GATE Computer Science & IT 2017 — GATE 2017 · CS · Set 2

The representation of the value of a 16-bit unsigned integer $X$ in hexadecimal number system is BCA9. The representation of the value of $X$ in octal number system is

Match the following:

$\begin{array}{|ll|ll|}\hline P. & \text{static char var ;} & \text{i.} & \text{Sequence of memory locations to store addresses} \\\hline Q. & \text{m = malloc(10); m =NULL ;} & \text{ii.} & \text{A variable located in data section of memory} \\\hline R. & \text{char *ptr[10] ;} & \text{iii.} & \text{Request to allocate a CPU register to store data} \\\hline S. & \text{ register int varl;} & \text{iv.} & \text{A lost memory which cannot be freed} \\\hline\end{array}$

Match the algorithms with their time complexities:

Let $L_1$, $L_2$ be any two context-free languages and $R$ be any regular language. Then which of the following is/are CORRECT?

I.    $L_1 \cup L_2$ is context-free

II.    $\overline{L_1}$ is context-free

III.    $L_1 - R$ is context-free

IV.    $L_1 \cap L_2$ is context-free

Match the following according to input (from the left column) to the compiler phase (in the right column) that processes it:

$\begin{array}{|l|l|}\hline \text{P. Syntax tree} & \text{i. Code generator} \\\hline \text{Q. Character stream} & \text{ii. Syntax analyser} \\\hline \text{R. Intermediate representation} & \text{iii. Semantic analyser} \\\hline \text{S. Token stream} & \text{iv. Lexical analyser} \\\hline \end{array}$

Which of the following statements about parsers is/are CORRECT?

I. Canonical LR (CLR) is more powerful than SLR.

II. SLR is more powerful than LALR.

III. SLR is more powerful than Canonical LR (CLR).

Which of the following is/are shared by all the threads in a process?

I.    Program counter

II.    Stack

III.    Address space

IV.    Registers

In a file allocation system, which of the following allocation scheme(s) can be used if no external fragmentation is allowed?
I. Contiguous II. Linked III. Indexed

Consider the following statements about the routing protocols. Routing Information Protocol (RIP) and Open Shortest Path First (OSPF) in an IPv4 network.

I.    RIP uses distance vector routing

II.   RIP packets are sent using UDP

III.  OSPF packets are sent using TCP

IV.  OSPF operation is based on link-state routing

Which of the above statements are CORRECT?

If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S, f’\left(\frac{1}{2}\right) = \sqrt{2}$ and $\int_0^1 f(x) dx = \frac{2R}{\pi}$, then the constants $R$ and $S$ are

Let $p, q, r$ denote the statements ”It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold” is represented by

Given the following binary number in 32-bit (single precision) IEEE-754 format :

 00111110011011010000000000000000

The decimal value closest to this floating-point number is :

A circular queue has been implemented using a singly linked list where each node consists of a value and a single pointer pointing to the next node. We maintain exactly two external pointers FRONT and REAR pointing to the front node and the rear node of the queue, respectively. Which of the following statements is/are CORRECT for such a circular queue, so that insertion and deletion operations can be performed in $O(1)$ time?

I.    Next pointer of front node points to the rear node.

II.   Next pointer of rear node points to the front node.

Consider the following function implemented in C:

void printxy(int x, int y) { int *ptr; x=0; ptr=&x; y=*ptr; *ptr=1; printf(“%d, %d”, x, y); }

The output of invoking  printxy(1,1) is:

The Breadth First Search (BFS) algorithm has been implemented using the queue data structure. Which one of the following is a possible order of visiting the nodes in the graph below?

Identify the language generated by the following grammar, where $S$ is the start variable.

$S \rightarrow XY$

$X \rightarrow aX \mid a$

$Y \rightarrow aYb \mid \epsilon$

An ER model of a database consists of entity types A and B. These are connected by a relationship R which does not have its own attribute. Under which one of the following conditions, can the relational table for R be merged with that of A?

Consider socket API on a Linux machine that supports connected UDP sockets. A connected UDP socket is a UDP socket on which connect function has already been called. Which of the following statements is/are CORRECT?

