Questions by Arjun / GATE Overflow for GATE CSE

48 votes

14 answers

401

GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________

Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T...

19.0k views

asked Feb 18, 2021

16 votes

3 answers

402

GATE CSE 2021 Set 2 | Question: 25
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________

Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that fo...

6.3k views

asked Feb 18, 2021

13 votes

2 answers

403

GATE CSE 2021 Set 2 | Question: 26
Consider the string $\textrm{abbccddeee}$. Each letter in the string must be assigned a binary code satisfying the following properties: For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter. ... which satisfy the above two properties, what is the minimum length of the encoded string? $21$ $23$ $25$ $30$

Consider the string $\textrm{abbccddeee}$. Each letter in the string must be assigned a binary code satisfying the following properties:For any two letters, the code assi...

9.6k views

asked Feb 18, 2021

18 votes

2 answers

404

GATE CSE 2021 Set 2 | Question: 27
Assume a two-level inclusive cache hierarchy, $L1$ and $L2$, where $L2$ is the larger of the two. Consider the following statements. $S_1$: Read misses in a write through $L1$ cache do not result in writebacks of dirty lines to the $L2$ $S_2$: Write ... false $S_1$ is false and $S_2$ is true $S_1$ is true and $S_2$ is true $S_1$ is false and $S_2$ is false

Assume a two-level inclusive cache hierarchy, $L1$ and $L2$, where $L2$ is the larger of the two. Consider the following statements.$S_1$: Read misses i...

8.2k views

asked Feb 18, 2021

23 votes

3 answers

405

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...

8.7k views

asked Feb 18, 2021

27 votes

4 answers

406

GATE CSE 2021 Set 2 | Question: 29
In an examination, a student can choose the order in which two questions ($\textsf{QuesA}$ and $\textsf{QuesB}$) must be attempted. If the first question is answered wrong, the student gets zero marks. If the first question is answered correctly and the ... $22$. First $\textsf{QuesA}$ and then $\textsf{QuesB}$. Expected marks $16$.

In an examination, a student can choose the order in which two questions ($\textsf{QuesA}$ and $\textsf{QuesB}$) must be attempted.If the first question is answered wrong...

7.6k views

asked Feb 18, 2021

19 votes

2 answers

407

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;...

9.9k views

asked Feb 18, 2021

16 votes

2 answers

408

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...

6.3k views

asked Feb 18, 2021

13 votes

2 answers

409

GATE CSE 2021 Set 2 | Question: 32
Let $S$ be the following schedule of operations of three transactions $T_1$, $T_2$ and $T_3$ in a relational database system: $R_2(Y), R_1(X), R_3(Z), R_1(Y)W_1(X), R_2(Z), W_2(Y), R_3(X), W_3(Z)$ Consider the statements $P$ and $Q$ below: $P$ ... Both $P$ and $Q$ are true $P$ is true and $Q$ is false $P$ is false and $Q$ is true Both $P$ and $Q$ are false

Let $S$ be the following schedule of operations of three transactions $T_1$, $T_2$ and $T_3$ in a relational database system:$$R_2(Y), R_1(X), R_3(Z), R_1(...

7.2k views

asked Feb 18, 2021

36 votes

4 answers

410

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 ...

11.0k views

asked Feb 18, 2021

9 votes

2 answers

411

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...

6.5k views

asked Feb 18, 2021

17 votes

2 answers

412

GATE CSE 2021 Set 2 | Question: 35
Consider the following $\text{ANSI C}$ program: #include <stdio.h> #include <stdlib.h> struct Node{ int value; struct Node *next;}; int main( ) { struct Node *boxE, *head, *boxN; int index=0; boxE=head= (struct ... which will be reported as an error by the compiler It dereferences an uninitialized pointer that may result in a run-time error

Consider the following $\text{ANSI C}$ program:#include <stdio.h #include <stdlib.h struct Node{ int value; struct Node *next;}; int main( ) { struct Node *boxE, *head, *...

9.7k views

asked Feb 18, 2021

32 votes

1 answer

413

GATE CSE 2021 Set 2 | Question: 36
Consider the following two statements about regular languages: $S_1$: Every infinite regular language contains an undecidable language as a subset. $S_2$: Every finite language is regular. Which one of the following choices is correct? Only $S_1$ is true Only $S_2$ is true Both $S_1$ and $S_2$ are true Neither $S_1$ nor $S_2$ is true

Consider the following two statements about regular languages:$S_1$: Every infinite regular language contains an undecidable language as a subset.$S_2$:...

12.1k views

asked Feb 18, 2021

21 votes

1 answer

414

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 $\mathcal{L}$ ...

7.2k views

asked Feb 18, 2021

12 votes

4 answers

415

GATE CSE 2021 Set 2 | Question: 38
For a statement $S$ in a program, in the context of liveness analysis, the following sets are defined: $\text{USE}(S)$ : the set of variables used in $S$ $\text{IN}(S)$ : the set of variables that are live at the entry of $S$ $\text{OUT}(S)$ : the set of variables ... S_2$) }\cup \text{ OUT ($S_2$)}$ $\text{OUT ($S_1$)} = \text{USE ($S_1$)} \cup \text{IN ($S_2$)}$

For a statement $S$ in a program, in the context of liveness analysis, the following sets are defined:$\text{USE}(S)$ : the set of variables used in $S$$\text{IN}(S)$ : t...

6.8k views

asked Feb 18, 2021

19 votes

3 answers

416

GATE CSE 2021 Set 2 | Question: 39
For constants $a \geq 1$ and $b>1$, consider the following recurrence defined on the non-negative integers: $T(n) = a \cdot T \left(\dfrac{n}{b} \right) + f(n)$ Which one of the following options is correct about the recurrence $T(n)$? If $f(n)$ is $n \log_2(n)$, ... $f(n)$ is $\Theta(n^{\log_b(a)})$, then $T(n)$ is $\Theta(n^{\log_b(a)})$

For constants $a \geq 1$ and $b>1$, consider the following recurrence defined on the non-negative integers:$$T(n) = a \cdot T \left(\dfrac{n}{b} \right) + f(n)$$ Which on...

8.3k views

asked Feb 18, 2021

18 votes

3 answers

417

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

asked Feb 18, 2021

27 votes

2 answers

418

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

asked Feb 18, 2021

25 votes

4 answers

419

GATE CSE 2021 Set 2 | Question: 42
Consider the following multi-threaded code segment (in a mix of C and pseudo-code), invoked by two processes $P_1$ and $P_2$, and each of the processes spawns two threads $T_1$ and $T_2$: int x = 0; // global Lock L1; // global main () { create a ... the value of $y$ as $2.$ Both $T_1$ and $T_2$, in both the processes, will print the value of $y$ as $1.$

Consider the following multi-threaded code segment (in a mix of C and pseudo-code), invoked by two processes $P_1$ and $P_2$, and each of the processes ...

10.5k views

asked Feb 18, 2021

35 votes

2 answers

420

GATE CSE 2021 Set 2 | Question: 43
Consider a computer system with multiple shared resource types, with one instance per resource type. Each instance can be owned by only one process at a time. Owning and freeing of resources are done by holding a global lock $(L)$. ... not occur The scheme may lead to live-lock The scheme may lead to starvation The scheme violates the mutual exclusion property

Consider a computer system with multiple shared resource types, with one instance per resource type. Each instance can be owned by only one process at a time. Owning and ...

9.9k views

asked Feb 18, 2021

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