Answers by zxy123 / GATE Overflow for GATE CSE

1 votes

1

NIELIT 2018-18
If $y^a$ is an integrating factor of the differential equation $2xydx-(3x^2-y^2)dy=0$, then the value of $a$ is $-4$ $4$ $-1$ $1$

If $y^a$ is an integrating factor of the differential equation $2xydx-(3x^2-y^2)dy=0$, then the value of $a$ is$-4$$4$$-1$$1$

704 views

answered Dec 9, 2023

4 votes

2

GATE CSE 2021 Set 2 | Question: 34
Consider the cyclic redundancy check $\text{(CRC)}$ based error detecting scheme having the generator polynomial $X^3+X+1$. Suppose the message $m_4m_3m_2m_1m_0=11000$ is to be transmitted. Check bits $c_2c_1c_0$ are appended at the end of the ... is denoted by $m_4m_3m_2m_1m_0c_2c_1c_0$. The value of the checkbit sequence $c_2c_1c_0$ is $101$ $110$ $100$ $111$

Consider the cyclic redundancy check $\text{(CRC)}$ based error detecting scheme having the generator polynomial $X^3+X+1$. Suppose the message $m_4m_3m_2m_1m_0=11000$ is...

6.4k views

answered Feb 18, 2021

6 votes

3

GATE CSE 2021 Set 1 | Question: 32
Let $r_i(z)$ and $w_i(z)$ denote read and write operations respectively on a data item $z$ by a transaction $T_i$. Consider the following two schedules. $S_1: r_1(x)r_1(y)r_2(x)r_2(y)w_2(y)w_1(x)$ ... serializable, and $S_2$ is conflict serializable Both $S_1$ and $S_2$ are conflict serializable Niether $S_1$ nor $S_2$ is conflict serializable

Let $r_i(z)$ and $w_i(z)$ denote read and write operations respectively on a data item $z$ by a transaction $T_i$. Consider the following two schedules.$S_1: r_1(x)r_1(y)...

5.6k views

answered Feb 18, 2021

4 votes

4

GATE CSE 2021 Set 1 | Question: 28
Consider a $3$-bit counter, designed using $T$ flip-flops, as shown below: Assuming the initial state of the counter given by $\text{PQR}$ as $000$, what are the next three states? $011,101,000$ $001,010,111$ $011,101,111$ $001,010,000$

Consider a $3$-bit counter, designed using $T$ flip-flops, as shown below:Assuming the initial state of the counter given by $\text{PQR}$ as $000$, what are the next thre...

7.4k views

answered Feb 18, 2021

53 votes

5

GATE CSE 2021 Set 1 | Question: 23
A relation $r(A, B)$ in a relational database has $1200$ tuples. The attribute $A$ has integer values ranging from $6$ to $20$, and the attribute $B$ has integer values ranging from $1$ to $20$. Assume that the attributes $A$ and $B$ are independently distributed. The estimated number of tuples in the output of $\sigma _{(A>10)\vee(B=18)}(r)$ is ____________.

A relation $r(A, B)$ in a relational database has $1200$ tuples. The attribute $A$ has integer values ranging from $6$ to $20$, and the attribute $B$ has integer values r...

13.1k views

answered Feb 18, 2021

10 votes

6

GATE CSE 2021 Set 1 | Question: 14
Which of the following standard $C$ library functions will always invoke a system call when executed from a single-threaded process in a $\text{UNIX/Linux}$ operating system? $\textsf{exit}$ $\textsf{malloc}$ $\textsf{sleep}$ $\textsf{strlen}$

Which of the following standard $C$ library functions will always invoke a system call when executed from a single-threaded process in a $\text{UNIX/Linux}$ operating sys...

10.8k views

answered Feb 18, 2021

0 votes

7

GATE CSE 2021 Set 1 | Question: 9
Consider the following array.$\begin{array}{|l|l|l|l|l|l|} \hline 23&32&45&69&72&73&89&97 \\ \hline\end{array}$ Which algorithm out of the following options uses the least number of comparisons ( ... elements) to sort the above array in ascending order? Selection sort Mergesort Insertion sort Quicksort using the last element as pivot

Consider the following array.$$\begin{array}{|l|l|l|l|l|l|} \hline 23&32&45&69&72&73&89&97 \\ \hline\end{array}$$ Which algorithm out of the following options uses the le...

