Search results for ds / GATE Overflow for GATE CSE

1 votes

2 answers

1

GATE DS&AI 2024 | GA Question: 1
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [sick $\rightarrow$ infirm $\rightarrow$ moribund] is analogous to [silly $\rightarrow \_\_\_\_\_\_\_ \longrightarrow$ daft]. Which one of the given options is appropriate to fill the blank? frown fawn vein vain

If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [sick $\rightarrow$ infirm $\rightarrow$ moribund] is analogous t...

Arjun

4.0k views

Arjun asked Feb 16

0 votes

4 answers

2

GATE DS&AI 2024 | GA Question: 3
How many $4$-digit positive integers divisible by $3$ can be formed using only the digits $\{1,3,4,6,7\}$, such that no digit appears more than once in a number? $24$ $48$ $72$ $12$

How many $4$-digit positive integers divisible by $3$ can be formed using only the digits $\{1,3,4,6,7\}$, such that no digit appears more than once in a number?$24$$48$$...

Arjun

2.0k views

Arjun asked Feb 16

1 votes

4 answers

3

GATE DS&AI 2024 | GA Question: 5
In an election, the share of valid votes received by the four candidates $\text{A, B, C}$, and $\mathrm{D}$ is represented by the pie chart shown. The total number of votes cast in the election were $1,15,000$, out of which $5,000$ were invalid ... of valid votes received by the candidates $\mathrm{B}$ and $\mathrm{C}$ is $45,000$ $49,500$ $51,750$ $54,000$

In an election, the share of valid votes received by the four candidates $\text{A, B, C}$, and $\mathrm{D}$ is represented by the pie chart shown. The t...

Arjun

1.6k views

Arjun asked Feb 16

0 votes

4 answers

4

GATE DS&AI 2024 | GA Question: 7
The probability of a boy or a girl being born is $1 / 2$. For a family having only three children, what is the probability of having two girls and one boy? $3 / 8$ $1 / 8$ $1 / 4$ $1 / 2$

The probability of a boy or a girl being born is $1 / 2$. For a family having only three children, what is the probability of having two girls and one boy?$3 / 8$$1 / 8$$...

Arjun

2.4k views

Arjun asked Feb 16

3 votes

3 answers

5

GATE DS&AI 2024 | GA Question: 4
The sum of the following infinite series is \[ 2+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{8}+\frac{1}{9}+\frac{1}{16}+\frac{1}{27}+\cdots \] $11 / 3$ $7 / 2$ $13 / 4$ $9 / 2$

The sum of the following infinite series is\[2+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{8}+\frac{1}{9}+\frac{1}{16}+\frac{1}{27}+\cdots\]$11 / 3$$7 ...

Arjun

1.5k views

Arjun asked Feb 16

1 votes

1 answer

6

GATE DS&AI 2024 | Question: 1
Consider the following statements: The mean and variance of a Poisson random variable are equal. For a standard normal random variable, the mean is zero and the variance is one. Which ONE of the following options is correct? Both $\text{(i)}$ and $\text{(ii)}$ are true ... $\text{(i)}$ is false Both $\text{(i)}$ and $\text{(ii)}$ are false

Consider the following statements:The mean and variance of a Poisson random variable are equal.For a standard normal random variable, the mean is zero and the...

Arjun

1.2k views

Arjun asked Feb 16

0 votes

2 answers

7

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).

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})=...

Arjun

692 views

Arjun asked Feb 16

1 votes

1 answer

8

GATE DS&AI 2024 | Question: 26
A fair six-sided die (with faces numbered $1,2,3,4,5,6$ ) is repeatedly thrown independently. What is the expected number of times the die is thrown until two consecutive throws of even numbers are seen? $2$ $4$ $6$ $8$

A fair six-sided die (with faces numbered $1,2,3,4,5,6$ ) is repeatedly thrown independently.What is the expected number of times the die is thrown until t...

