Questions by Arjun / GATE Overflow for GATE CSE

19 votes

4 answers

281

GATE CSE 2022 | Question: 10
Consider the following two statements with respect to the matrices $\textit{A}_{m \times n}, \textit{B}_{n \times m}, \textit{C}_{n \times n}$ and $ \textit{D}_{n \times n}.$ Statement $1: tr \text{(AB)} = tr \text{(BA)}$ ... $2$ is correct. Both Statement $1$ and Statement $2$ are correct. Both Statement $1$ and Statement $2$ are wrong.

Consider the following two statements with respect to the matrices $\textit{A}_{m \times n}, \textit{B}_{n \times m}, \textit{C}_{n \times n}$ and $ \textit{D}_{n \times ...

10.9k views

asked Feb 15, 2022

12 votes

3 answers

282

GATE CSE 2022 | Question: 11
What is printed by the following $\text{ANSI C}$ program? #include<stdio.h> int main(int argc, char *argv[]) { int x = 1, z[2] = {10, 11}; int *p = NULL; p = &x; *p = 10; p = &z[1]; *(&z[0] + 1) += 3; printf(“%d, %d, %d\n”, x, z[0], z[1]); return 0; } $1, 10, 11$ $1, 10, 14$ $10, 14, 11$ $10, 10, 14$

What is printed by the following $\text{ANSI C}$ program?#include<stdio.h int main(int argc, char *argv[]) { int x = 1, z = {10, 11}; int *p = NULL; p = &x; *p = 10; p =...

5.8k views

asked Feb 15, 2022

22 votes

3 answers

283

GATE CSE 2022 | Question: 12
Consider an enterprise network with two Ethernet segments, a web server and a firewall, connected via three routers as shown below. What is the number of subnets inside the enterprise network? $3$ $12$ $6$ $8$

Consider an enterprise network with two Ethernet segments, a web server and a firewall, connected via three routers as shown below.What is the number of subnets inside th...

14.5k views

asked Feb 15, 2022

6 votes

2 answers

284

GATE CSE 2022 | Question: 13
Which of the following statements is/are $\text{TRUE}?$ Every subset of a recursively enumerable language is recursive. If a language $\textit{L}$ and its complement $\overline{\textit{L}}$ are both recursively enumerable, then $\textit{L}$ must be recursive. ... $\textit{L}_{1} \cap \textit{L}_{2}$ must be deterministic context-free.

Which of the following statements is/are $\text{TRUE}?$Every subset of a recursively enumerable language is recursive.If a language $\textit{L}$ and its complement $\over...

15.4k views

asked Feb 15, 2022

21 votes

1 answer

285

GATE CSE 2022 | Question: 14
Let $\text{WB}$ and $\text{WT}$ be two set associative cache organizations that use $\text{LRU}$ algorithm for cache block replacement. $\text{WB}$ is a write back cache and $\text{WT}$ ... cache to main memory. A read miss in $\text{WB}$ will never lead to eviction of a dirty block from $\text{WB}.$

Let $\text{WB}$ and $\text{WT}$ be two set associative cache organizations that use $\text{LRU}$ algorithm for cache block replacement. $\text{WB}$ is a write back cache ...

7.8k views

asked Feb 15, 2022

15 votes

2 answers

286

GATE CSE 2022 | Question: 15
Consider the following three relations in a relational database. $\text{Employee} (\underline{\text{eId}},\text{Name}), \; \text{Brand}(\underline{\text{bId}},\text{bName}), \; \text{Own}(\underline{\text{eId}},\underline{\text{bId}})$ Which of the following relational ... $ \Pi_{eId} \left( (\Pi_{eId}(Own) \times \Pi_{bId} (Own)) / \Pi_{bId} (Brand) \right)$

Consider the following three relations in a relational database.$\text{Employee} (\underline{\text{eId}},\text{Name}), \; \text{Brand}(\underline{\text{bId}},\text{bName}...

8.5k views

asked Feb 15, 2022

12 votes

2 answers

287

GATE CSE 2022 | Question: 16
Which of the following statements is/are $\text{TRUE}$ with respect to deadlocks? Circular wait is a necessary condition for the formation of deadlock. In a system where each resource has more than one instance, a cycle in its wait-for graph ... the resource-allocation graph of a system, if every edge is an assignment edge, then the system is not in deadlock state.

Which of the following statements is/are $\text{TRUE}$ with respect to deadlocks?Circular wait is a necessary condition for the formation of deadlock.In a system where ea...

12.5k views

asked Feb 15, 2022

14 votes

2 answers

288

GATE CSE 2022 | Question: 17
Which of the following statements is/are $\text{TRUE}$ for a group $\textit{G}?$ If for all $x,y \in \textit{G}, \; (xy)^{2} = x^{2} y^{2},$ then $\textit{G}$ is commutative. If for all $x \in \textit{G}, \; x^{2} = 1,$ then ... $2,$ then $\textit{G}$ is commutative. If $\textit{G}$ is commutative, then a subgroup of $\textit{G}$ need not be commutative.

Which of the following statements is/are $\text{TRUE}$ for a group $\textit{G}?$If for all $x,y \in \textit{G}, \; (xy)^{2} = x^{2} y^{2},$ then $\textit{G}$ is commutati...

7.6k views

asked Feb 15, 2022

41 votes

3 answers

289

GATE CSE 2022 | Question: 18
Suppose a binary search tree with $1000$ distinct elements is also a complete binary tree. The tree is stored using the array representation of binary heap trees. Assuming that the array indices start with $0,$ the $3^{\text{rd}}$ largest element of the tree is stored at index ______________ .