12.4k views

answered Feb 18, 2021

25 votes

8

GATE CSE 2021 Set 2 | Question: 52
Consider a Boolean function $f(w,x,y,z)$ such that $\begin{array}{lll} f(w,0,0,z) & = & 1 \\ f(1,x,1,z) & =& x+z \\ f(w,1,y,z) & = & wz +y \end{array}$The number of literals in the minimal sum-of-products expression of $f$ is _________

Consider a Boolean function $f(w,x,y,z)$ such that $$\begin{array}{lll} f(w,0,0,z) & = & 1 \\ f(1,x,1,z) & =& x+z \\ f(w,1,y,z) & = & wz +y \end{array}$$The number of li...

13.5k views

answered Feb 18, 2021

22 votes

9

GATE CSE 2021 Set 2 | Question: 49
Consider the following $\text{ANSI C}$ program #include <stdio.h> int foo(int x, int y, int q) { if ((x<=0) && (y<=0)) return q; if (x<=0) return foo(x, y-q, q); if (y<=0) return foo(x-q, y, q); return foo(x, ... ); } int main( ) { int r = foo(15, 15, 10); printf( %d , r); return 0; } The output of the program upon execution is _________

Consider the following $\text{ANSI C}$ program#include <stdio.h int foo(int x, int y, int q) { if ((x<=0) && (y<=0)) return q; if (x<=0) return foo(x, y-q, q); if (y<=0)...

8.4k views

answered Feb 18, 2021

16 votes

10

GATE CSE 2021 Set 2 | Question: 47
Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume that the string $\epsilon$ is divisible by three. $(0+1(01^*0)^*1)^*$ $(0+11+10(1+00)^*01)^*$ $(0^*(1(01^*0)^*1)^*)^*$ $(0+11+11(1+00)^*00)^*$

Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume that the string $\epsilon$ is divisible by three...

12.4k views

answered Feb 18, 2021

7 votes

11

GATE CSE 2021 Set 2 | Question: 41
For a string $w$, we define $w^R$ to be the reverse of $w$. For example, if $w=01101$ then $w^R=10110$. Which of the following languages is/are context-free? $\{ wxw^Rx^R \mid w,x \in \{0,1\} ^* \}$ $\{ ww^Rxx^R \mid w,x \in \{0,1\} ^* \}$ $\{ wxw^R \mid w,x \in \{0,1\} ^* \}$ $\{ wxx^Rw^R \mid w,x \in \{0,1\} ^* \}$

For a string $w$, we define $w^R$ to be the reverse of $w$. For example, if $w=01101$ then $w^R=10110$.Which of the following languages is/are context-free?$\{ wxw^Rx^R \...

7.3k views

answered Feb 18, 2021

21 votes

12

GATE CSE 2021 Set 2 | Question: 40
Suppose the following functional dependencies hold on a relation $U$ with attributes $P,Q,R,S$, and $T$: $P \rightarrow QR$ $RS \rightarrow T$ Which of the following functional dependencies can be inferred from the above functional dependencies? $PS \rightarrow T$ $R \rightarrow T$ $P \rightarrow R$ $PS \rightarrow Q$

Suppose the following functional dependencies hold on a relation $U$ with attributes $P,Q,R,S$, and $T$:$P \rightarrow QR$$RS \rightarrow T$Which of the following functio...

7.4k views

answered Feb 18, 2021

32 votes

13

GATE CSE 2021 Set 2 | Question: 37
For two $n$-dimensional real vectors $P$ and $Q$, the operation $s(P,Q)$ is defined as follows: $s(P,Q) = \displaystyle \sum_{i=1}^n (P[i] \cdot Q[i])$ Let $\mathcal{L}$ be a set of $10$-dimensional non-zero real vectors such that for every pair ... $s(P,Q)=0$. What is the maximum cardinality possible for the set $\mathcal{L}$? $9$ $10$ $11$ $100$

For two $n$-dimensional real vectors $P$ and $Q$, the operation $s(P,Q)$ is defined as follows:$$s(P,Q) = \displaystyle \sum_{i=1}^n (P[i] \cdot Q[i])$$Let $\mathcal{L}$ ...

