Answers by shishir__roy / GATE Overflow for GATE CSE

0 votes

1

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...

1.3k views

answered Feb 17

0 votes

2

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})=...

719 views

answered Feb 17

0 votes

3

GATE DS&AI 2024 | Question: 14
Consider five random variables $U, V, W, X$, and $Y$ whose joint distribution satisfies: \[ P(U, V, W, X, Y)=P(U) P(V) P(W \mid U, V) P(X \mid W) P(Y \mid W) \] Which ONE of the following statements is FALSE? ... $U$ given $W$ $U$ and $V$ are conditionally independent given $W$ $Y$ and $X$ are conditionally independent given $W$

Consider five random variables $U, V, W, X$, and $Y$ whose joint distribution satisfies:\[P(U, V, W, X, Y)=P(U) P(V) P(W \mid U, V) P(X \mid W) P(Y \mid...

905 views

answered Feb 17

1 votes

4

GATE CSE 2024 | Set 1 | GA: 6
In the given text, the blanks are numbered $\text{(i) - (iv)}$. Select the best match for all the blanks. Steve was advised to keep his head (i) before heading (ii) to bat; for, while he had a head (iii) batting, he could only do so with a cool head iv his shoulders. (i ... ii) down (iii) for (iv) on (i) down (ii) out (iii) for (iv) on (i) on (ii) out (iii) on (iv) for

In the given text, the blanks are numbered $\text{(i) - (iv)}$. Select the best match for all the blanks.Steve was advised to keep his head (i) before heading (ii) ...

4.6k views

answered Feb 17

3 votes

5

GATE CSE 2024 | Set 1 | Question: 47
Consider the following code snippet using the fork () and wait () system calls. Assume that the code compiles and runs correctly, and that the system calls run successfully without any errors. int x=3; while (x>0){ fork (); printf("hello"); wait (NULL) ; X-- ; } The total number of times the printf statement is executed is __________.

Consider the following code snippet using the fork () and wait () system calls. Assume that the code compiles and runs correctly, and that the system calls run successful...

2.5k views

answered Feb 17

0 votes

6

GATE CSE 2024 | Set 1 | Question: 50
The number of edges present in the forest generated by the $\text{DFS}$ traversal of an undirected graph $G$ with $100$ vertices is $40$. The number of connected components in $G$ is __________.

The number of edges present in the forest generated by the $\text{DFS}$ traversal of an undirected graph $G$ with $100$ vertices is $40$. The number of connected componen...

1.9k views

answered Feb 17

2 votes

7

GATE CSE 2024 | Set 1 | Question: 52
Consider a memory management system that uses a page size of $2 \mathrm{~KB}$. Assume that both the physical and virtual addresses start from $0$. Assume that the pages $0,1,2$, and $3$ ... $0$, respectively. The physical address (in decimal format) corresponding to the virtual address $2500$ (in decimal format) is ___________.

Consider a memory management system that uses a page size of $2 \mathrm{~KB}$. Assume that both the physical and virtual addresses start from $0$. Assume that the pages $...

2.4k views

answered Feb 17

1 votes

8

GATE CSE 2024 | Set 1 | Question: 45
The baseline execution time of a program on a $2 \mathrm{GHz}$ single core machine is $100$ nanoseconds ( $n s)$. The code corresponding to $90 \%$ of the execution time can be fully parallelized. The overhead for using an ... the parallelized code for an equal amount of time. The number of cores that minimize the execution time of the program is __________.

The baseline execution time of a program on a $2 \mathrm{GHz}$ single core machine is $100$ nanoseconds ( $n s)$. The code corresponding to $90 \%$ of the execution time ...

1.8k views

answered Feb 16

1 votes

9

GATE CSE 2024 | Set 1 | Question: 44
Consider a $512$ GB hard disk with $32$ storage surfaces. There are $4096$ sectors per track and each sector holds $1024$ bytes of data. The number of cylinders in the hard disk is _________.

