection point of $f(x)$ if the second derivative $f^{\prime \prime}(x)$ changes sign at ... only inflection point. $x_0=0$ and $x_0=6$, both are inflection points. The function does not have an inflection point.
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6
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75
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 12
Let $x$ be a random variable possessing the probability density function $ f(x)= \begin{cases}c x & , x \in[0,10] \\ 0 & , \text { otherwise }\end{cases} $ where $c \in \mathbb{R}$. The probability that $x \in[1,2]$ is ______. $\dfrac{1}{100}$ $\dfrac{3}{100}$ $\dfrac{5}{100}$ $\dfrac{7}{100}$
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7
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76
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 13
If $A$ is a $3 \times 3$ matrix such that $A\left(\begin{array}{l}0 \\ 1 \\ 2\end{array}\right)=\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)$ ... $\left(\begin{array}{r}1 \\ -1 \\ 0\end{array}\right)$ $\left(\begin{array}{r}9 \\ 10 \\ 11\end{array}\right)$
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3
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77
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 28
A group $G$ in which $(a b)^2=a^2 b^2$ for all $a, b$ in $G$ is necessarily finite cyclic abelian none of the above
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4
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78
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 30
A university's mathematics department has $10$ professors and will offer $20$ different courses next semester. Each professor will be assigned to teach exactly $2$ of the courses, and each course will have exactly one professor assigned to teach it. If any ... $10^{20}-2^{10}$ $\dfrac{20 ! 10 !}{2^{10}}$
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9
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2
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79
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 43
Let $A$ be a $2 \times 2$ matrix for which there is a constant $k$ such that the sum of the entries in each row and each column is $k$. Which of the following must be an eigenvector of $A?$ ... $\left[\begin{array}{l}1 \\ 1\end{array}\right]$. I only II only III only I and II only
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4
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80
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 44
Football teams $T_1$ and $T_2$ play two games against each other in the Premier League. It is assumed that the outcomes of the two games are independent of each other. The probabilities of $T_1$ winning, drawing and losing against $T_2$ ... What will be the value of $P(X=Y)?$ $1 / 3$ $13 / 36$ $1 / 36$ $1 / 18$
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