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151
GATE DS&AI 2024 | Question: 46
Let $X$ be a random variable uniformly distributed in the interval $[1,3]$ and $Y$ be a random variable uniformly distributed in the interval $[2, 4]$. If $X$ and $Y$ are independent of each other, the probability $P(X \geq Y)$ is $\_\_\_\_\_\_\_\_$ (rounded off to three decimal places).
Arjun
asked
in
Others
Feb 16
by
Arjun
792
views
gate-ds-ai-2024
numerical-answers
0
votes
1
answer
152
GATE DS&AI 2024 | Question: 47
Let $X$ be a random variable exponentially distributed with parameter $\lambda>0$. The probability density function of $X$ is given by: \[ f_{X}(x)=\left\{\begin{array}{ll} \lambda e^{-\lambda x}, \quad x \geq 0 \\ 0, & \text { otherwise } \end ... variance of $X$, respectively, the value of $\lambda$ is $\_\_\_\_\_\_\_\_$ (rounded off to one decimal place).
Arjun
asked
in
Probability
Feb 16
by
Arjun
595
views
gate-ds-ai-2024
numerical-answers
probability
random-variable
0
votes
1
answer
153
GATE DS&AI 2024 | Question: 48
Consider two events $T$ and $S$. Let $\bar{T}$ denote the complement of the event $T$. The probability associated with different events are given as follows: \[ P(\bar{T})=0.6, \quad P(S \mid T)=0.3, \quad P(S \mid \bar{T})=0.6 \] Then, $P(T \mid S)$ is $\_\_\_\_\_\_\_\_$ (rounded off to two decimal places).
Arjun
asked
in
Probability
Feb 16
by
Arjun
634
views
gate-ds-ai-2024
numerical-answers
probability
0
votes
1
answer
154
GATE DS&AI 2024 | Question: 49
Consider a joint probability density function of two random variables $X$ and $Y$ \[ f_{X, Y}(x, y)=\left\{\begin{array}{rll}2 x y, & 0<x<2, & 0<y<x \\ 0, & \text { otherwise } & \end{array}\right. \] Then, $E[Y \mid X=1.5]$ is $\_\_\_\_\_\_\_\_\_$
Arjun
asked
in
Others
Feb 16
by
Arjun
935
views
gate-ds-ai-2024
numerical-answers
1
vote
1
answer
155
GATE DS&AI 2024 | Question: 50
Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
Arjun
asked
in
Calculus
Feb 16
by
Arjun
768
views
gate-ds-ai-2024
numerical-answers
limits
engineering-mathematics
0
votes
1
answer
156
GATE DS&AI 2024 | Question: 51
Let $\text{u}=\left[\begin{array}{l}1 \\ 2 \\ 3 \\ 4 \\ 5\end{array}\right]$, and let $\sigma_{1}, \sigma_{2}, \sigma_{3}, \sigma_{4}, \sigma_{5}$ be the singular values of the matrix $\text{M}=\text{u} \text{u}^{\text{T}}$ (where $\text{u}^{\text{T}}$ is the transpose of $\text{u}$ ). The value of $\sum_{i=1}^{5} \sigma_{i}$ is $\_\_\_\_\_\_\_\_\_$
Arjun
asked
in
Others
Feb 16
by
Arjun
918
views
gate-ds-ai-2024
numerical-answers
0
votes
1
answer
157
GATE DS&AI 2024 | Question: 52
Details of ten international cricket games between two teams "Green" and "Blue" are given in Table $\mathrm{C}$. This table consists of matches played on different pitches, across formats along with their winners. The attribute Pitch can take one of two values: spin-friendly ( ... $S$ $O$ Green $8$ $F$ $T$ Blue $9$ $F$ $O$ Blue $10$ $S$ $O$ Green
Arjun
asked
in
Others
Feb 16
by
Arjun
769
views
gate-ds-ai-2024
numerical-answers
0
votes
1
answer
158
GATE DS&AI 2024 | Question: 53
Given the two-dimensional dataset consisting of $5$ data points from two classes (circles and squares) and assume that the Euclidean distance is used to measure the distance between two points. The minimum odd value of $k$ in $k$-nearest neighbor algorithm for which the diamond $(\diamond)$ shaped data point is assigned the label square is $\_\_\_\_\_\_\_$.
Arjun
asked
in
Others
Feb 16
by
Arjun
959
views
gate-ds-ai-2024
numerical-answers
0
votes
2
answers
159
GATE DS&AI 2024 | Question: 54
Given the following Bayesian Network consisting of four Bernoulli random variables and the associated conditional probability tables: \begin{array}{|c|c|} \hline & P(\cdot) \\ \hline U=0 & 0.5 \\ \hline U=1 & 0.5 \\ \hline \end{array} \begin{array}{|c|c|c|} \ ... The value of $P(U=1, V=1, W=1, Z=1)= \_\_\_\_\_\_\_$ (rounded off to three decimal places).
Arjun
asked
in
Others
Feb 16
by
Arjun
1.0k
views
gate-ds-ai-2024
numerical-answers
0
votes
1
answer
160
GATE DS&AI 2024 | Question: 55
Two fair coins are tossed independently. $X$ is a random variable that takes a value of $1$ if both tosses are heads and $0$ otherwise. $Y$ is a random variable that takes a value of $1$ if at least one of the tosses is heads and $0$ otherwise. The value of the covariance of $X$ and $Y$ is $\_\_\_\_\_\_\_$ (rounded off to three decimal places).
