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GATE 2017 Computer Science Set 2 Questions and Solutions

Recent questions tagged gate2017-2

78 votes
16 answers
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 ______
asked Feb 14, 2017 in Databases Madhav 27.4k views
33 votes
7 answers
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 $\Theta(\log \log n)$ $\Theta( \log n)$ $\Theta (\sqrt{n})$ $\Theta(n)$
asked Feb 14, 2017 in Algorithms Madhav 7.2k views
30 votes
6 answers
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 _______
asked Feb 14, 2017 in Linear Algebra Madhav 5k views
27 votes
5 answers
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
asked Feb 14, 2017 in Theory of Computation Madhav 3.8k views
21 votes
9 answers
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 _______
asked Feb 14, 2017 in CO and Architecture Madhav 4.3k views
27 votes
4 answers
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
asked Feb 14, 2017 in Theory of Computation Madhav 3.5k views
47 votes
1 answer
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 _________
asked Feb 14, 2017 in CO and Architecture Madhav 11.9k views
30 votes
8 answers
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 _________ .
asked Feb 14, 2017 in Graph Theory Madhav 5.8k views
32 votes
5 answers
9
Match the following according to input (from the left column) to the compiler phase (in the right column) that processes it: ... $\text{P-iii; Q-iv; R-i; S-ii}$ $\text{P-i; Q-iv; R-ii; S-iii}$
asked Feb 14, 2017 in Compiler Design Madhav 4k views
25 votes
4 answers
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 ____
asked Feb 14, 2017 in Databases Madhav 4.6k views
25 votes
3 answers
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 ______
asked Feb 14, 2017 in Operating System Madhav 4.9k views
21 votes
4 answers
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 ... $T_1 = Q_1+Q_0, \quad T_0= \bar{Q_1} \bar{Q_0}$ $T_1 = \bar{Q_1}Q_0, \quad T_0= Q_1 + Q_0$
asked Feb 14, 2017 in Digital Logic khushtak 4.2k views
18 votes
5 answers
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 $q=50$
asked Feb 14, 2017 in Computer Networks Madhav 3.2k views
32 votes
4 answers
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 ___.
asked Feb 14, 2017 in Probability Kantikumar 6.1k views
22 votes
5 answers
15
If $w, x, y, z$ are Boolean variables, then which one of the following is INCORRECT? $wx+w(x+y)+x(x +y) = x+wy$ $\overline{w \bar{x}(y+\bar{z})} + \bar{w}x = \bar{w} + x + \bar{y}z$ $(w \bar{x}(y+x\bar{z}) + \bar{w} \bar{x}) y = x \bar{y}$ $(w+y)(wxy+wyz) = wxy+wyz$
asked Feb 14, 2017 in Digital Logic khushtak 4.5k views
30 votes
2 answers
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
asked Feb 14, 2017 in Operating System khushtak 5.2k views
28 votes
4 answers
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 : $1.45*10^1$ $1.45*10^{-1}$ $2.27*10^{-1}$ $2.27*10^1$
asked Feb 14, 2017 in Digital Logic khushtak 8.6k views
34 votes
3 answers
18
The maximum number of IPv4 router addresses that can be listed in the record route (RR) option field of an IPv4 header is______.
asked Feb 14, 2017 in Computer Networks khushtak 7.5k views
20 votes
5 answers
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? $P$ $Q$ $R$ $S$
asked Feb 14, 2017 in Numerical Ability Arjun 4k views
24 votes
4 answers
20
The number of roots of $e^{x}+0.5x^{2}-2=0$ in the range $[-5,5]$ is $0$ $1$ $2$ $3$
asked Feb 14, 2017 in Numerical Ability Arjun 6.3k views
23 votes
4 answers
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
asked Feb 14, 2017 in Numerical Ability Arjun 5k views
16 votes
7 answers
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
asked Feb 14, 2017 in Numerical Ability Arjun 4.3k views
11 votes
5 answers
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'
asked Feb 14, 2017 in Verbal Ability Arjun 4.2k views
12 votes
7 answers
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 $\dfrac{1}{5}$ $\dfrac{7}{30}$ $\dfrac{1}{4}$ $\dfrac{4}{15}$
asked Feb 14, 2017 in Numerical Ability Arjun 4.8k views
9 votes
5 answers
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? $12$ $15$ $18$ $19$
asked Feb 14, 2017 in Numerical Ability Arjun 2.5k views
12 votes
5 answers
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? $V$ $W$ $X$ $Y$
asked Feb 14, 2017 in Numerical Ability Arjun 1.9k views
10 votes
9 answers
27
Saturn is ___________ to be seen on a clear night with the naked eye. enough bright bright enough as enough bright bright as enough
asked Feb 14, 2017 in Verbal Ability Arjun 2.2k views
5 votes
4 answers
28
Choose the option with words that are not synonyms. aversion, dislike luminous, radiant plunder, loot yielding, resistant
asked Feb 14, 2017 in Verbal Ability Arjun 2.3k views
27 votes
4 answers
29
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 ______.
asked Feb 14, 2017 in Algorithms Arjun 6k views
39 votes
8 answers
30
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 ___________ .
asked Feb 14, 2017 in Combinatory Arjun 7.5k views
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