GATE CS question library

Consider the following function. double f(double x){ if( abs(x*x - 3) < 0.01) return x; else return f(x/2 + 1.5/x); } Give a value $q$ (to $2$ decimals) such that $f(q)$ will return $q$:_____.

Consider the expression tree shown. Each leaf represents a numerical value, which can either be $0$ or $1$. Over all possible choices of the values at the leaves, the maximum possible value of the expression represented by the tree is ___.

Suppose $P, Q, R, S, T$ are sorted sequences having lengths $20, 24, 30, 35, 50$ respectively. They are to be merged into a single sequence by merging together two sequences at a time. The number of comparisons that will be needed in the worst case by the optimal algorithm for doing this is ____.

Consider two strings $A$ = "qpqrr" and $B$ = "pqprqrp". Let $x$ be the length of the longest common subsequence (not necessarily contiguous) between $A$ and $B$ and let $y$ be the number of such longest common subsequences between $A$ and $B$. Then $x +10y=$ ___.

Let $L_1=\{w\in\{0,1\}^*\mid w$ $\text{ has at least as many occurrences of }$ $(110)'\text{s as }$ $(011)'\text{s} \}$. Let $L_2=\{w \in\{0,1\}^*\ \mid w$ $\text{ has at least as many occurrences of }$ $(000)'\text{s as}$ $(111)'\text{s} \}$. Which one of the following is TRUE?

Let $\langle M \rangle$ be the encoding of a Turing machine as a string over $\Sigma=\left\{0,1\right\}$. Let $$L=\left\{\langle M \rangle \mid M \text{ is a Turing machine}\\\text{ that accepts a string of length 2014} \right\}.$$ Then $L$ is:

For a C program accessing $\mathbf{X[i] [j] [k]}$, the following intermediate code is generated by a compiler. Assume that the size of an integer is $32$ bits and the size of a character is $8$ bits. t0 = i ∗ 1024 t1 = j ∗ 32 t2 = k ∗ 4 t3 = t1 + t0 t4 = t3 + t2 t5 = X[t4] Which one of the following statements about the source code for the C program is …

A computer has twenty physical page frames which contain pages numbered $101$ through $120$. Now a program accesses the pages numbered $\text{1, 2, ..., 100}$ in that order, and repeats the access sequence THRICE. Which one of the following page replacement policies experiences the same number of page faults as the optimal page replacement policy for …

Three processes $A$, $B$ and $C$ each execute a loop of $100$ iterations. In each iteration of the loop, a process performs a single computation that requires $t_c$ CPU milliseconds and then initiates a single I/O operation that lasts for $t_{io}$ milliseconds. It is assumed that the computer where the processes execute has sufficient number of …

Consider the procedure below for the Producer-Consumer problem which uses semaphores: semaphore n = 0; semaphore s = 1; void producer() { while(true) { produce(); semWait(s); addToBuffer(); semSignal(s); semSignal(n); } } void consumer() { while(true) { semWait(s); semWait(n); removeFromBuffer(); semSignal(s); consume(); } } Which one of the following is …

Consider a join (relation algebra) between relations $r(R)$ and $s(S)$ using the nested loop method. There are $3$ buffers each of size equal to disk block size, out of which one buffer is reserved for intermediate results. Assuming $\text{size}(r(R))<\text{size}(s(S)),$ the join will have fewer number of disk block accesses if

Consider the following schedule S of transactions $T1, T2, T3, T4:$ …

A graphical HTML browser resident at a network client machine $Q$ accesses a static HTML webpage from a HTTP server $S$. The static HTML page has exactly one static embedded image which is also at $S$. Assuming no caching, which one of the following is correct about the HTML webpage loading (including the embedded image)?

An IP machine $Q$ has a path to another $IP\ machine\ H$ via three $IP\ routers \ R1, R2,$ and $R3$. $Q-R1-R2-R3-H$ $H$ acts as an $\text{HTTP}\ server$, and $Q$ connects to $H$ via $\text{HTTP}$ and downloads a file. Session layer encryption is used, with $\text{DES}$ as the shared key encryption protocol. Consider the following four …

Consider the store and forward packet switched network given below. Assume that the bandwidth of each link is $10^6$ bytes / sec. A user on host $A$ sends a file of size $10^3$ bytes to host $B$ through routers $R1$ and $R2$ in three different ways. In the first case a single packet containing the complete file is transmitted from $A$ to $B$. …

In the diagram shown below, $L1$ is an Ethernet LAN and $L2$ is a Token-Ring LAN. An $IP$ packet originates from sender $S$ and traverses to $R$, as shown. The links within each $\text{ISP}$ and across the two $\text{ISP}$s, are all point-to-point optical links. The initial value of the $\text{TTL}$ field is $32$. The maximum possible value …

Which of the following socket API functions converts an unconnected active TCP socket into a passive socket?

Which of the following is TRUE about the interior gateway routing protocols $-$ Routing Information Protocol $(RIP)$ and Open Shortest Path First $(OSPF)$

Given an instance of the STUDENTS relation as shown as below …

The maximum number of superkeys for the relation schema $R(E,F,G,H)$ with $E$ as the key is _____.