Suppose a binary search tree with $1000$ distinct elements is also a complete binary tree. The tree is stored using the array representation of binary heap trees. Assumin...

15.3k views

asked Feb 15, 2022

6 votes

3 answers

290

GATE CSE 2022 | Question: 19
Consider the augmented grammar with $\{ +, {\ast}, (,),\text{id} \}$ as the set of terminals. $S' \rightarrow S$ $S \rightarrow S + R\; |\; R$ $R \rightarrow R {\ast} P \;| \;P$ $P \rightarrow (S)\; |\; \text{id} $ If $I_{0}$ is ... $\{ [S' \rightarrow S.], [S \rightarrow S. + R] \}$, then $\textit{goto(closure}(I_{0}), +)$ contains exactly ______________ items.

Consider the augmented grammar with $\{ +, {\ast}, (,),\text{id} \}$ as the set of terminals.$S’ \rightarrow S$$S \rightarrow S + R\; |\; R$$R \rightarrow R {\ast} P \;...

7.3k views

asked Feb 15, 2022

19 votes

5 answers

291

GATE CSE 2022 | Question: 20
Consider a simple undirected graph of $10$ vertices. If the graph is disconnected, then the maximum number of edges it can have is _______________ .

Consider a simple undirected graph of $10$ vertices. If the graph is disconnected, then the maximum number of edges it can have is _______________ .

8.9k views

asked Feb 15, 2022

15 votes

1 answer

292

GATE CSE 2022 | Question: 21
Consider a relation $R (A, B, C, D, E)$ with the following three functional dependencies. $AB \rightarrow C; \; BC \rightarrow D; \; C \rightarrow E;$ The number of superkeys in the relation $R$ is ______________ .

Consider a relation $R (A, B, C, D, E)$ with the following three functional dependencies.$AB \rightarrow C; \; BC \rightarrow D; \; C \rightarrow E;$The number of superke...

8.7k views

asked Feb 15, 2022

18 votes

3 answers

293

GATE CSE 2022 | Question: 22
The number of arrangements of six identical balls in three identical bins is _____________ .

The number of arrangements of six identical balls in three identical bins is _____________ .

10.5k views

asked Feb 15, 2022

13 votes

2 answers

294

GATE CSE 2022 | Question: 23
A cache memory that has a hit rate of $0.8$ has an access latency $10 \; \text{ns}$ and miss penalty $100 \; \text{ns}.$ An optimization is done on the cache to reduce the miss rate. However, the optimization results ... (rounded off to two decimal places) needed after the optimization such that it should not increase the average memory access time is _______________.

A cache memory that has a hit rate of $0.8$ has an access latency $10 \; \text{ns}$ and miss penalty $100 \; \text{ns}.$ An optimization is done on the cache to reduce th...

9.1k views

asked Feb 15, 2022

12 votes

4 answers

295

GATE CSE 2022 | Question: 24
The value of the following limit is ________________. $\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$

The value of the following limit is ________________.$$\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$$

6.5k views

asked Feb 15, 2022

16 votes

4 answers

296

GATE CSE 2022 | Question: 25
Consider the resolution of the domain name $\textsf{www.gate.org.in}$ by a $\text{DNS}$ resolver. Assume that no resource records are cached anywhere across the $\text{DNS}$ servers and that iterative query mechanism is used in the resolution. The number of $\text{DNS}$ query-response pairs involved in completely resolving the domain name is ________________.

Consider the resolution of the domain name $\textsf{www.gate.org.in}$ by a $\text{DNS}$ resolver. Assume that no resource records are cached anywhere across the $\text{DN...

11.4k views

asked Feb 15, 2022

26 votes

6 answers

297

GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$

Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below?$$ a_{n} = \left\{\begin{matrix} n + 1, &...

9.6k views

asked Feb 15, 2022

14 votes

3 answers

298

GATE CSE 2022 | Question: 27
Consider a simple undirected unweighted graph with at least three vertices. If $\textit{A}$ is the adjacency matrix of the graph, then the number of $3–$cycles in the graph is given by the trace of $\textit{A}^{3}$ $\textit{A}^{3}$ divided by $2$ $\textit{A}^{3}$ divided by $3$ $\textit{A}^{3}$ divided by $6$

Consider a simple undirected unweighted graph with at least three vertices. If $\textit{A}$ is the adjacency matrix of the graph, then the number of $3–$cycles in the g...

7.6k views

asked Feb 15, 2022

23 votes

2 answers

299

GATE CSE 2022 | Question: 28
Which one of the following statements is $\text{FALSE}?$ The $\text{TLB}$ performs an associative search in parallel on all its valid entries using page number of incoming virtual address. If the virtual address of a word given by $\text{CPU}$ has a ... $\text{V2}$ map to the same value while hashing, then the memory access time of these addresses will not be the same.

Which one of the following statements is $\text{FALSE}?$The $\text{TLB}$ performs an associative search in parallel on all its valid entries using page number of incoming...

8.1k views

asked Feb 15, 2022

12 votes

2 answers

300

GATE CSE 2022 | Question: 29
Let $\textit{R}_{i}(z)$ and $\textit{W}_{i}(z)$ denote read and write operations on a data element $z$ by a transaction $\textit{T}_{i},$ respectively. Consider the schedule $\textit{S}$ ... $T_{4} \rightarrow T_{1} \rightarrow T_{3} \rightarrow T_{2}$ $T_{3} \rightarrow T_{1} \rightarrow T_{4} \rightarrow T_{2}$

Let $\textit{R}_{i}(z)$ and $\textit{W}_{i}(z)$ denote read and write operations on a data element $z$ by a transaction $\textit{T}_{i},$ respectively. Consider the sched...

8.7k views

asked Feb 15, 2022

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