GATE CS question library

Which one of the following is FALSE?

Suppose a disk has $201$ cylinders, numbered from $0$ to $200$. At some time the disk arm is at cylinder $100$, and there is a queue of disk access requests for cylinders $30, 85, 90, 100, 105, 110, 135$ and $145$. If Shortest-Seek Time First (SSTF) is being used for scheduling the disk access, the request for cylinder $90$ is serviced after …

Match the following: 1) Waterfall model a) Specifications can be developed incrementally 2) Evolutionary model b) Requirements compromises are inevitable 3) Component-based software engineering c) Explicit recognition of risk 4) Spiral development d) Inflexible partitioning of the project into stages

Consider the finite automaton in the following figure: What is the set of reachable states for the input string $0011$?

Which one of the following is TRUE?

Which one of the following is FALSE?

Consider the directed graph below given. Which one of the following is TRUE?

Let $P$ be quicksort program to sort numbers in ascending order using the first element as the pivot. Let $t_1$ and $t_2$ be the number of comparisons made by P for the inputs $[1 \ 2 \ 3 \ 4 \ 5]$ and $[4 \ 1 \ 5 \ 3 \ 2]$ respectively. Which one of the following holds?

Consider a rooted n node binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having exactly $4$ nodes is $O(n^a\log^bn)$. Then the value of $a+10b$ is __________.

Let $G$ be a graph with $n$ vertices and $m$ edges. What is the tightest upper bound on the running time of Depth First Search on $G$, when $G$ is represented as an adjacency matrix?

Consider the following program in C language: #include <stdio.h> main() { int i; int*pi = &i; scanf("%d",pi); printf("%d\n", i+5); } Which one of the following statements is TRUE?

The base (or radix) of the number system such that the following equation holds is____________. $\frac{312}{20} = 13.1$

A machine has a $32\text{-bit}$ architecture, with $1\text{-word}$ long instructions. It has $64$ registers, each of which is $32$ bits long. It needs to support $45$ instructions, which have an immediate operand in addition to two register operands. Assuming that the immediate operand is an unsigned integer, the maximum value of the immediate …

Consider the following Boolean expression for F: $F(P,Q,R,S)= PQ + \bar{P}QR + \bar{P}Q\bar{R}S$ The minimal sum$-$of$-$products form of $F$ is

Let the function $$f(\theta) = \begin{vmatrix} \sin\theta & \cos\theta & \tan\theta \\ \sin(\frac{\pi}{6}) & \cos(\frac{\pi}{6}) & \tan(\frac{\pi}{6}) & \\ \sin(\frac{\pi}{3}) & \cos(\frac{\pi}{3}) & \tan(\frac{\pi}{3}) \end{vmatrix}$$ where $\theta \in \left[ \frac{\pi}{6},\frac{\pi}{3} \right]$ and $f'(\theta)$ denote the …

The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a $4-by-4$ symmetric positive definite matrix is ___________

Consider the following system of equations: $3x + 2y = 1$ $4x + 7z = 1$ $x + y + z = 3$ $x - 2y + 7z = 0$ The number of solutions for this system is ______________

Let $G=(V,E)$ be a directed graph where $V$ is the set of vertices and $E$ the set of edges. Then which one of the following graphs has the same strongly connected components as $G$ ?

Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .

When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines?