GATE CS question library

Consider two hosts $P$ and $Q$ connected through a router $R$. The maximum transfer unit $\text{(MTU)}$ value of the link between $P$ and $R$ is $1500$ bytes, and between $R$ and $Q$ is $820$ bytes. A $\text{TCP}$ segment of size $1400$ bytes was transferred from $P$ to $Q$ through $R$, with $\text{IP}$ identification value as …

Consider the following pseudocode, where $\textsf{S}$ is a semaphore initialized to $5$ in line $\#2$ and $\textsf{counter}$ is a shared variable initialized to $0$ in line $\#1$. Assume that the increment operation in line $\#7$ is $\textit{not}$ atomic. 1. int counter = 0; 2. Semaphore S = init(5); 3. void parop(void) 4. { 5. wait(S); 6. …

Consider a $\textit{dynamic}$ hashing approach for $4$-bit integer keys: There is a main hash table of size $4$. The $2$ least significant bits of a key is used to index into the main hash table. Initially, the main hash table entries are empty. Thereafter, when more keys are hashed into it, to resolve collisions, the set of all keys corresponding to …

Consider the following $\text{ANSI C}$ function: int SimpleFunction(int Y[], int n, int x) { int total = Y[0], loopIndex; for (loopIndex=1; loopIndex<=n-1; loopIndex++) total=x*total +Y[loopIndex]; return total; } Let $\textsf{Z}$ be an array of $10$ elements with $\textsf{Z}[i]=1$, for all $i$ such that $0 \leq i \leq 9$. The value returned …

Consider the sliding window flow-control protocol operating between a sender and a receiver over a full-duplex error-free link. Assume the following: The time taken for processing the data frame by the receiver is negligible. The time taken for processing the acknowledgement frame by the sender is negligible. The sender has infinite number of frames …

In a pushdown automaton $P=(Q, \Sigma, \Gamma, \delta, q_0, F)$, a transition of the form, where $p,q \in Q$, $a \in \Sigma \cup \{ \epsilon \}$, and $X,Y \in \Gamma \cup \{ \epsilon \}$, represents $$(q,Y) \in \delta(p,a,X).$$Consider the following pushdown automaton over the input alphabet $\Sigma = \{a,b\}$ and stack alphabet …

Consider the following $C$ code segment: a = b + c; e = a + 1; d = b + c; f = d + 1; g = e + f; In a compiler, this code segment is represented internally as a directed acyclic graph $\text{(DAG)}$. The number of nodes in the $\text{DAG}$ is _____________

Consider the following matrix.$$\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$$The largest eigenvalue of the above matrix is __________.

A five-stage pipeline has stage delays of $150, 120, 150, 160$ and $140$ nanoseconds. The registers that are used between the pipeline stages have a delay of $5$ nanoseconds each. The total time to execute $100$ independent instructions on this pipeline, assuming there are no pipeline stalls, is _______ nanoseconds.

Consider the following instruction sequence where registers $\text{R1}, \text{R2}$ and $\text{R3}$ are general purpose and $\text{MEMORY[X]}$ denotes the content at the memory location $\text{X}.$ …

A sender $(\textsf{S})$ transmits a signal, which can be one of the two kinds: $H$ and $L$ with probabilities $0.1$ and $0.9$ respectively, to a receiver $(\textsf{R})$. In the graph below, the weight of edge $(u,v)$ is the probability of receiving $v$ when $u$ is transmitted, where $u,v \in \{H,L\}$. For example, the probability that the …

Gauri said that she can play the keyboard __________ her sister.

A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ___________.

If $\theta$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, $\cos \theta =$

$\text{Pen : Write :: Knife :}$ _______ Which one of the following options maintains a similar logical relation in the above?

Listening to music during exercise improves performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while students who did not need any external stimulation benefited from music. Which …

​​​​​​If $\left( x – \dfrac{1}{2} \right)^2 – \left( x- \dfrac{3}{2} \right) ^2 = x+2$, then the value of $x$ is:

A jigsaw puzzle has $2$ pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.

The number of students in three classes is in the ratio $3:13:6$. If $18$ students are added to each class, the ratio changes to $15:35:21$. The total number of students in all the three classes in the beginning was:

The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year $3$ was ₹$\;1$, which was half the cost/unit in Year $2$. The cost/unit in Year $3$ was one-third of the cost/unit in Year $1$. Taxes were paid on the selling price at $10 \%$, $13 \%$, and …