Consider a $512$ GB hard disk with $32$ storage surfaces. There are $4096$ sectors per track and each sector holds $1024$ bytes of data. The number of cylinders in the ha...

1.7k views

answered Feb 16

0 votes

10

GATE CSE 2024 | Set 1 | Question: 42
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE? Operator $\diamond$ ... $\square$ obeys the distributive law Operator $\square$ over the operator $\diamond$ obeys the distributive law

Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE?Ope...

1.8k views

answered Feb 16

4 votes

11

GATE CSE 2024 | Set 1 | Question: 53
A bag contains $10$ red balls and $15$ blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to $3$ decimal places) that both balls drawn are red is ___________.

A bag contains $10$ red balls and $15$ blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off ...

2.2k views

answered Feb 16

3 votes

12

GATE CSE 2024 | Set 1 | Question: 38
Consider the following $\mathrm{C}$ ... the return value is less than $2^{10}$ If the inputs are $x=10, y=20$, then the return value is greater than $2^{20}$

Consider the following $\mathrm{C}$ function definition.int f (int x, int y){ for (int i=0 ; i<y ; i++ ) { x= x + x + y; } return x; }Which of the following stateme...

2.2k views

answered Feb 16

1 votes

13

GATE CSE 2024 | Set 1 | Question: 37
Consider a Boolean expression given by $\text{F(X, Y, Z)}=\sum(3,5,6,7)$. Which of the following statements is/are CORRECT? $\text{F(X, Y, Z)}=\Pi(0,1,2,4)$ $\text{F(X, Y, Z)=X Y+Y Z+X Z}$ $\text{F(X, Y, Z)}$ is independent of input $\text{Y}$ $\text{F(X, Y, Z)}$ is independent of input $\text{X}$

Consider a Boolean expression given by $\text{F(X, Y, Z)}=\sum(3,5,6,7)$.Which of the following statements is/are CORRECT?$\text{F(X, Y, Z)}=\Pi(0,1,2,4)$ $\text{F(X, Y, ...

2.0k views

answered Feb 16

1 votes

14

GATE CSE 2024 | Set 1 | Question: 33
Consider a binary min-heap containing $105$ distinct elements. Let $k$ be the index (in the underlying array) of the maximum element stored in the heap. The number of possible values of $k$ is $53$ $52$ $27$ $1$

Consider a binary min-heap containing $105$ distinct elements. Let $k$ be the index (in the underlying array) of the maximum element stored in the heap. The number of pos...

2.3k views

answered Feb 16

1 votes

15

GATE CSE 2024 | Set 1 | Question: 31
An array $[82,101,90,11,111,75,33,131,44,93]$ is heapified. Which one of the following options represents the first three elements in the heapified array? $82,90,101$ $82,11,93$ $131,11,93$ $131,111,90$

An array $[82,101,90,11,111,75,33,131,44,93]$ is heapified. Which one of the following options represents the first three elements in the heapified array?$...

2.3k views

answered Feb 16

1 votes

16

GATE CSE 2024 | Set 1 | Question: 30
Consider the following two threads $\mathrm{T} 1$ and $\mathrm{T} 2$ that update two shared variables $\mathrm{a}$ and $\mathrm{b}$. Assume that initially $\mathrm{a}=\mathrm{b}=1$ ...

Consider the following two threads $\mathrm{T} 1$ and $\mathrm{T} 2$ that update two shared variables $\mathrm{a}$ and $\mathrm{b}$. Assume that initially $\math...

2.1k views

answered Feb 16

3 votes

17

GATE CSE 2024 | Set 1 | Question: 27
Consider the following syntax-directed definition $\text{(SDD)}$. $S \rightarrow D H T U$ $ \left\{S.v a l = D.val + H.val + T.val + U.val\right\};$ $D \rightarrow ^{"} \mathrm{M}^{"} D_1$ ... the following options is the $\text{CORRECT}$ value computed by the $\text{SDD}$ (in the attribute $S.val$)? $45$ $50$ $55$ $65$

Consider the following syntax-directed definition $\text{(SDD)}$.$S \rightarrow D H T U$$ \left\{S.v a l = D.val + H.val + T.val + U.val\right\};$$D \rightarrow ^{"} \...

