Recent questions in Others / GATE Overflow for GATE CSE

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31

GATE DS&AI 2024 | Question: 34
Consider a state space where the start state is number $1$. The successor function for the state numbered $n$ returns two states numbered $n+1$ and $n+2$. Assume that the states in the unexpanded state list are expanded in the ascending order of ... than BFS. Both BFS and DFS expand equal number of states. Both BFS and DFS do not reach the goal state number $6$.

Consider a state space where the start state is number $1$. The successor function for the state numbered $n$ returns two states numbered $n+1$ and $n+2$. ...

Arjun

835 views

Arjun asked Feb 16

1 votes

1 answer

32

GATE DS&AI 2024 | Question: 37
Select all choices that are subspaces of $\mathbb{R}^{3}$. Note: $\mathbb{R}$ ...

Select all choices that are subspaces of $\mathbb{R}^{3}$.Note: $\mathbb{R}$ denotes the set of real numbers.$\left\{\mathbf{x}=\left[\begin{array}{l}x_{1} \\ x_{2} \\ x_...

Arjun

901 views

Arjun asked Feb 16

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1 answer

33

GATE DS&AI 2024 | Question: 38
Which of the following statements is/are TRUE? Note: $\mathbb{R}$ denotes the set of real numbers. There exist $\text{M} \in \mathbb{R}^{3 \times 3}, \text{p} \in \mathbb{R}^{3}$, and $\text{q} \in \mathbb{R}^{3}$ ... $\text{Mx}=\text{p}$ has a unique solution and $\text{M x}=\text{q}$ has no solutions.

Which of the following statements is/are TRUE?Note: $\mathbb{R}$ denotes the set of real numbers.There exist $\text{M} \in \mathbb{R}^{3 \times 3}, \tex...

Arjun

837 views

Arjun asked Feb 16

0 votes

1 answer

34

GATE DS&AI 2024 | Question: 39
Let $\mathbb{R}$ be the set of real numbers, $U$ be a subspace of $\mathbb{R}^{3}$ and $\text{M} \in \mathbb{R}^{3 \times 3}$ be the matrix corresponding to the projection on to the subspace $U$. Which of the following statements is/are TRUE? If $U$ is a ... of $\mathbb{R}^{3}$, then the null space of $\text{M}$ is a $1$-dimensional subspace. $M^{2}=M$ $M^{3}=M$

Let $\mathbb{R}$ be the set of real numbers, $U$ be a subspace of $\mathbb{R}^{3}$ and $\text{M} \in \mathbb{R}^{3 \times 3}$ be the matrix corresponding t...

Arjun

754 views

Arjun asked Feb 16

0 votes

2 answers

35

GATE DS&AI 2024 | Question: 40
Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ where $\mathbb{R}$ is the set of all real numbers. \[ f(x)=\frac{x^{4}}{4}-\frac{2 x^{3}}{3}-\frac{3 x^{2}}{2}+1 \] Which of the following statements is/are TRUE? $x=0$ is a local maximum of $f$ $x=3$ is a local minimum of $f$ $x=-1$ is a local maximum of $f$ $x=0$ is a local minimum of $f$

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ where $\mathbb{R}$ is the set of all real numbers.\[f(x)=\frac{x^{4}}{4}-\frac{2 x^{3}}{3}-\fr...

Arjun

739 views

Arjun asked Feb 16

0 votes

2 answers

36

GATE DS&AI 2024 | Question: 42
Let $H, I, L$, and $N$ represent height, number of internal nodes, number of leaf nodes, and the total number of nodes respectively in a rooted binary tree. Which of the following statements is/are always TRUE? $L \leq I+1$ $H+1 \leq N \leq 2^{H+1}-1$ $H \leq I \leq 2^{H}-1$ $H \leq L \leq 2^{H-1}$

Let $H, I, L$, and $N$ represent height, number of internal nodes, number of leaf nodes, and the total number of nodes respectively in a rooted binary tree...

Arjun

863 views

Arjun asked Feb 16

0 votes

1 answer

37

GATE DS&AI 2024 | Question: 43
Consider the following figures representing datasets consisting of two-dimensional features with two classes denoted by circles and squares. Which of the following is/are TRUE? $\text{(i)}$ is linearly separable. $\text{(ii)}$ is linearly separable. $\text{(iii)}$ is linearly separable. $\text{(iv)}$ is linearly separable.