I.    A connected UDP socket can be used to communicate with multiple peers simultaneously.

II.   A process can successfully call connect function again for an already connected UDP socket.

Consider the following tables T1 and T2

In table T1, P is the primary key and Q is the foreign key referencing R in table T2 with on-delete cascade and on-update cascade. In table T2, R is the primary key and S is the foreign key referencing P  in table T1 with on-delete set NULL and on-update cascade. In order to delete record ⟨3,8⟩ from the table T1, the number of additional records that need to be deleted from table T1 is _______

The maximum number of IPv4 router addresses that can be listed in the record route (RR) option field of an IPv4 header is______.

Consider the set  $X=\{a, b, c, d, e\}$ under partial ordering  

$R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$

The Hasse diagram of the partial order $(X, R)$ is shown below.

The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______

Let 

Then the rank of (P+Q) is ___________ .

$G$  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 _________ .

Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x$ = 5 and $x$ = 6. Then $b$ = _____

The minimum possible number of states of a deterministic finite automaton that accepts the regular language $L = w_{1}aw_{2} | w_{1},w_{2} \in \left \{ a,b \right \}^{*} \left | w_{1} \right | = 2, \left | w_{2} \right |\geq 3$ is ______________ .

P and Q are considering to apply for a job. The probability that P applies for the job is $\frac {1} {4}$, the probability that P applies for the job given that Q applies for the job is $\frac {1} {2}$, and the probability that Q applies for the job given that P applies for the job is $\frac {1} {3}$. Then the probability that P does not apply for the job given that Q does not apply for this job is

If $w, x, y, z$ are Boolean variables, then which one of the following is INCORRECT?

Given $f(w, x, y, z) = \Sigma_m(0,1, 2, 3, 7, 8, 10) + \Sigma_d(5, 6, 11, 15)$; where $d$ represents the 'don't-care' condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of $f(w, x, y, z)$?

In a two-level cache system, the access times of  $L_1$ and $L_2$ caches are 1 and 8 clock cycles, respectively. The miss penalty from the $L_2$ cache to main memory is 18 clock cycles. The miss rate of $L_1$ cache is twice that of$​​L_2$. The average memory access time (AMAT) of this cache system is 2 cycles. The miss rates of $L_1$ and $​​L_2$ respectively are

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

For any discrete random variable $X$, with probability mass function

$P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomial function $g_x(z) = \Sigma_{j=0}^N \: p_j \: z^j$. For a certain discrete random variable $Y$, there exists a scalar $\beta \in [0,1]$ such that $g_y(z) =(1- \beta+\beta z)^N$. The expectation of $Y$ is

Consider the following expression grammar G:

Which of the following grammars are not left recursive, but equivalent to G ?

A system shares 9 tape drives. The current allocation and maximum requirement of tape drives for that processes are shown below:

Which of the following best describes the current state of the system?

Consider the binary code that consists of only four valid codewords as given below:

00000,01011,10101,11110

Let the minimum Hamming distance of the code $p$ and the maximum number of erroneous bits that can be corrected by the code be $q$. Then the values of $p$ and $q$ are

Consider two hosts $X$ and $Y$, connected by a single direct link of rate 106bits/sec. The distance between the two hosts is 10,000km and the propagation speed along the link is 2×108m/sec. Host $X$ sends a file of 50,000 bytes as one large message to host $Y$ continuously. Let the transmission and propagation delays be $p$ milliseconds and $q$ milliseconds respectively. Then the value of $p$ and $q$ are

The pre-order traversal of a binary search tree is given by 12,8,6,2,7,9,10,16,15,19,17,20.

Then the post-order traversal of this tree is

Consider the C program fragment below which is meant to divide $x$ by $y$ using repeated subtractions. The variables $x,y,q$ and $r$ are all unsigned int.

while (r >= y) { r=r-y; q=q+1; }

Which of the following conditions on the variables   $x,y,q$ and $r$ before the execution of the fragment will ensure that the loop terminated in a state satisfying the condition $x==(y*q + r)$ ?

