# Recent questions tagged gate2021-cse-set2

1
Gauri said that she can play the keyboard __________ her sister. as well as as better as as nicest as as worse as
2
A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ___________.
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, $\cos \theta =$ $\frac{1}{2} \\$ $\frac{1}{\sqrt{3}} \\$ $\frac{1}{\sqrt{2}} \\$ $\frac{\sqrt{3}}{2}$
4
​​​​​​If $\left( x – \dfrac{1}{2} \right)^2 – \left( x- \dfrac{3}{2} \right) ^2 = x+2$, then the value of $x$ is: $2$ $4$ $6$ $8$
1 vote
5
$\text{Pen : Write :: Knife :}$ _______ Which one of the following options maintains a similar logical relation in the above? Vegetables Sharp Cut Blunt
6
Listening to music during exercise improves performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while ... clear positive effect on learning in all students. Music has a positive effect only in some students who exercise
7
A jigsaw puzzle has $2$ pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.
8
The number of students in three classes is in the ratio $3:13:6$. If $18$ students are added to each class, the ratio changes to $15:35:21$. The total number of students in all the three classes in the beginning was: $22$ $66$ $88$ $110$
9
The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year $3$ was $₹\;1$, which was half the cost/unit in Year $2$. The cost/unit in Year $3$ was one-third of the cost/unit in Year $1$. ... The ratio of the selling price in Year $2$ to the selling price in Year $3$ is _________. $4:3$ $1:1$ $3:4$ $1:2$
10
Six students $\text{P, Q, R, S, T and U}$, with distinct heights, compare their heights and make the following observations. $\text{Observation I}$: $\text{S}$ is taller than $\text{R}$. $\text{Observation II}$: $\text{Q}$ is the shortest of all. $\text{Observation III}$: ... $\text{R}$ is the same as the number of students shorter than ____________. $\text{T}$ $\text{R}$ $\text{S}$ $\text{P}$
11
Let $G$ be a connected undirected weighted graph. Consider the following two statements. $S_1$: There exists a minimum weight edge in $G$ which is present in every minimum spanning tree of $G$. $S_2$: If every edge in $G$ has distinct weight, then $G$ has a unique minimum spanning ... $S_1$ is true and $S_2$ is false $S_1$ is false and $S_2$ is true Both $S_1$ and $S_2$ are false
12
​​​​​Let $H$ be a binary min-heap consisting of $n$ elements implemented as an array. What is the worst case time complexity of an optimal algorithm to find the maximum element in $H$? $\Theta (1)$ $\Theta (\log n)$ $\Theta (n)$ $\Theta (n \log n)$
13
Consider the following $\text{ANSI C}$ program: int main () { Integer x; return 0; } Which one of the following phases in a seven-phase $C$ compiler will throw an error? Lexical analyzer Syntax analyzer Semantic analyzer Machine dependent optimizer
14
The format of the single-precision floating point representation of a real number as per the $\text{IEEE 754}$ ... $=00000000$ and mantissa $=0000000000000000000000001$ exponent $=00000001$ and mantissa $=0000000000000000000000000$ exponent $=00000001$ and mantissa $=0000000000000000000000001$
15
Which one of the following circuits implements the Boolean function given below? $f(x,y,z) = m_0+m_1+m_3+m_4+m_5+m_6$, where $m_i$ is the $i^{\text{th}}$ minterm.
16
Consider the following statements $S1$ and $S2$ about the relational data model: $S1$: A relation scheme can have at most one foreign key. $S2$: A foreign key in a relation scheme $R$ cannot be used to refer to tuples of $R.$ Which one of the following choices is correct? Both $S1$ and $S2$ are true $S1$ is true and $S2$ is false $S1$ is false and $S2$ is true Both $S1$ and $S2$ are false
17
Consider the three-way handshake mechanism followed during $\text{TCP}$ connection establishment between hosts $P$ and $Q$. Let $X$ and $Y$ be two random $32$-bit starting sequence numbers chosen by $P$ and $Q$ respectively. Suppose $P$ sends a $\text{TCP}$ connection request message to $Q$ with a ... $\text{SEQ}$ number $=Y$, $\text{ACK}$ bit $=1$, $\text{ACK}$ number $=X$, $\text{FIN}$ bit $=0$
18
What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size $n$? $\Theta ( \sqrt{n})$ $\Theta (\log _2(n))$ $\Theta(n^2)$ $\Theta(n)$
19
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? $L-\{01\}$ $L \cup \{01\}$ $\{0,1\}^* – L$ $L \cdot L$
20
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? $14$ $20$ $24$ $30$
21
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 $\{0,1,2, \dots, n^2-1\}$ to the set $\{0, 1, 2\}$ Which of the following ... to $S_2$ 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 $S_2$
22
Let $L_1$ be a regular language and $L_2$ be a context-free language. Which of the following languages is/are context-free? $L_1 \cap \overline{L_2} \\$ $\overline{\overline{L_1} \cup \overline{L_2}} \\$ $L_1 \cup (L_2 \cup \overline{L_2}) \\$ $(L_1 \cap L_2) \cup (\overline{L_1} \cap L_2)$
1 vote
23
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
1 vote
24
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 can be used even when the $\text{CPU}$ time required by each of the processes is not known apriori Implementing preemptive scheduling needs hardware support
25
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 $S$
26
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 _____________
27
Consider the following deterministic finite automaton $\text{(DFA)}$ The number of strings of length $8$ accepted by the above automaton is ___________
28
If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________
29
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 _________
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 $\text{2 MHz}$ processor. If $0.5 \%$ processor cycles are used for $\text{DMA}$, the data transfer rate of the device is __________ bits per second.