GATE CS question library

Consider the following Syntax Directed Translation Scheme $( SDTS )$, with non-terminals $\{S,A \}$ and terminals $\{a,b \}$. $S \to aA \quad \{\text{print }1\}$ $S \to a \quad \{\text{print }2\}$ $A \to Sb \quad \{\text{print }3\}$ Using the above $SDTS$ , the output printed by a bottom-up parser, for the input $aab$ is:

The size of the data count register of a $\text{DMA}$ controller is $16\;\text{bits}$. The processor needs to transfer a file of $29,154$ kilobytes from disk to main memory. The memory is byte addressable. The minimum number of times the $\text{DMA}$ controller needs to get the control of the system bus from the processor to transfer the file from …

The attribute of three arithmetic operators in some programming language are given below. …

A sender uses the Stop-and-Wait $\text{ARQ}$ protocol for reliable transmission of frames. Frames are of size $1000$ bytes and the transmission rate at the sender is $80\;\textsf{Kbps} (1\textsf{Kbps} = 1000\;\text{ bits/second}).$ Size of an acknowledgment is $100$ bytes and the transmission rate at the receiver is $8\;\textsf{Kbps.}$ The one-way …

Consider that $B$ wants to send a message $m$ that is digitally signed to $A$. Let the pair of private and public keys for $A$ and $B$ be denoted by ${K_{x}}^-$ and ${K_{x}}^+$ for $x=A, B$, respectively. Let $K_{x}(m)$ represent the operation of encrypting $m$ with a key $K_{x}$ and $H(m)$ represent the message digest. Which one of …

The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.

The stage delays in a $4$-stage pipeline are $800, 500, 400$ and $300$ picoseconds. The first stage (with delay $800$ picoseconds) is replaced with a functionality equivalent design involving two stages with respective delays $600$ and $350$ picoseconds. The throughput increase of the pipeline is ___________ percent.

Consider a computer system with $40$-bit virtual addressing and page size of sixteen kilobytes. If the computer system has a one-level page table per process and each page table entry requires $48$ bits, then the size of the per-process page table is __________ megabytes.

Consider a carry look ahead adder for adding two $n$-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is

Let $G$ be a weighted connected undirected graph with distinct positive edge weights. If every edge weight is increased by the same value, then which of the following statements is/are TRUE? $P$: Minimum spanning tree of $G$ does not change. $Q$: Shortest path between any pair of vertices does not change.

Consider the following code segment. x = u - t; y = x * v; x = y + w; y = t - z; y = x * y; The minimum number of total variables required to convert the above code segment to static single assignment form is __________.

Let $Q$ denote a queue containing sixteen numbers and $S$ be an empty stack. $Head(Q)$ returns the element at the head of the queue $Q$ without removing it from $Q$. Similarly $Top(S)$ returns the element at the top of $S$ without removing it from $S$. Consider the algorithm given below. while Q is not Empty do if S is Empty OR Top(S) ≤ Head …

We want to design a synchronous counter that counts the sequence $0-1-0-2-0-3$ and then repeats. The minimum number of $\text{J-K}$ flip-flops required to implement this counter is _____________.

Consider the following directed graph: The number of different topological orderings of the vertices of the graph is _____________.

A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are performed efficiently. Which one of the following statements is CORRECT ($n$ refers to the number of items in the queue) ?

Let $p, q, r, s$ represents the following propositions. $p:x\in\left\{8, 9, 10, 11, 12\right\}$ $q:$ $x$ is a composite number. $r:$ $x$ is a perfect square. $s:$ $x$ is a prime number. The integer $x\geq2$ which satisfies $\neg\left(\left(p\Rightarrow q\right) \wedge \left(\neg r \vee \neg s\right)\right)$ is ____________.

A probability density function on the interval $[a, 1]$ is given by $1/x^{2}$ and outside this interval the value of the function is zero. The value of $a$ is _________.

The worst case running times of Insertion sort , Merge sort and Quick sort, respectively are:

Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths submitted at the same time to a computer system. Which one of the following process scheduling algorithms would minimize the average waiting time in the ready queue?

Which of the following decision problems are undecidable? Given NFAs $N_1$ and $N_2$ , is $L(N_1) \cap L(N_2) = \Phi$ Given a CFG $G = (N,\Sigma,P,S)$ and a string $x \in \Sigma^{*}$, does $x \in L(G)$} ? Given CFGs $G_1$ and $G_2$, is $L (G_1) = L(G_2)$? Given a TM $M$, is $L(M)=\Phi$ ?