1.9k views

answered Feb 16

1 votes

18

GATE CSE 2024 | Set 1 | Question: 22
Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions $\text{(i)}$ from $A$ to $B$ and $\text{(ii)}$ from $A \times A$ to $A \cup B$. The number of possible values of $\text{|A|}$ is ___________.

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions $\text{(i)}$ from $A$ to $B$ and $\text{(ii)}$ from $A \times A$ to $A \cup B...

1.8k views

answered Feb 16

4 votes

19

GATE CSE 2024 | Set 1 | Question: 7
Given an integer array of size $N$, we want to check if the array is sorted (in either ascending or descending order). An algorithm solves this problem by making a single pass through the array and comparing each element of the array only with its adjacent elements. The ... $\Omega(N)$ but not $\mathrm{O}(N)$ neither $\mathrm{O}(N)$ nor $\Omega(N)$

Given an integer array of size $N$, we want to check if the array is sorted (in either ascending or descending order). An algorithm solves this problem by making a single...

3.4k views

answered Feb 16

1 votes

20

GATE CSE 2024 | Set 1 | Question: 4
Consider a permutation sampled uniformly at random from the set of all permutations of $\{1,2,3, \cdots, n\}$ for some $n \geq 4$. Let $X$ be the event that $1$ occurs before $2$ in the permutation, and $Y$ the event that $3$ occurs before ... The events $X$ and $Y$ are independent Either event $X$ or $Y$ must occur Event $X$ is more likely than event $Y$

Consider a permutation sampled uniformly at random from the set of all permutations of $\{1,2,3, \cdots, n\}$ for some $n \geq 4$. Let $X$ be the event that $1$ occurs be...

2.4k views

answered Feb 16

2 votes

21

TIFR CSE 2023 | Part B | Question: 4
Amar, Balu, and Chhaya are three friends and they play the following game. Chhaya first chooses a number $k \in U$ where $U=\{1,2, \ldots, 127\}$. She either gives $k$ to both Amar and Balu, or else she gives $k$ to Amar and $k+1$ to Balu ... differed by $1.$ What is the minimal $n$ that allows Balu to distinguish between these two cases? $1$ $2$ $7$ $127$ $128$

Amar, Balu, and Chhaya are three friends and they play the following game. Chhaya first chooses a number $k \in U$ where $U=\{1,2, \ldots, 127\}$. She either gives $k$ to...

399 views

answered Sep 2, 2023

4 votes

22

TIFR CSE 2023 | Part A | Question: 2
How many distinct rectangles can be formed using the vertices in the grid shown below? Squares are also counted as rectangles, and two rectangles are distinct if either their top-left vertices are different or their bottom-right vertices are different. ... $16$ $25$ $36$ $64$ $100$

How many distinct rectangles can be formed using the vertices in the grid shown below? Squares are also counted as rectangles, and two rectangles are distinct if either t...

703 views

answered Jun 11, 2023

2 votes

23

self doubt on Combinatory Discrete Mathematics
A power series expression has been converted to Partial Fractions to get :- $\frac{3}{1+5x} - \frac{2}{7-2x}+ \frac{5x}{3+2x} + \frac{7x}{5-2x}$ Find the Coefficient of $x^{n}$ where n represents natural number.

A power series expression has been converted to Partial Fractions to get :-$\frac{3}{1+5x} - \frac{2}{7-2x}+ \frac{5x}{3+2x} + \frac{7x}{5-2x}$Find the Coefficient of $x^...