Arjun

1.1k views

Arjun asked Feb 16

0 votes

4 answers

9

GATE DS&AI 2024 | GA Question: 2
The $15$ parts of the given figure are to be painted such that no two adjacent parts with shared boundaries (excluding corners) have the same color. The minimum number of colors required is $4$ $3$ $5$ $6$

The $15$ parts of the given figure are to be painted such that no two adjacent parts with shared boundaries (excluding corners) have the same color. The...

Arjun

3.3k views

Arjun asked Feb 16

1 votes

1 answer

10

GATE DS&AI 2024 | Question: 3
Consider the matrix $\boldsymbol{M}=\left[\begin{array}{cc}2 & -1 \\ 3 & 1\end{array}\right]$. Which ONE of the following statements is TRUE? The eigenvalues of $\boldsymbol{M}$ are non-negative and real. The eigenvalues of ... zero. One eigenvalue of $\boldsymbol{M}$ is non-negative and real, and another eigenvalue of $\boldsymbol{M}$ is negative and real.

Consider the matrix $\boldsymbol{M}=\left[\begin{array}{cc}2 & -1 \\ 3 & 1\end{array}\right]$.Which ONE of the following statements is TRUE?The eigenvalues of...

Arjun

917 views

Arjun asked Feb 16

1 votes

1 answer

11

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

894 views

Arjun asked Feb 16

0 votes

2 answers

12

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

854 views

Arjun asked Feb 16

1 votes

1 answer

13

GATE DS&AI 2024 | Question: 11
Consider performing uniform hashing on an open address hash table with load factor $\alpha=\frac{n}{m}<1$, where $n$ elements are stored in the table with $m$ slots. The expected number of probes in an unsuccessful search is at most $\frac{1}{1-\alpha}$. Inserting ... $\frac{1}{1-\alpha}$ $1+\frac{\alpha}{2}$ $\frac{1}{1+\alpha}$

Consider performing uniform hashing on an open address hash table with load factor $\alpha=\frac{n}{m}<1$, where $n$ elements are stored in the table wi...

Arjun

766 views

Arjun asked Feb 16

0 votes

2 answers

14

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

1 votes

1 answer

15

GATE DS&AI 2024 | Question: 50
Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]

Evaluate the following limit:\[\lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]

Arjun

820 views

Arjun asked Feb 16

1 votes

1 answer

16

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).

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}...

Arjun

664 views

Arjun asked Feb 16

0 votes

1 answer

17

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

912 views

Arjun asked Feb 16

0 votes

3 answers

18

GATE DS&AI 2024 | GA Question: 10
Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what shape does the outer boundary of the resulting cross-section make? A rhombus A triangle An ellipse A hexagon

Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes thro...

Arjun

2.1k views

Arjun asked Feb 16

0 votes

2 answers

19

GATE DS&AI 2024 | GA Question: 8
Person $1$ and Person $2$ invest in three mutual funds $\text{A, B}$, and $\text{C}$. The amounts they invest in each of these mutual funds are given in the table. \begin{array}{|c|c|c|c|} \hline & \text{Mutual fund A} & \text{Mutual fund B} ... $\mathrm{A}$? $7.5 \%$ $10 \%$ $15 \%$ $20 \%$

Person $1$ and Person $2$ invest in three mutual funds $\text{A, B}$, and $\text{C}$. The amounts they invest in each of these mutual funds are given in th...

Arjun

1.3k views

Arjun asked Feb 16

0 votes

3 answers

20

GATE DS&AI 2024 | Question: 20
Consider sorting the following array of integers in ascending order using an inplace Quicksort algorithm that uses the last element as the pivot. \begin{array}{|l|l|l|l|l|} \hline 60 & 70 & 80 & 90 & 100 \\ \hline \end{array} The minimum number of swaps performed during this Quicksort is $\_\_\_\_\_\_\_\_$.

Consider sorting the following array of integers in ascending order using an inplace Quicksort algorithm that uses the last element as the pivot.\begin{array}{|l|l|l|l|l|...

Arjun

1.2k views

Arjun asked Feb 16

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