GATE CS question library

Which of the following Boolean algebraic equation(s) is/are CORRECT?

Despite his initial hesitation, Rehman's ____________ to contribute to the success of the project never wavered. Select the most appropriate option to complete the above sentence.

​​​​​Bird : Nest :: Bee : ______

​​​​​​If $P \: e^{x} = Q \: e^{-x}$ for all real values of $x$, which one of the following statements is true?

The paper as showin the figure is folded to make a cube where each square corresponds to a particular face of the cube. Which one of the following options correctly represents the cube? Note: The figures showin are representative.

​​​​​Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which one of the following statemetns is correct for all values of $p_1$ and $p_2$?

​​​​​Based only on the conversation below, identify the logically correct inference: "Even if I had known that you were in the hospital, I would not have gone there to see you", Ramya told Josephine.

​​​​If IMAGE and FIELD are coded as FHBNJ and EMFJG respectively then, which one among the given options is the most appropriate code for BEACH?

Which one of the following options is correct for the given data in the table? …

In the Given figure, PQRS is a square of side $2$ cm and PLMN is a rectangle. The corner L of teh rectangle is on the side QR. Side MN of the rectangle passes through the corner S of the square. What is the area (in $cm^2$) of the rectangle PLMN? Note: The figure shown is representative.

​​​​​​The diagram below shows a river system consisting of $7$ segments, marked $P, Q, R, S, T, U,$ and $V.$ It splits the land into $5$ zones, marked $Z1, Z2, Z3, Z4,$ and $Z5$. We need to connect these zones using the least number of bridges, Out of the following options, which one is correct? Note: The figure shown is representative.

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x)=\max \left\{x, x^3\right\}, x \in \mathbb{R}$, where $\mathbb{R}$ is the set of all real numbers. The set of all points where $f(x)$ is NOT differentiable is

The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is

Consider a system that uses $5$ bits for representing signed integers in $2$ 's complement format. In this system, two integers $A$ and $B$ are represented as $A$=$01010$ and $B$=$11010$. Which one of the following operations will result in either an arithmetic overflow or an arithmetic underflow?

Consider a permutation sampled uniformly at random from the set of all permutations of $\{1,2,3, \cdots, n\}$ for some $n \geq 4$. Let $X$ be the event that $1$ occurs before $2$ in the permutation, and $Y$ the event that $3$ occurs before $4$. Which one of the following statements is TRUE?

​​​​Which one of the following statements is FALSE?

A user starts browsing a webpage hosted at a remote server. The browser opens a single TCP connection to fetch the entire webpage from the server. The webpage consists of a top-level index page with multiple embedded image objects. Assume that all caches (e.g., DNS cache, browser cache) are all initially empty. The following packets leave the user's computer …

Given an integer array of size $N$, we want to check if the array is sorted (in either ascending or descending order). An algorithm solves this problem by making a single pass through the array and comparing each element of the array only with its adjacent elements. The worst-case time complexity of this algorithm is

Consider the following $\mathrm{C}$ program: #include <stdio.h> int main() { int a=6; int b = 0; while (a<10) { a = a / 12+1 ; a += b ;} printf ("%d", a); return 0 ; } Which one of the following statements is CORRECT?

​​​Consider the following $\mathrm{C}$ program: #include <stdio.h> void fX (); int main(){ fX(); return 0 }; void fX () { char a; if ((a=g e t c h a r()) ! = '\n') fX(); if (a ! = '\n') putchar (a); } Assume that the input to the program from the command line is $1234$ followed by a newline character. Which one of the following statements is …