Previous GATE Questions / GATE Overflow for GATE CSE

1 votes

2 answers

41

GATE CSE 2024 | Set 2 | Question: 31
Let $\text{M}$ be the $5$-state $\text{NFA}$ with $\epsilon$-transitions shown in the diagram below. Which one of the following regular expressions represents the language accepted by $\text{M}$? $(00)^{*}+1(11)^{*}$ $0^{*}+\left(1+0(00)^{*}\right)(11)^{*}$ $(00)^{*}+\left(1+(00)^{*}\right)(11)^{*}$ $0^{+}+1(11)^{*}+0(11)^{*}$

Let $\text{M}$ be the $5$-state $\text{NFA}$ with $\epsilon$-transitions shown in the diagram below.Which one of the following regular expressions represents the la...

Arjun

2.3k views

Arjun asked Feb 16

3 votes

2 answers

42

GATE CSE 2024 | Set 2 | Question: 32
Consider an array $\mathrm{X}$ that contains $\mathrm{n}$ positive integers. A subarray of $\mathrm{X}$ is defined to be a sequence of array locations with consecutive indices. The $\mathrm{C}$ code snippet given below has been written to compute the length of the longest ... $\text{(P) } \text{len} 2+1$ $\text{(Q) } \text{len} 1+1$

Consider an array $\mathrm{X}$ that contains $\mathrm{n}$ positive integers. A subarray of $\mathrm{X}$ is defined to be a sequence of array locations with co...

Arjun

1.9k views

Arjun asked Feb 16

2 votes

1 answer

43

GATE CSE 2024 | Set 2 | Question: 33
Consider the following expression: $x[i]=(p+r) *-s[i]+u / w$. The following sequence shows the list of triples representing the given expression, with entries missing for triples $(1), (3)$, and $(6)$ ... $(1)$ [ ]$=s i \quad(3)-(0)(2) \quad(6)=[ ] x i$

Consider the following expression: $x[i]=(p+r) *-s[i]+u / w$. The following sequence shows the list of triples representing the given expression, with entries missing ...

Arjun

1.6k views

Arjun asked Feb 16

2 votes

3 answers

44

GATE CSE 2024 | Set 2 | Question: 34
Let $x$ and $y$ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let $z=x y$ and let the mean values of $x, y, z$ be $\bar{x}, \bar{y}, \bar{z}$ ... $\bar{z} \leq \bar{x} \bar{y}$ $\bar{z} \geq \bar{x} \bar{y}$ $\bar{z} \leq \bar{x}$

Let $x$ and $y$ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let $z=x y$ and let the mean values of $x, y, z$ be $\bar...

Arjun

2.6k views

Arjun asked Feb 16

2 votes

1 answer

45

GATE CSE 2024 | Set 2 | Question: 35
The relation schema, Person (pid, city), describes the city of residence for every person uniquely identified by pid. The following relational algebra operators are available: selection, projection, cross product, and rename. To find the list of cities ... above operators, the minimum number of cross product operations that must be used is $1$ $2$ $3$ $4$

The relation schema, Person (pid, city), describes the city of residence for every person uniquely identified by pid. The following relational algebra oper...

Arjun

2.2k views

Arjun asked Feb 16

2 votes

1 answer

46

GATE CSE 2024 | Set 2 | Question: 36
Consider a multi-threaded program with two threads $\mathrm{T} 1$ and $\mathrm{T} 2$. The threads share two semaphores: $s1$ (initialized to $1$) and $s2$ (initialized to $0$). The threads also share a global variable $\mathrm{x}$ ( ... not print anything (deadlock) $\mathrm{T} 2$ runs first and prints $1, \mathrm{~T} 1$ does not print anything (deadlock)

Consider a multi-threaded program with two threads $\mathrm{T} 1$ and $\mathrm{T} 2$. The threads share two semaphores: $s1$ (initialized to $1$) and $s2$ ...

Arjun

2.2k views

Arjun asked Feb 16

6 votes

2 answers

47

GATE CSE 2024 | Set 2 | Question: 37
Let $A$ be an $n \times n$ matrix over the set of all real numbers $\mathbb{R}$. Let $B$ be a matrix obtained from $A$ by swapping two rows. Which of the following statements is/are TRUE? The determinant of $B$ is the negative of the ... If $A$ is symmetric, then $B$ is also symmetric If the trace of $A$ is zero, then the trace of $B$ is also zero

Let $A$ be an $n \times n$ matrix over the set of all real numbers $\mathbb{R}$. Let $B$ be a matrix obtained from $A$ by swapping two rows. Which of the f...