427 views

answered Jun 5, 2023

0 votes

24

TIFR CSE 2023 | Part A | Question: 10
Let $Q$ be a set with $n$ elements. Consider a system with states of the form $(S, R)$ where $S \subseteq Q$ and $R \subseteq Q$, with the further restriction that $R \subseteq S$. Note that $(\emptyset, \emptyset)$ is also a valid state of the system (here $\emptyset$ ... have? $3^{n}$ $2^{n}$ $4^{n}$ $n^{3}$ $\left(\begin{array}{l}n \\ 3\end{array}\right)$

Let $Q$ be a set with $n$ elements. Consider a system with states of the form $(S, R)$ where $S \subseteq Q$ and $R \subseteq Q$, with the further restriction that $R \su...

376 views

answered May 4, 2023

1 votes

25

TIFR CSE 2023 | Part B | Question: 9
Fix a positive integer $n$, and let $n=p_{1}^{e_{1}} p_{2}^{e_{2}} \cdots p_{k}^{e_{k}}$ be the prime factorization of $n$. Here, $p_{1}, \ldots, p_{k}$ are prime numbers and $e_{i} \geq 1$ for all $1 \leq i \leq k$ ... None of the above

Fix a positive integer $n$, and let $n=p_{1}^{e_{1}} p_{2}^{e_{2}} \cdots p_{k}^{e_{k}}$ be the prime factorization of $n$. Here, $p_{1}, \ldots, p_{k}$ are prime numbers...

313 views

answered Apr 18, 2023

1 votes

26

TIFR CSE 2023 | Part A | Question: 15
Consider the $n \times n$ matrix $M$ ... $S$ have? $1$ $\left(\begin{array}{l}n \\ 2\end{array}\right)$ $n$ ! $(n !)^{2}$ $n$

Consider the $n \times n$ matrix $M$ defined as follows:$$M=\left(\begin{array}{cccc}1 & 2 & \ldots & n \\n+1 & n+2 & \ldots & 2 n \\2 n+1 & 2 n+2 & \ldots & 3 n \\\vdots...

542 views

answered Apr 6, 2023

19 votes

27

GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 18
In this problem, consider the $4 \times 4$ matrix $A$ whose columns are vectors $\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3, \mathbf{a}_4 \in \mathbb{R}^4$ ... a element in matrix $\text{A}$ at $\mathrm{i}^{\text {th }}$ row and $\mathrm{j}^{\text{th}}$ column.

In this problem, consider the $4 \times 4$ matrix $A$ whose columns are vectors $\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3, \mathbf{a}_4 \in \mathbb{R}^4$ :$$A=\left[\math...

757 views

answered Apr 6, 2023

4 votes

28

TIFR CSE 2023 | Part A | Question: 3
$A$ is an $n \times n$ matrix with real-valued entries. Further, there exists a vector $x \neq 0$ such that $A x=0$. Now consider a given vector $b$ in $\mathbb{R}^{n}$. How many possible vectors $z$ exist, so that $A z=b?$ $0$ $1$ $n-1$ $n$ Either $0$ or infinite

$A$ is an $n \times n$ matrix with real-valued entries. Further, there exists a vector $x \neq 0$ such that $A x=0$. Now consider a given vector $b$ in $\mathbb{R}^{n}$. ...

451 views

answered Apr 6, 2023

2 votes

29

Flamingos Fanny and Freddy have three offspring: Happy, Glee, and Joy. These five flamingos are to be distributed to seven different zoos so that no zoo gets both a parent and a child :(. It is not required that every zoo gets a flamingo. In how many different ways can this be done? here if i am using case method on children i am getting a different answer than when i am using case methon on parents, why is that?

479 views

answered Apr 5, 2023

6 votes

30

GO Classes 2023 | IIITH Mock Test 1 | Question: 60
If $4$ Maths books are selected from $6$ different Maths books and $3$ English books are chosen from $5$ different English books, how many ways can the seven books be arranged on a shelf if a Maths is at the beginning and an English book is in the middle of the shelf $216000$ $218000$ $206000$ $226000$

If $4$ Maths books are selected from $6$ different Maths books and $3$ English books are chosen from $5$ different English books, how many ways can the seven books be arr...

862 views

answered Mar 28, 2023

tags	tag:apple
author	user:martin
title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true