All 65 questions of GATE 2016 CS (Set 1)

Archimedes said, “Give me a lever long enough and a fulcrum on which to place it, and I will move the world.”

The sentence above is an example of a ___________ statement.

A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube.

The resulting surface area of the body, in square units, after the removal is __________.

A rewording of something written or spoken is a ______________.

If ‘relftaga’ means carefree, ‘otaga’ means careful and ‘fertaga’ means careless, which of the following could mean ‘aftercare’?

Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.

In a process, the number of cycles to failure decreases exponentially with an increase in load.

At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure.

The load for which the failure will happen in 5000 cycles is ________.

If

which of the following is a factor of $f(x)$?

A shaving set company sells 4 different types of razors: Elegance, Smooth, Soft and Executive.

Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece.

The table below shows the numbers of each razor sold in each quarter of a year.

Which product contributes the greatest fraction to the revenue of the company in that year?

Consider the following statements relating to the level of poker play of four players P, Q, R and S.

I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q

Which of the following can be logically inferred from the above statements?

(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set

Indian currency notes show the denomination indicated in at least seventeen languages.

If this is not an indication of the nation’s diversity, nothing else is.

Which of the following can be logically inferred from the above sentences?

Which of the following is not a superkey in a relational schema with attributes $V,W,X,Y,Z$ and primary key $VY$?

Which of the following languages is generated by the grammar?

A database of research articles in a journal uses the following schema:

(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)

The primary key is:

(VOLUME, NUMBER, STARTPAGE, ENDPAGE)

and the following functional dependencies exist in the schema:

The database is redesigned to use the following schemas:

(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)

(VOLUME, NUMBER, YEAR)

Which is the weakest normal form that the new database satisfies, but the old one does not?

The worst case running times of Insertion sort, Merge sort and Quick sort, respectively, are:

Let $G$ be a weighted connected undirected graph with distinct positive edge weights.

If every edge weight is increased by the same value, then which of the following statements is/are true?

P: Minimum spanning tree of $G$ does not change.

Q: Shortest path between any pair of vertices does not change.

Let $a_n$ be the number of $n$-bit strings that do not contain two consecutive 1s.

Which one of the following is the recurrence relation for $a_n$?

Which of the following decision problems are undecidable?

I. Given NFAs $N_1$ and $N_2$, is $L(N_1)\cap L(N_2)=\emptyset$?

II. Given a CFG $G=(N,\Sigma,P,S)$ and a string $x\in\Sigma^*$, does $x\in L(G)$?

III. Given CFGs $G_1$ and $G_2$, is $L(G_1)=L(G_2)$?

IV. Given a Turing machine $M$, is $L(M)=\emptyset$?

Which of the following is/are example(s) of stateful application layer protocols?

(i) HTTP
(ii) FTP
(iii) TCP
(iv) POP3

Evaluate:

The value is __________.

Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive 0s and two consecutive 1s?

Consider the following directed graph:

The number of different topological orderings of the vertices of the graph is __________.

The 16-bit 2's complement representation of an integer is:

1111 1111 1111 0101

Its decimal representation is __________.

Consider the following C program.

#include <stdio.h>

void mystery(int *ptra, int *ptrb) {
    int *temp;
    temp = ptrb;
    ptrb = ptra;
    ptra = temp;
}

int main() {
    int a = 2016, b = 0, c = 4, d = 42;

    mystery(&a, &b);

    if (a < c)
        mystery(&c, &a);

    mystery(&a, &d);

    printf("%d\n", a);
}

The output of the program is __________.

Consider the Boolean operator # with the following properties:

Then $x\#y$ is equivalent to:

Which one of the following protocols is not used to resolve one form of address to another one?

Consider the following C program.

void f(int, short);

void main()
{
    int i = 100;
    short s = 12;
    short *p = &s;

    __________ ;  // call to f()
}

Which one of the following expressions, when placed in the blank above, will not result in a type checking error?

Consider the following code segment.

x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;

The minimum number of total variables required to convert the above code segment to static single assignment form is __________.

A processor can support a maximum memory of 4 GB, where the memory is word-addressable and one word consists of two bytes.

The size of the address bus of the processor is at least __________ bits.

Two eigenvalues of a $3\times3$ real matrix $P$ are

and

The determinant of $P$ is __________.

Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths submitted at the same time to a computer system.

Which one of the following process scheduling algorithms would minimize the average waiting time in the ready queue?

We want to design a synchronous counter that counts the sequence:

and then repeats.

