All 65 questions of GATE 2017 CS (Set 2)

Choose the option with words that are not synonyms.

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:

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?

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

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?

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?

X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number $X^3$ will have:

“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 labelled.

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?

The number of roots of

in the range $[-5,5]$ is:

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

The minimum possible number of states of a deterministic finite automaton that accepts the regular language

is __________.

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

Let

and

be two matrices.

Then the rank of $P+Q$ is __________.

Let $L_1, L_2$ be any two context-free languages and $R$ be any regular language. 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.

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

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:

Match the algorithms with their time complexities:

If

and

then the constants $R$ and $S$ are respectively:

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.

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

I. Program counter
II. Stack
III. Address space
IV. Registers

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:

$G$ 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 __________.

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

I. Canonical LR is more powerful than SLR.
II. SLR is more powerful than LALR.
III. SLR is more powerful than Canonical LR.

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

00111110011001100110011000000000

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

Consider the following tables T1 and T2.

T1

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 table T1, the number of additional records that need to be deleted from table T1 is __________.

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

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 __________.

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?

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?

Match the following:

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.

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

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:

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 statements above are CORRECT?

Consider a quadratic equation

with coefficients in a base $b$.

The solutions of this equation in the same base $b$ are $x=5$ and $x=6$.

Then $b$ is __________.

Consider the following expression grammar $G$:

Which one of the following grammars is not left recursive, but is equivalent to $G$?

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

and

define the polynomial function

For a certain discrete random variable $Y$, there exists a scalar $\beta\in[0,1]$ such that

The expectation of $Y$ is:

Consider the following languages.

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.

Given

where $d$ represents the don't-care condition in Karnaugh maps.

Which one of the following is a minimum product-of-sums (POS) form of $f(w,x,y,z)$?

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 integers.

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 terminates in a state satisfying the condition

Let $L(R)$ be the language represented by regular expression $R$. Let $L(G)$ be the language generated by context-free grammar $G$. Let $L(M)$ be the language accepted by 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 $\Sigma$?

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

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);
        }
    }
}

The time complexity of fun in terms of $\Theta$ notation is:

Consider two hosts $X$ and $Y$, connected by a single direct link of rate $10^6$ bits/sec.

The distance between the two hosts is 10,000 km and the propagation speed along the link is $2\times10^8$ m/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 values of $p$ and $q$ are:

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

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

The next-state table of a 2-bit saturating up-counter is given below.

The counter is built as a synchronous sequential circuit using T flip-flops.

The expressions for $T_1$ and $T_0$ are:

$P$ and $Q$ are considering applying 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 $\frac{1}{2}$.

The probability that $Q$ applies for the job given that $P$ applies for the job is $\frac{1}{3}$.

The probability that $P$ does not apply for the job given that $Q$ does not apply for the job is:

Consider the recurrence function

Then $T(n)$ 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:

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

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

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

Then the values of $p$ and $q$ are:

The pre-order traversal of a binary search tree is given by:

Then the post-order traversal of this tree is:

Consider the following database table named top_scorer.

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 __________.

Consider the following C program.

#include <stdio.h>
#include <string.h>

int main() {
    char* c = "GATECSIT2017";
    char* p = c;

    printf("%d", (int) strlen(c + 2[p] - 6[p] - 1));
    return 0;
}

The output of the program is __________.

If the characteristic polynomial of a $3\times3$ matrix $M$ over $\mathbb{R}$ is

and one eigenvalue of $M$ is 2, then the largest among the absolute values of the eigenvalues of $M$ is __________.

If the ordinary generating function of a sequence $\{a_n\}_{n=0}^{\infty}$ is

then $a_3-a_0$ is equal to __________.

Two transactions $T_1$ and $T_2$ are given as:

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 __________.

A message is made up entirely of characters from the set

The table of probabilities for each of the characters is shown below.

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

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

The read access time of main memory is 90 nanoseconds. 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 C program.

#include <stdio.h>

int main() {
    int m = 10;
    int n, n1;

    n = ++m;
    n1 = m++;
    n--;
    --n1;
    n -= n1;

    printf("%d", n);
    return 0;
}

The output of the program is __________.

Consider the set of processes with arrival time in milliseconds, CPU burst time in milliseconds, and priority shown below. Priority 0 is the highest priority. None of the processes have I/O burst time.

The average waiting time in milliseconds of all the processes using preemptive priority scheduling algorithm 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 __________.

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

Consider the following snippet of a C program. Assume that swap(&x, &y) exchanges the contents 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 __________.

If a random variable $X$ has a Poisson distribution with mean 5, then the expectation

equals __________.