Questions by Arjun

17 votes

3 answers

121

GATE CSE 2021 Set 2 | Question: 9
Let $L \subseteq \{0,1\}^*$ be an arbitrary regular language accepted by a minimal $\text{DFA}$ with $k$ states. Which one of the following languages must necessarily be accepted by a minimal $\text{DFA}$ with $k$ states? $L-\{01\}$ $L \cup \{01\}$ $\{0,1\}^* – L$ $L \cdot L$

asked in Theory of Computation Feb 18, 2021

5.3k views

23 votes

9 answers

122

GATE CSE 2021 Set 2 | Question: 10
Consider the following $\text{ANSI C}$ program. #include <stdio.h> int main() { int arr[4][5]; int i, j; for (i=0; i<4; i++) { for (j=0; j<5; j++) { arr[i][j] = 10 * i + j; } } printf(“%d”, *(arr[1]+9)); return 0; } What is the output of the above program? $14$ $20$ $24$ $30$

asked in Programming Feb 18, 2021

21.8k views

17 votes

3 answers

123

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 $S_2$

asked in Set Theory & Algebra Feb 18, 2021

3.9k views

13 votes

2 answers

124

GATE CSE 2021 Set 2 | Question: 12
Let $L_1$ be a regular language and $L_2$ be a context-free language. Which of the following languages is/are context-free? $L_1 \cap \overline{L_2} \\$ $\overline{\overline{L_1} \cup \overline{L_2}} \\$ $L_1 \cup (L_2 \cup \overline{L_2}) \\$ $(L_1 \cap L_2) \cup (\overline{L_1} \cap L_2)$

asked in Theory of Computation Feb 18, 2021

6.1k views

6 votes

4 answers

125

GATE CSE 2021 Set 2 | Question: 13
In the context of compilers, which of the following is/are $\text{NOT}$ an intermediate representation of the source program? Three address code Abstract Syntax Tree $\text{(AST)}$ Control Flow Graph $\text{(CFG)}$ Symbol table

asked in Compiler Design Feb 18, 2021

4.3k views

15 votes

2 answers

126

GATE CSE 2021 Set 2 | Question: 14
Which of the following statement(s) is/are correct in the context of $\text{CPU}$ scheduling? Turnaround time includes waiting time The goal is to only maximize $\text{CPU}$ utilization and minimize throughput Round-robin policy ... $\text{CPU}$ time required by each of the processes is not known apriori Implementing preemptive scheduling needs hardware support

asked in Operating System Feb 18, 2021

6.4k views

12 votes

5 answers

127

GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$

asked in Mathematical Logic Feb 18, 2021

4.6k views

7 votes

3 answers

128

GATE CSE 2021 Set 2 | Question: 16
Consider a complete binary tree with $7$ nodes. Let $A$ denote the set of first $3$ elements obtained by performing Breadth-First Search $\text{(BFS)}$ starting from the root. Let $B$ denote the set of first $3$ elements obtained by performing Depth-First Search $\text{(DFS)}$ starting from the root. The value of $\mid A-B \mid $ is _____________

asked in DS Feb 18, 2021

7.1k views

16 votes

6 answers

129

GATE CSE 2021 Set 2 | Question: 17
Consider the following deterministic finite automaton $\text{(DFA)}$ The number of strings of length $8$ accepted by the above automaton is ___________

asked in Theory of Computation Feb 18, 2021

5.4k views

11 votes

3 answers

130

GATE CSE 2021 Set 2 | Question: 18
If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________

asked in Digital Logic Feb 18, 2021

2.9k views

11 votes

4 answers

131

GATE CSE 2021 Set 2 | Question: 19
Consider a set-associative cache of size $\text{2KB (1KB} =2^{10}$ bytes$\text{)}$ with cache block size of $64$ bytes. Assume that the cache is byte-addressable and a $32$ -bit address is used for accessing the cache. If the width of the tag field is $22$ bits, the associativity of the cache is _________

asked in CO and Architecture Feb 18, 2021

4.2k views

19 votes

3 answers

132

GATE CSE 2021 Set 2 | Question: 20
Consider a computer system with $\text{DMA}$ support. The $\text{DMA}$ module is transferring one $8$-bit character in one $\text{CPU}$ cycle from a device to memory through cycle stealing at regular intervals. Consider a $\text{2 MHz}$ ... $\text{DMA}$, the data transfer rate of the device is __________ bits per second.

asked in CO and Architecture Feb 18, 2021

6.4k views

13 votes

1 answer

133

GATE CSE 2021 Set 2 | Question: 21
A data file consisting of $1,50,000$ student-records is stored on a hard disk with block size of $4096$ bytes. The data file is sorted on the primary key $\textrm{RollNo}$. The size of a record pointer for this disk is $7$ bytes. ... that the records of data file and index file are not split across disk blocks. The number of blocks in the index file is ________

asked in Databases Feb 18, 2021

5.2k views

10 votes

1 answer

134

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 _________

asked in Probability Feb 18, 2021

3.4k views

6 votes

2 answers

135

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 __________

asked in Algorithms Feb 18, 2021

2.9k views

25 votes

7 answers

136

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 __________

asked in Linear Algebra Feb 18, 2021

9.4k views

10 votes

2 answers

137

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 __________

asked in Calculus Feb 18, 2021

3.4k views

9 votes

2 answers

138

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? $21$ $23$ $25$ $30$

asked in Algorithms Feb 18, 2021

5.4k views

12 votes

2 answers

139

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

asked in CO and Architecture Feb 18, 2021

4.7k views

15 votes

3 answers

140

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 $0$ ... $\begin{array}{l} t=s+b \\ y=s \overline{b} \end{array}$

asked in Theory of Computation Feb 18, 2021

4.5k views

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