GATE 2017 Computer Science Set 2 Questions and Solutions

# Recent questions tagged gate2017-2 1
Two transactions $T_1$ and $T_2$ are given as $T_1:r_1(X)w_1(X)r_1(Y)w_1(Y)$ $T_2:r_2(Y)w_2(Y)r_2(Z)w_2(Z)$ where $r_i(V)$ denotes a $\textit{read}$ operation by transaction $T_i$ on a variable $V$ and $w_i(V)$ denotes a $\textit{write}$ operation by transaction $T_i$ on a variable $V$. The total number of conflict serializable schedules that can be formed by $T_1$ and $T_2$ is ______
2
Consider the recurrence function $T(n) = \begin{cases} 2T(\sqrt{n})+1, & n>2 \\ 2, & 0 < n \leq 2 \end{cases}$ Then $T(n)$ in terms of $\Theta$ notation is $\Theta(\log \log n)$ $\Theta( \log n)$ $\Theta (\sqrt{n})$ $\Theta(n)$
3
If the characteristic polynomial of a 3 $\times$ 3 matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, and one eigenvalue of $M$ is 2, then the largest among the absolute values of the eigenvalues of $M$ is _______
4
Consider the following languages. $L_1 = \{a^p \mid p \text{ is a prime number} \}$ $L_2 = \{ a^nb^mc^{2m} \mid n \geq 0, m \geq 0 \}$ $L_3 = \{a^n b^n c^{2n} \mid n \geq 0 \}$ $L_4 = \{ a^n b^n \mid n \geq 1\}$ Which of the ... $L_2$ is not context free $L_3$ is not context free but recursive $L_4$ is deterministic context free I, II and IV only II and III only I and IV only III and IV only
5
Consider a machine with a byte addressable main memory of $2^{32}$ bytes divided into blocks of size 32 bytes. Assume that a direct mapped cache having 512 cache lines is used with this machine. The size of the tag field in bits is _______
6
Let $L(R)$ be the language represented by regular expression $R$. Let $L(G)$ be the language generated by a context free grammar $G$. Let $L(M)$ be the language accepted by a Turing machine $M$. Which of the following decision problems are undecidable? Given a regular expression $R$ and a ... $w$, is $w \in L(M)$? I and IV only II and III only II, III and IV only III and IV only
7
The read access times and the hit ratios for different caches in a memory hierarchy are as given below: $\begin{array}{|l|c|c|} \hline \text {Cache} & \text{Read access time (in nanoseconds)}& \text{Hit ratio} \\\hline \text{$ ... are for instruction fetch and $40$% are for memory operand fetch. The average read access time in nanoseconds (up to $2$ decimal places) is _________
8
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .
9
Match the following according to input (from the left column) to the compiler phase (in the right column) that processes it: ... $\text{P-iii; Q-iv; R-i; S-ii}$ $\text{P-i; Q-iv; R-ii; S-iii}$
10
In a B+ Tree , if the search-key value is $8$ bytes long , the block size is $512$ bytes and the pointer size is $2$ B , then the maximum order of the B+ Tree is ____
11
Consider the set of process with arrival time (in milliseonds), CPU burst time (in millisecods) and priority ($0$ ... The average waiting time (in milli seconds) of all the process using premtive priority scheduling algorithm is ______
12
The next state table of a $2-$bit saturating up-counter is given below. $\begin{array}{cc|cc} Q_1 & Q_0 & Q_1^+ & Q_0^+ \\ \hline 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 1 & 1 \\ 1 & 1 & 1 & 1 \end{array}$ The counter is built as a synchronous sequential circuit ... $T_1 = Q_1+Q_0, \quad T_0= \bar{Q_1} \bar{Q_0}$ $T_1 = \bar{Q_1}Q_0, \quad T_0= Q_1 + Q_0$
13
Consider two hosts $X$ and $Y$, connected by a single direct link of rate $10^6 \hspace{0.1cm} bits/sec$. The distance between the two hosts is $10,000 \hspace{0.1cm} km$ and the propagation speed along the link is $2 \times 10^8 \hspace{0.1cm} m/sec$. Host $X$ ... value of $p$ and $q$ are $p=50$ and $q=100$ $p=50$ and $q=400$ $p=100$ and $q=50$ $p=400$ and $q=50$
14
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
15
If $w, x, y, z$ are Boolean variables, then which one of the following is INCORRECT? $wx+w(x+y)+x(x +y) = x+wy$ $\overline{w \bar{x}(y+\bar{z})} + \bar{w}x = \bar{w} + x + \bar{y}z$ $(w \bar{x}(y+x\bar{z}) + \bar{w} \bar{x}) y = x \bar{y}$ $(w+y)(wxy+wyz) = wxy+wyz$
16
In a file allocation system, which of the following allocation scheme(s) can be used if no external fragmentation is allowed ? Contiguous Linked Indexed 1 and 3 only 2 only 3 only 2 and 3 only
17
Given the following binary number in $32$-bit (single precision) $IEEE-754$ format : $\large 00111110011011010000000000000000$ The decimal value closest to this floating-point number is : $1.45*10^1$ $1.45*10^{-1}$ $2.27*10^{-1}$ $2.27*10^1$
18
The maximum number of IPv4 router addresses that can be listed in the record route (RR) option field of an IPv4 header is______.
19
An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at $0.05$ bar intervals in this plot. If the possibility of a thunderstorm is given by how ... or drops over a region, which of the following regions is most likely to have a thunderstorm? $P$ $Q$ $R$ $S$
20
The number of roots of $e^{x}+0.5x^{2}-2=0$ in the range $[-5,5]$ is $0$ $1$ $2$ $3$
21
$X$ is a $30$ digit number starting with the digit $4$ followed by the digit $7$. Then the number $X^3$ will have $90$ digits $91$ digits $92$ digits $93$ digits
22
There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labeled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box ... of all three boxes? The box labeled Apples' The box labeled Apples and Oranges' The box labeled Oranges' Cannot be determined
23
We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent - namely ideology. This was a country where all gestures, even the most private, were interpreted in political ... s belief that ideology is not as important as literature is revealed by the word: culture' seemingly' urgent' political'
24
There are $3$ red socks, $4$ green socks and $3$ blue socks.You choose $2$ socks. The probability that they are of the same colour is $\dfrac{1}{5}$ $\dfrac{7}{30}$ $\dfrac{1}{4}$ $\dfrac{4}{15}$
25
A test has twenty questions worth $100$ marks in total. There are two types of questions. Multiple choice questions are worth $3$ marks each and essay questions are worth $11$ marks each. How many multiple choice questions does the exam have? $12$ $15$ $18$ $19$
26
There are five buildings called $V$, $W$, $X$, $Y$ and $Z$ in a row (not necessarily in that order). $V$ is to the West of $W$. $Z$ is to the East of $X$ and the West of $V$. $W$ is to the West of $Y$. Which is the building in the middle? $V$ $W$ $X$ $Y$
27
Saturn is ___________ to be seen on a clear night with the naked eye. enough bright bright enough as enough bright bright as enough
A message is made up entirely of characters from the set $X=\{P, Q, R, S, T\}$. The table of probabilities for each of the characters is shown below:$\begin{array}{|c|c|}\hline \textbf{Character} & \textbf{Probability } \\\hline \text{$ ... $100$ characters over $X$ is encoded using Huffman coding, then the expected length of the encoded message in bits is ______.
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .