GATE CS question library

​​​​​​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:

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?

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 _______.

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?

___________ is to surgery as writer is to ___________ Which one of the following options maintains a similar logical relation in the above sentence?

$$\begin{array}{|c|c|c|c|} \hline \textbf{Items} & \textbf{Cost} & \textbf{Profit \%} & \textbf{Marked Price} \\ & \text{(₹)} & & \text{(₹)} \\ \hline P &5,400 &---&5,860\\ \hline Q&---&25&10,000\\ \hline\end{array}$$ Details of prices of two items $P$ and $Q$ are presented in the above table. The ratio of …

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 __________

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. $\text{Conclusion I:}$ Some pathogens are bacteria. $\text{Conclusion II:}$ All pathogens are not bacteria. Based on the above statements and …

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 passage?

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?

​​​​​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?

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?

Consider the following statements. $S_1:$ The sequence of procedure calls corresponds to a preorder traversal of the activation tree. $S_2:$ The sequence of procedure returns corresponds to a postorder traversal of the activation tree. Which one of the following options is correct?

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 $n$. Which one of the following options is correct?

Let the representation of a number in base $3$ be $210$. What is the hexadecimal representation of the number?

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?

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?

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?

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 $T$?

In the context of operating systems, which of the following statements is/are correct with respect to paging?