Consider the following C function

int fun(int n) { int i, j; for(i=1; i<=n; i++) { for (j=1; j<n; j+=i) { printf("%d %d", i, j); } } }

Time complexity of $fun$ in terms of $\Theta$ notation is

Let $\delta$ denote the transition function and $\widehat{\delta}$ denote the extended transition function of the $\epsilon$-NFA whose transition table is given below:

Then $\widehat{\delta}(q_2, aba)$ is

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 following are CORRECT?

I.    $L_1$ is context free but not regular

II.   $L_2$ is not context free

III.   $L_3$ is not context free but recursive

IV.   $L_4$ is deterministic context free

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?

I.    Given a regular expression $R$ and a string $w$, is $w \in L(R)$?

II.   Given a context-free grammar $G$, is $L(G) = \emptyset$

III.  Given a context-free grammar $G$, is $L(G) = \Sigma^*$ for some alphabet $Σ$ ?

IV.  Given a Turing machine $M$ and a string $w$, is $w \in L(M)$?

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 using $T$ flip-flops. The expressions for $T_1$ and $T_0$ are

Consider the following snippet of a C program. Assume that swap $(\&x, \&y)$ exchanges the content of $x$ and $y$:

int main () {

int array[] = {3, 5, 1, 4, 6, 2};

int done =0;

int i;

while (done==0) {

done =1;

for (i=0; i<=4; i++) {

if (array[i] < array[i+1]) {

swap(&array[i], &array[i+1]);

done=0;

}

}

for (i=5; i>=1; i--) {

if (array[i] > array[i-1]) {

swap(&array[i], &array[i-1]);

done =0;

}

}

}

printf(“%d”, array[3]);

}

The output of the program is _______

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 read operation by transaction $T_i$ on a variable $V$ and $w_i(V)$ denotes a 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 ______

The read access times and the hit ratios for different caches in a memory hierarchy are as given below:

The read access time of main memory in 90nanoseconds. Assume that the caches use the referred-word-first read policy and the write-back policy. Assume that all the caches are direct mapped caches. Assume that the dirty bit is always 0 for all the blocks in the caches. In execution of a program, 60% of memory reads are for instruction fetch and 40% are for memory operand fetch. The average read access time in nanoseconds (up to 2 decimal places) is _________

Consider the following database table named 

Consider the following SQL query:

SELECT ta.player FROM top_scorer AS ta

WHERE ta.goals >ALL (SELECT tb.goals

FROM top_scorer AS tb

WHERE tb.country = 'Spain')

AND ta.goals > ANY (SELECT tc.goals

FROM top_scorer AS tc

WHERE tc.country='Germany')

The number of tuples returned by the above SQL query 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 ___________ .

If a random variable $X$ has a Poisson distribution with mean 5, then the expectation $E\left [ \left ( X+2 \right )^{2} \right ]$ equals ___.

In a B+ Tree , if the search-key value is 8 bytes long , the block size is 512 bytes and the pointer size is 2B , then the maximum order of the B+ Tree is ____

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{\(P\)} & \text{$0.22$} \\ \text{$Q$} & \text{$0.34$} \\ \text{$R$} & \text{$0.17$} \\ \text{$S$} & \text{$0.19$} \\ \text{$T$} & \text{$0.08$} \\ \hline\text{Total} & \text{$1.00$} \\\hline \end{array}\)

If a message of 100 characters over $X$ is encoded using Huffman coding, then the expected length of the encoded message in bits is ______.

Consider the set of process with arrival time (in milliseonds), CPU burst time (in millisecods) and priority (0 is the highest priority)  shown below. None of the process have I/O burst time

The average waiting time (in milli seconds) of all the process using premtive priority scheduling algorithm is ______

If the characteristic polynomial of a  3×3  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 _______

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 _______

Consider the following C program.

The output of the program is ______

Consider the following C program.

The output of the program is _______

Choose the option with words that are not synonyms.

Saturn is ___________ to be seen on a clear night with the naked eye.

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?

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?

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

“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 terms.”

The author’s belief that ideology is not as important as literature is revealed by the word:

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 would you open to determine the contents of all three boxes?

X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X3 will have

The number of roots of $e^{x}+0.5x^{2}-2=0$ in the range $[-5,5]$ is

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 fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?