7.1k views

answered Feb 18, 2021

15 votes

14

GATE CSE 2021 Set 2 | Question: 33
A bag has $r$ red balls and $b$ black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of ...

A bag has $r$ red balls and $b$ black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and ...

10.9k views

answered Feb 18, 2021

3 votes

15

GATE CSE 2021 Set 2 | Question: 31
The relation scheme given below is used to store information about the employees of a company, where $\textsf{empId}$ is the key and $\textsf{deptId}$ indicates the department to which the employee is assigned. Each employee ... average salary of employees in the department employees in the company female employees in the department female employees in the company

The relation scheme given below is used to store information about the employees of a company, where $\textsf{empId}$ is the key and $\textsf{deptId}$ indicates the depar...

6.2k views

answered Feb 18, 2021

33 votes

16

GATE CSE 2021 Set 2 | Question: 30
Consider the following $\text{ANSI C}$ code segment: z=x + 3 + y->f1 + y->f2; for (i = 0; i < 200; i = i + 2) { if (z > i) { p = p + x + 3; q = q + y->f1; } else { p = p + y->f2; q = q + x + 3; } ... $\textsf{y ->f2}$) in the optimized code, respectively, are: $403$ and $102$ $203$ and $2$ $303$ and $102$ $303$ and $2$

Consider the following $\text{ANSI C}$ code segment:z=x + 3 + y->f1 + y->f2; for (i = 0; i < 200; i = i + 2) { if (z i) { p = p + x + 3; q = q + y->f1;...

9.8k views

answered Feb 18, 2021

14 votes

17

GATE CSE 2021 Set 2 | Question: 28
Suppose we want to design a synchronous circuit that processes a string of $0$'s and $1$'s. Given a string, it produces another string by replacing the first $1$ in any subsequence of consecutive $1$'s by a $0$ ... $\begin{array}{l} t=s+b \\ y=s \overline{b} \end{array}$

Suppose we want to design a synchronous circuit that processes a string of $0$’s and $1$’s. Given a string, it produces another string by replacing the first $1$ in a...

8.6k views

answered Feb 18, 2021

6 votes

18

GATE CSE 2021 Set 2 | Question: 23
Consider the following $\text{ANSI C}$ function: int SomeFunction (int x, int y) { if ((x==1) || (y==1)) return 1; if (x==y) return x; if (x > y) return SomeFunction(x-y, y); if (y > x) return SomeFunction (x, y-x); } The value returned by $\textrm{SomeFunction(15, 255)}$ is __________

Consider the following $\text{ANSI C}$ function:int SomeFunction (int x, int y) { if ((x==1) || (y==1)) return 1; if (x==y) return x; if (x y) return SomeFunction(x-y, y...

5.1k views

answered Feb 18, 2021

21 votes

19

GATE CSE 2021 Set 2 | Question: 22
For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value is the number of times that head appeared in these $1,000$ tosses. The standard deviation of $X$ (rounded to $2$ decimal place) is _________

For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value ...

6.1k views

answered Feb 18, 2021

40 votes

20

GATE CSE 2021 Set 2 | Question: 11
Consider the following sets, where $n \geq 2$: $S_1$: Set of all $n \times n$ matrices with entries from the set $\{ a, b, c\}$ $S_2$: Set of all functions from the set $\{0,1,2, \dots, n^2-1\}$ ... There exists a surjection from $S_1$ to $S_2$ There exists a bijection from $S_1$ to $S_2$ There does not exist an injection from $S_1$ to $S_2$

Consider the following sets, where $n \geq 2$:$S_1$: Set of all $n \times n$ matrices with entries from the set $\{ a, b, c\}$$S_2$: Set of all functions from the set $\{...

