GATE CS question library

Given below are four statements. Statement $1:$ All students are inquisitive. Statement $2:$ Some students are inquisitive. Statement $3:$ No student is inquisitive. Statement $4:$ Some students are not inquisitive. From the given four statements, find the two statements that $\text{CANNOT BE TRUE}$ simultaneously, assuming that there is at least …

A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters. From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome. The player should use all the five plates exactly …

Some people believe that “what gets measured, improves”. Some others believe that “what gets measured, gets gamed”. One possible reason for the difference in the beliefs is the work culture in organizations. In organizations with good work culture, metrics help improve outcomes. However, the same metrics are counterproductive in organizations with poor work …

In a recently conducted national entrance test, boys constituted $65 \%$ of those who appeared for the test. Girls constituted the remaining candidates and they accounted for $60 \%$ of the qualified candidates. Which one of the following is the correct logical inference based on the information provided in the above passage?

A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is replaced with another orange ball. First ball is drawn. What is the probability of getting an orange …

The corners and mid-points of the sides of a triangle are named using the distinct letters $\text{P, Q, R, S, T}$ and $\text{U,}$ but not necessarily in the same order. Consider the following statements: The line joining $\text{P}$ and $\text{R}$ is parallel to the line joining $\text{Q}$ and $\text{S}.$ $\text{P}$ is placed on the side …

A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land has equally spaced poles, marked as dots in the below figure. Two ropes, $\text{R1}$ and $\text{R2},$ are already present and cannot be moved. What is the least number of $\textsf{additional}$ straight …

​​​​​​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?