# Recent questions tagged gate2021-cse-set1

1
​​​​​​The ratio of boys to girls in a class is $7$ to $3$. Among the options below, an acceptable value for the total number of students in the class is: $21$ $37$ $50$ $73$
2
A polygon is convex if, for every pair of points, $\text{P}$ and $\text{Q}$ belonging to the polygon, the line segment $\text{PQ}$ lies completely inside or on the polygon. Which one of the following is $\underline{\text{NOT}}$ a convex polygon?
3
Consider the following sentences: Everybody in the class is prepared for the exam. Babu invited Danish to his home because he enjoys playing chess. Which of the following is the $\text{CORRECT}$ observation about the above two sentences? $\text{(i)}$ is grammatically correct and ... correct and $\text{(ii)}$ is ambiguous $\text{(i)}$ is grammatically incorrect and $\text{(ii)}$ is ambiguous
4
A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like _______.
5
___________ is to surgery as writer is to ___________ Which one of the following options maintains a similar logical relation in the above sentence? Plan, outline Hospital, library Doctor, book Medicine, grammar
6
We have $2$ rectangular sheets of paper, $\text{M}$ and $\text{N}$, of dimensions $\text{6 cm$\times$1 cm}$ each. Sheet $\text{M}$ is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet $\text{N}$ is cut into equal square patches and assembled ... volume of the cylinder to that of the cube is _________. $\frac{\pi}{2}$ $\frac{3}{\pi}$ $\frac{9}{\pi}$ $3\pi$
7
$\begin{array}{|c|c|c|c|} \hline \textbf{Items} & \textbf{Cost} & \textbf{Profit %} & \textbf{Marked Price} \\ & (₹) & & (₹) \\\hline P &5,400 &---&5,860\\\hline Q&---&25&10,000\\\hline\end{array}$ Details of prices of two items $P$ and $Q$ are presented in ... $Q$, as a percentage of its marked price, is _______ $25$ $12.5$ $10$ $5$
8
There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is __________ $0.3024$ $0.4235$ $0.6976$ $0.8125$
9
Given below are two statements $1$ and $2$, and two conclusions $\text{I}$ and $\text{II}$ $\text{Statement 1:}$ All bacteria are microorganisms. $\text{Statement 2:}$ All pathogens are microorganisms. $\text{Conclusion I:}$ ... is correct Either conclusion $\text{I}$ or $\text{II}$ is correct Neither conclusion $\text{I}$ nor $\text{II}$ is correct
10
Some people suggest anti-obesity measures $\text{(AOM)}$ such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality. Which one of the following statements summarizes the ... $\text{AOM}$ are addressing the problem superficially
1 vote
11
Suppose that $L_1$ is a regular language and $L_2$ is a context-free language. Which one of the following languages is $\text{NOT}$ necessarily context-free? $L_1 \cap L_2$ $L_1 \cdot L_2$ $L_1- L_2$ $L_1\cup L_2$
12
Let $P$ be an array containing $n$ integers. Let $t$ be the lowest upper bound on the number of comparisons of the array elements, required to find the minimum and maximum values in an arbitrary array of $n$ elements. Which one of the following choices is correct? $t>2n-2$ ... $t>n \text{ and } t\leq 3\lceil \frac{n}{2}\rceil$ $t>\lceil \log_2(n)\rceil \text{ and } t\leq n$
13
Consider the following three functions. $f_1=10^n\quad f_2=n^{\log n}\quad f_3=n^{\sqrt {n}}$ Which one of the following options arranges the functions in the increasing order of asymptotic growth rate? $f_3, f_2, f_1$ $f_2, f_1, f_3$ $f_1, f_2,f_3$ $f_2, f_3, f_1$
14
Consider the following statements. $S_1:\quad$ The sequence of procedure calls corresponds to a preorder traversal of the activation tree. $S_2:\quad$ The sequence of procedure returns corresponds to a postorder traversal of the activation tree. Which one of the following options is correct? $S_1$ is ... $S_2$ is true $S_1$ is true and $S_2$ is true $S_1$ is false and $S_2$ is false
1 vote
15
Consider the following statements. $S_1:$ Every $\text{SLR(1)}$ grammar is unambiguous but there are certain unambiguous grammars that are not $\text{SLR(1)}$. $S_2:$ For any context-free grammar, there is a parser that takes at most $O(n^3)$ time to parse a string of length $n$. ... $S_2$ is 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
1 vote
16
Let the representation of a number in base $3$ be $210$. What is the hexadecimal representation of the number? $15$ $21$ $\text{D}2$ $528$
1 vote
17
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and $S_2$ are tautologies ... tautology but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology
1 vote
18
Consider the following two statements. $S_1$: Destination $\text{MAC}$ address of an $\text{ARP}$ reply is a broadcast address. $S_2$: Destination $\text{MAC}$ address of an $\text{ARP}$ request is a broadcast address. Which one of the following choices is correct? Both $S_1$ and $S_2$ are true $S_1$ is true and $S_2$ is false $S_1$ is false and $S_2$ is true Both $S_1$ and $S_2$ are false
1 vote
19
Consider the following array.$\begin{array}{|l|l|l|l|l|l|} \hline 23&32&45&69&72&73&89&97 \\ \hline\end{array}$ Which algorithm out of the following options uses the least number of comparisons (among the array elements) to sort the above array in ascending order? Selection sort Mergesort Insertion sort Quicksort using the last element as pivot
20
A binary search tree $T$ contains $n$ distinct elements. What is the time complexity of picking an element in $T$ that is smaller than the maximum element in $T$? $\Theta(n\log n)$ $\Theta(n)$ $\Theta(\log n)$ $\Theta (1)$
21
In the context of operating systems, which of the following statements is/are correct with respect to paging? Paging helps solve the issue of external fragmentation Page size has no impact on internal fragmentation Paging incurs memory overheads Multi-level paging is necessary to support pages of different sizes
22
Let $\langle M \rangle$ denote an encoding of an automaton $M$. Suppose that $\Sigma = \{0,1\}$. Which of the following languages is/are $\text{NOT}$ recursive? $L= \{ \langle M \rangle \mid M$ is a $\text{DFA}$ such that $L(M)=\emptyset \}$ $L= \{ \langle M \rangle \mid M$ is ... $L(M)=\emptyset \}$ $L= \{ \langle M \rangle \mid M$ is a $\text{PDA}$ such that $L(M)=\Sigma ^* \}$
23
Suppose a database system crashes again while recovering from a previous crash. Assume checkpointing is not done by the database either during the transactions or during recovery. Which of the following statements is/are correct? The same undo and redo list ... any further All the transactions that are already undone and redone will not be recovered again The database will become inconsistent
24
Which of the following standard $C$ library functions will always invoke a system call when executed from a single-threaded process in a $\text{UNIX/Linux}$ operating system? $\textsf{exit}$ $\textsf{malloc}$ $\textsf{sleep}$ $\textsf{strlen}$
1 vote
25
Consider a linear list based directory implementation in a file system. Each directory is a list of nodes, where each node contains the file name along with the file metadata, such as the list of pointers to the data blocks. Consider a given directory $\textsf{foo}$. Which of ... file from $\textsf{foo}$ Renaming of an existing file in $\textsf{foo}$ Opening of an existing file in $\textsf{foo}$
1 vote
26
In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is _________.
27
Consider the following undirected graph with edge weights as shown: The number of minimum-weight spanning trees of the graph is ___________.
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter $2$. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to $2$ decimal places) is ____________.
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.
Consider the following expression. $\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$ The value of the above expression (rounded to 2 decimal places) is ___________.