6.5k views

answered Feb 18, 2021

2 votes

21

GATE CSE 2021 Set 2 | GA Question: 4
If $\left( x – \dfrac{1}{2} \right)^2 – \left( x- \dfrac{3}{2} \right) ^2 = x+2$, then the value of $x$ is: $2$ $4$ $6$ $8$

If $\left( x – \dfrac{1}{2} \right)^2 – \left( x- \dfrac{3}{2} \right) ^2 = x+2$, then the value of $x$ is:$2$$4$$6$$8$

3.6k views

answered Feb 18, 2021

10 votes

22

GATE CSE 2021 Set 2 | GA Question: 3
If $\theta$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, $\cos \theta =$ $\frac{1}{2} \\$ $\frac{1}{\sqrt{3}} \\$ $\frac{1}{\sqrt{2}} \\$ $\frac{\sqrt{3}}{2}$

If $\theta$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, $\cos \theta =$$\frac{1}{2} \\$$\frac{1}{\sqrt{...

8.2k views

answered Feb 18, 2021

12 votes

23

GATE CSE 2021 Set 2 | GA Question: 2
A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ___________.

A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ___________.

3.2k views

answered Feb 18, 2021

9 votes

24

GATE CSE 2021 Set 2 | GA Question: 1
Gauri said that she can play the keyboard __________ her sister. as well as as better as as nicest as as worse as

Gauri said that she can play the keyboard __________ her sister.as well asas better asas nicest asas worse as

7.8k views

answered Feb 18, 2021

12 votes

25

GATE CSE 2021 Set 1 | GA Question: 10
Some people suggest anti-obesity measures $\text{(AOM)}$ such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality. Which one of the ... $\text{AOM}$ are addressing the problem superficially

Some people suggest anti-obesity measures $\text{(AOM)}$ such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems t...

3.4k views

answered Feb 18, 2021

17 votes

26

GATE CSE 2021 Set 1 | GA Question: 9
Given below are two statements $1$ and $2$, and two conclusions $\text{I}$ and $\text{II}$ $\text{Statement 1:}$ All bacteria are microorganisms. $\text{Statement 2:}$ All pathogens are microorganisms. $\text{Conclusion I:}$ Some pathogens are ... Either conclusion $\text{I}$ or $\text{II}$ is correct Neither conclusion $\text{I}$ nor $\text{II}$ is correct

Given below are two statements $1$ and $2$, and two conclusions $\text{I}$ and $\text{II}$$\text{Statement 1:}$ All bacteria are microorganisms.$\text{Statement 2:}$ All ...

14.4k views

answered Feb 18, 2021

24 votes

27

GATE CSE 2021 Set 1 | GA Question: 8
There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is __________ $0.3024$ $0.4235$ $0.6976$ $0.8125$

There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.The probability that at least two chocolates are iden...

10.9k views

answered Feb 18, 2021

11 votes

28

GATE CSE 2021 Set 1 | GA Question: 7
... $Q$, as a percentage of its marked price, is _______ $25$ $12.5$ $10$ $5$

$$\begin{array}{|c|c|c|c|} \hline \textbf{Items} & \textbf{Cost} & \textbf{Profit %} & \textbf{Marked Price} \\ & \text{(₹)} & & \text{(₹)} \\\hline P &5,400 & -&5,86...

5.0k views

answered Feb 18, 2021

15 votes

29

GATE CSE 2021 Set 1 | GA Question: 6
We have $2$ rectangular sheets of paper, $\text{M}$ and $\text{N}$, of dimensions $\text{6 cm $\times$ 1 cm}$ each. Sheet $\text{M}$ is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet $\text{N}$ is cut into equal ... of the cylinder to that of the cube is _________. $\frac{\pi}{2}$ $\frac{3}{\pi}$ $\frac{9}{\pi}$ $3\pi$

We have $2$ rectangular sheets of paper, $\text{M}$ and $\text{N}$, of dimensions $\text{6 cm $\times$ 1 cm}$ each. Sheet $\text{M}$ is rolled to form an open cylinder by...

4.7k views

answered Feb 18, 2021

8 votes

30

GATE CSE 2021 Set 1 | GA Question: 5
___________ is to surgery as writer is to ___________ Which one of the following options maintains a similar logical relation in the above sentence? Plan, outline Hospital, library Doctor, book Medicine, grammar

___________ is to surgery as writer is to ___________Which one of the following options maintains a similar logical relation in the above sentence?Plan, outlineHospital, ...

2.8k views

answered Feb 18, 2021

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