Arjun

2.2k views

Arjun asked Feb 16

1 votes

1 answer

48

GATE CSE 2024 | Set 2 | Question: 38
Let $\mathrm{S} 1$ and $\mathrm{S} 2$ be two stacks. $\mathrm{S} 1$ has capacity of $4$ elements. $\mathrm{S} 2$ has capacity of $2$ elements. $\text{S1}$ already has $4$ elements: $100,200,300$, and $400$ ... output sequences can be generated by using the above operations? $100,200,400,300$ $200,300,400,100$ $400,200,100,300$ $300,200,400,100$

Let $\mathrm{S} 1$ and $\mathrm{S} 2$ be two stacks. $\mathrm{S} 1$ has capacity of $4$ elements. $\mathrm{S} 2$ has capacity of $2$ elements. $\text{S1}$ ...

Arjun

2.0k views

Arjun asked Feb 16

1 votes

1 answer

49

GATE CSE 2024 | Set 2 | Question: 39
Which of the following is/are EQUAL to $224$ in radix - $5$ (i.e., base - $5$) notation? $64$ in radix -10 $100$ in radix -8 $50$ in radix -16 $121$ in radix -7

Which of the following is/are EQUAL to $224$ in radix - $5$ (i.e., base - $5$) notation?$64$ in radix -10$100$ in radix -8$50$ in radix -16$121$ in radix -7

Arjun

1.7k views

Arjun asked Feb 16

3 votes

1 answer

50

GATE CSE 2024 | Set 2 | Question: 40
Consider $4$-variable functions $f 1, f 2, f 3, f 4$ expressed in sum-of-minterms form as given below. \[ \begin{array}{l} f 1=\sum(0,2,3,5,7,8,11,13) \\ f 2=\sum(1,3,5,7,11,13,15) \\ f 3=\sum(0,1,4,11) \\ f 4=\sum(0,2,6,13) \end{array} \] With ... $\boldsymbol{Y}=\sum(0,1,2,3,4,5,6,7)$ $\boldsymbol{Y}=\Pi(8,9,10,11,12,13,14,15)$

Consider $4$-variable functions $f 1, f 2, f 3, f 4$ expressed in sum-of-minterms form as given below.\[\begin{array}{l}f 1=\sum(0,2,3,5,7,8,11,13) \\f 2=\sum(1,3,5,7,11,...

Arjun

1.8k views

Arjun asked Feb 16

1 votes

1 answer

51

GATE CSE 2024 | Set 2 | Question: 41
Let $\text{G}$ be an undirected connected graph in which every edge has a positive integer weight. Suppose that every spanning tree in $\text{G}$ has even weight. Which of the following statements is/are TRUE for every such graph $\text{G}$ ... $\text{C}$ have even weight $\text{OR}$ all edges in $\text{C}$ have odd weight

Let $\text{G}$ be an undirected connected graph in which every edge has a positive integer weight. Suppose that every spanning tree in $\text{G}$ has even weight. Which o...

Arjun

2.0k views

Arjun asked Feb 16

2 votes

1 answer

52

GATE CSE 2024 | Set 2 | Question: 42
Consider a context-free grammar $\text{G}$ with the following $3$ rules. \[ S \rightarrow a S, S \rightarrow a S b S , S \rightarrow c \] Let $w \in L(G)$. Let $ n_{a}(w), n_{b}(w), n_{c}(w) $ denote the number of times $a, b, c$ occur in $w$, respectively. Which of ... $n_{a}(w)>n_{c}(w)-2$ $n_{c}(w)=n_{b}(w)+1$ $n_{c}(w)=n_{b}(w) * 2$

Consider a context-free grammar $\text{G}$ with the following $3$ rules.\[S \rightarrow a S, S \rightarrow a S b S , S \rightarrow c\]Let $w \in L(G)$...