Arjun
asked
in
Others
Feb 16
by
Arjun
1.7k
views
gate-ds-ai-2024
numerical-answers
1
vote
2
answers
161
GATE CSE 2024 | Set 2 | GA Question: 1
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [walk $\rightarrow$ jog $\rightarrow$ sprint] is analogous to [bothered $\rightarrow$ ________$\rightarrow$ daunted]. Which one of the given options is appropriate to fill the blank? phased phrased fazed fused
Arjun
asked
in
Verbal Aptitude
Feb 16
by
Arjun
4.9k
views
gatecse2024-set2
verbal-aptitude
3
votes
1
answer
162
GATE CSE 2024 | Set 2 | GA Question: 2
Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. They also decide to work independently. After trying all possible combination ... work. How many attempts does each wizard make before coming to this conclusion, independently? $24$ $48$ $16$ $12$
Arjun
asked
in
Quantitative Aptitude
Feb 16
by
Arjun
3.6k
views
gatecse2024-set2
quantitative-aptitude
5
votes
3
answers
163
GATE CSE 2024 | Set 2 | GA Question: 3
In an engineering college of $10,000$ students, $1,500$ like neither their core branches nor other branches. The number of students who like their core branches is $1 / 4^{\text {th }}$ of the number of students who like other branches. The number ... branches is $500$. The number of students who like their core branches is $1,800$ $3,500$ $1,600$ $1,500$
Arjun
asked
in
Quantitative Aptitude
Feb 16
by
Arjun
5.3k
views
gatecse2024-set2
quantitative-aptitude
6
votes
5
answers
164
GATE CSE 2024 | Set 2 | GA Question: 4
For positive non-zero real variables $x$ and $y$, if \[ \ln \left(\frac{x+y}{2}\right)=\frac{1}{2}[\ln (x)+\ln (y)] \] then, the value of $\frac{x}{y}+\frac{y}{x}$ is $1$ $1 / 2$ $2$ $4$
Arjun
asked
in
Quantitative Aptitude
Feb 16
by
Arjun
2.5k
views
gatecse2024-set2
quantitative-aptitude
logarithms
3
votes
2
answers
165
GATE CSE 2024 | Set 2 | GA Question: 5
In the sequence $6,9,14, x, 30,41$, a possible value of $x$ is $25$ $21$ $18$ $20$
Arjun
asked
in
Analytical Aptitude
Feb 16
by
Arjun
2.1k
views
gatecse2024-set2
analytical-aptitude
4
votes
2
answers
166
GATE CSE 2024 | Set 2 | GA Question: 6
Sequence the following sentences in a coherent passage. $\text{P}$: This fortuitous geological event generated a colossal amount of energy and heat that resulted in the rocks rising to an average height of $4 \mathrm{~km}$ across the contact zone ... Plate collided with the massive Eurasian Plate. $\text{QPSR}$ $\text{QSPR}$ $\text{SPRQ}$ $\text{SRPQ}$
Arjun
asked
in
Verbal Aptitude
Feb 16
by
Arjun
2.5k
views
gatecse2024-set2
verbal-aptitude
4
votes
4
answers
167
GATE CSE 2024 | Set 2 | GA Question: 7
A person sold two different items at the same price. He made $10 \%$ profit in one item, and $10 \%$ loss in the other item. In selling these two items, the person made a total of $1 \%$ profit $2 \%$ profit $1 \%$ loss $2 \%$ loss
Arjun
asked
in
Quantitative Aptitude
Feb 16
by
Arjun
2.5k
views
gatecse2024-set2
quantitative-aptitude
profit-loss
5
votes
3
answers
168
GATE CSE 2024 | Set 2 | GA Question: 8
The pie charts depict the shares of various power generation technologies in the total electricity generation of a country for the years $2007$ and $2023$. The renewable sources of electricity generation consist of Hydro, Solar and Wind. Assuming that the total ... sources of electricity generation over this period? $25 \%$ $50 \%$ $77.5 \%$ $62.5 \%$
Arjun
asked
in
Quantitative Aptitude
Feb 16
by
Arjun
2.4k
views
gatecse2024-set2
quantitative-aptitude
2
votes
2
answers
169
GATE CSE 2024 | Set 2 | GA Question: 9
A cube is to be cut into $8$ pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube. The minimum number of such cuts required is $3$ $4$ $7$ $8$
Arjun
asked
in
Spatial Aptitude
Feb 16
by
Arjun
3.5k
views
gatecse2024-set2
spatial-aptitude
2
votes
3
answers
170
GATE CSE 2024 | Set 2 | GA Question: 10
In the $4 \times 4$ array shown below, each cell of the first three rows has either a cross $(X)$ or a number. The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross ( $X$ ). ... has no crosses $(X)$, the sum of the four numbers to be filled in the last row is $11$ $10$ $12$ $9$
Arjun
asked
in
Analytical Aptitude
Feb 16
by
Arjun
2.3k
views
gatecse2024-set2
analytical-aptitude
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