Consider the following figures representing datasets consisting of two-dimensional features with two classes denoted by circles and squares.Which of the following is/are ...

Arjun

736 views

Arjun asked Feb 16

0 votes

1 answer

38

GATE DS&AI 2024 | Question: 44
Let game(ball, rugby) be true if the ball is used in rugby and false otherwise. Let shape(ball, round) be true if the ball is round and false otherwise. Consider the following logical sentences: s1: $\forall$ ball $\neg$ game(ball, rugby) $\Rightarrow$ shape(ball, round) ... used in rugby"? $s 1 \wedge s 3$ $s 1 \wedge s 2$ $s 2 \wedge s 3$ $s 3 \wedge s 4$

Let game(ball, rugby) be true if the ball is used in rugby and false otherwise.Let shape(ball, round) be true if the ball is round and false otherwise.Cons...

Arjun

916 views

Arjun asked Feb 16

0 votes

1 answer

39

GATE DS&AI 2024 | Question: 45
An OTT company is maintaining a large disk-based relational database of different movies with the following schema: \[ \begin{array}{l} \text { Movie (ID, CustomerRating) } \\ \text { Genre (ID, Name) } \\ \text { Movie_Genre ... attributes. Hash index on Movie.CustomerRating and $\mathrm{B}^{+}$tree on the remaining attributes. Hash index on all the attributes.

An OTT company is maintaining a large disk-based relational database of different movies with the following schema:\[\begin{array}{l}\text { Movie (ID, ...

Arjun

834 views

Arjun asked Feb 16

0 votes

1 answer

40

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).

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...

Arjun

847 views

Arjun asked Feb 16

0 votes

1 answer

41

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 $\_\_\_\_\_\_\_\_\_$

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 { otherwi...

Arjun

967 views

Arjun asked Feb 16

0 votes

1 answer

42

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 $\_\_\_\_\_\_\_\_\_$

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 ...

Arjun

954 views

Arjun asked Feb 16

0 votes

1 answer

43

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

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 pitche...

Arjun

811 views

Arjun asked Feb 16

0 votes

1 answer

44

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 $\_\_\_\_\_\_\_$.

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 dista...

Arjun

1.0k views

Arjun asked Feb 16

0 votes

2 answers

45

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).

Given the following Bayesian Network consisting of four Bernoulli random variables and the associated conditional probability tables:\begin{array}{|c|c|}\hline & P(\cdot)...

Arjun

1.0k views

Arjun asked Feb 16

0 votes

1 answer

46

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).

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 take...

Arjun

1.7k views

Arjun asked Feb 16

0 votes

1 answer

47

lost my gate 2023 scorecard,, Help
Hello GO , I'm GO reader from last 2 years and I love this forum so I have given gate 2024 also but the thing is I lost my gate 2023 scorecard it wasn't good rank and I didn't know about last date to download I downloaded ... though it was bad rank but i qualified after studying what should i do , I sent mail to iitK today evening I'm worried

Hello GO , I'm GO reader from last 2 years and I love this forum so I have given gate 2024 also but the thing is I lost my gate 2023 scorecard it wasn't good rank and I d...

Aakashkk14

295 views

Aakashkk14 asked Feb 13

0 votes

0 answers

48

how i give free mock test on previous year

Shruti bhurse

80 views

Shruti bhurse asked Feb 7

0 votes

0 answers

49

TIFR Mathematics 2024 | Part B | Question: 1
If $\text{G}$ is a group of order $361$, then $\text{G}$ has a normal subgroup $\text{H}$ such that $H \cong G / H$.

If $\text{G}$ is a group of order $361$, then $\text{G}$ has a normal subgroup $\text{H}$ such that $H \cong G / H$.

admin

70 views

admin asked Jan 19

0 votes

1 answer

50

TIFR Mathematics 2024 | Part B | Question: 2
There exists a metric space $\text{X}$ such that the number of open subsets of $\text{X}$ is exactly $2024$.

There exists a metric space $\text{X}$ such that the number of open subsets of $\text{X}$ is exactly $2024$.

admin

98 views

admin asked Jan 19

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