Arjun

1.8k views

Arjun asked Feb 16

2 votes

1 answer

53

GATE CSE 2024 | Set 2 | Question: 43
Consider a disk with the following specifications: rotation speed of $6000$ RPM, average seek time of $5$ milliseconds, $500$ sectors/track, $512$-byte sectors. A file has content stored in $3000$ sectors located randomly on the disk. Assuming ... total time (in seconds, rounded off to $2$ decimal places) to read the entire file from the disk is ______________.

Consider a disk with the following specifications: rotation speed of $6000$ RPM, average seek time of $5$ milliseconds, $500$ sectors/track, $512$-byte sectors. A file ha...

Arjun

1.7k views

Arjun asked Feb 16

2 votes

2 answers

54

GATE CSE 2024 | Set 2 | Question: 44
Consider a $\text{TCP}$ connection operating at a point of time with the congestion window of size $12$ $\text{MSS}$ (Maximum Segment Size), when a timeout occurs due to packet loss. Assuming that all the segments transmitted in the next ... Time) are acknowledged correctly, the congestion window size (in $MSS$) during the third $\text{RTT}$ will be __________.

Consider a $\text{TCP}$ connection operating at a point of time with the congestion window of size $12$ $\text{MSS}$ (Maximum Segment Size), when a timeout occurs due to ...

Arjun

1.7k views

Arjun asked Feb 16

2 votes

2 answers

55

GATE CSE 2024 | Set 2 | Question: 45
Consider an Ethernet segment with a transmission speed of $10^{8} \mathrm{bits} / \mathrm{sec}$ and a maximum segment length of $500$ meters. If the speed of propagation of the signal in the medium is $2 \times 10^{8} \mathrm{~meters} / \mathrm{sec}$, then the minimum frame size (in bits) required for collision detection is ___________.

Consider an Ethernet segment with a transmission speed of $10^{8} \mathrm{bits} / \mathrm{sec}$ and a maximum segment length of $500$ meters. If the speed of propagation ...

Arjun

1.6k views

Arjun asked Feb 16

1 votes

1 answer

56

GATE CSE 2024 | Set 2 | Question: 46
A functional dependency $F: X \rightarrow Y$ is termed as a useful functional dependency if and only if it satisfies all the following three conditions: $\text{X}$ is not the empty set. $\text{Y}$ is not the empty set. Intersection ... set. For a relation $\text{R}$ with $4$ attributes, the total number of possible useful functional dependencies is __________.

A functional dependency $F: X \rightarrow Y$ is termed as a useful functional dependency if and only if it satisfies all the following three conditions:$\text{X}$ is not ...

Arjun

1.7k views

Arjun asked Feb 16

2 votes

1 answer

57

GATE CSE 2024 | Set 2 | Question: 47
A processor with $16$ general purpose registers uses a $32$-bit instruction format. The instruction format consists of an opcode field, an addressing mode field, two register operand fields, and a $16$-bit scalar field. If $8$ addressing modes are to be supported, the maximum number of unique opcodes possible for every addressing mode is ___________.

A processor with $16$ general purpose registers uses a $32$-bit instruction format. The instruction format consists of an opcode field, an addressing mode field, two regi...

Arjun

1.7k views

Arjun asked Feb 16

2 votes

0 answers

58

GATE CSE 2024 | Set 2 | Question: 48
A non-pipelined instruction execution unit operating at $2 \mathrm{GHz}$ takes an average of $6$ cycles to execute an instruction of a program $\text{P}$. The unit is then redesigned to operate on a $5$ ... hazards. The speedup (rounded off to one decimal place) obtained by the pipelined design over the non-pipelined design is ____________.

A non-pipelined instruction execution unit operating at $2 \mathrm{GHz}$ takes an average of $6$ cycles to execute an instruction of a program $\text{P}$. The unit is the...

Arjun

1.7k views

Arjun asked Feb 16

1 votes

1 answer

59

GATE CSE 2024 | Set 2 | Question: 49
The number of distinct minimum-weight spanning trees of the following graph is

The number of distinct minimum-weight spanning trees of the following graph is

Arjun

1.9k views

Arjun asked Feb 16

1 votes

3 answers

60

GATE CSE 2024 | Set 2 | Question: 50
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is __________.

The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is __________.

Arjun

1.9k views

Arjun asked Feb 16

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