The minimum number of J-K flip-flops required to implement this counter is __________.

A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are performed efficiently.

Which one of the following statements is correct? Here $n$ refers to the number of items in the queue.

Let $p,q,r,s$ represent the following propositions.

The integer $x \ge 2$ which satisfies

is __________.

A probability density function on the interval $[a,1]$ is given by

and outside this interval the value of the function is zero.

The value of $a$ is __________.

Which one of the following is not a part of the ACID properties of database transactions?

The following function computes the maximum value contained in an integer array p[] of size $n$, where $n \ge 1$.

int max(int *p, int n) {
    int a = 0, b = n - 1;

    while (__________) {
        if (p[a] <= p[b]) {
            a = a + 1;
        }
        else {
            b = b - 1;
        }
    }

    return p[a];
}

The missing loop condition is:

Consider a carry lookahead adder for adding two $n$-bit integers, built using gates of fan-in at most two.

The time to perform addition using this adder is:

What will be the output of the following pseudo-code when parameters are passed by reference and dynamic scoping is assumed?

a = 3;

void n(x) {
    x = x * a;
    print(x);
}

void m(y) {
    a = 1;
    a = y - a;
    n(a);
    print(a);
}

void main() {
    m(a);
}

Let $Q$ denote a queue containing sixteen numbers and $S$ be an empty stack.

Head(Q) returns the element at the head of the queue $Q$ without removing it from $Q$. Similarly, Top(S) returns the element at the top of $S$ without removing it from $S$.

Consider the algorithm given below.

while Q is not Empty do
    if S is Empty OR Top(S) <= Head(Q) then
        x := Dequeue(Q);
        Push(S, x);
    else
        x := Pop(S);
        Enqueue(Q, x);
    end
end

The maximum possible number of iterations of the while loop in the algorithm is __________.

The coefficient of $x^{12}$ in

is __________.

The stage delays in a 4-stage pipeline are 800, 500, 400 and 300 picoseconds.

The first stage, with delay 800 picoseconds, is replaced with a functionally equivalent design involving two stages with respective delays 600 and 350 picoseconds.

The throughput increase of the pipeline is __________ percent.

Consider the following experiment.

Step 1. Flip a fair coin twice.

Step 2. If the outcomes are TAILS, HEADS, then output Y and stop.

Step 3. If the outcomes are either HEADS, HEADS or HEADS, TAILS, then output N and stop.

Step 4. If the outcomes are TAILS, TAILS, then go to Step 1.

The probability that the output of the experiment is Y, up to two decimal places, is __________.

The size of the data count register of a DMA controller is 16 bits.

The processor needs to transfer a file of 29154 kilobytes from disk to main memory.

The memory is byte addressable.

The minimum number of times the DMA controller needs to get the control of the system bus from the processor to transfer the file from the disk to main memory is __________.

Consider the recurrence relation

Let

The value of $K$ is __________.

Consider the weighted undirected graph with 4 vertices, where the weight of edge $\{i,j\}$ is given by the entry $W_{ij}$ in the matrix $W$.

The largest possible integer value of $x$, for which at least one shortest path between some pair of vertices will contain the edge with weight $x$, is __________.

A function

defined on the set of positive integers $\mathbb{N}^+$ satisfies the following properties:

and

Let

be the set of distinct values that $f$ takes.

The maximum possible size of $R$ is __________.

Let $G$ be a complete undirected graph on 4 vertices, having 6 edges with weights being

The maximum possible weight that a minimum weight spanning tree of $G$ can have is __________.

Consider the following context-free grammars:

Which one of the following pairs of languages is generated by $G_1$ and $G_2$, respectively?

$G=(V,E)$ is an undirected simple graph in which each edge has a distinct weight, and $e$ is a particular edge of $G$.

Which of the following statements about the minimum spanning trees of $G$ is/are true?

I. If $e$ is the lightest edge of some cycle in $G$, then every MST of $G$ includes $e$.

II. If $e$ is the heaviest edge of some cycle in $G$, then every MST of $G$ excludes $e$.

Consider the two cascaded 2-to-1 multiplexers as shown in the figure.

The minimal sum of products form of the output $X$ is:

An operator delete(i) for a binary heap data structure is to be designed to delete the item in the $i$-th node.

Assume that the heap is implemented in an array and $i$ refers to the $i$-th index of the array.

If the heap tree has depth $d$, where depth is the number of edges on the path from the root to the farthest leaf, then what is the time complexity to re-fix the heap efficiently after the removal of the element?

What will be the output of the following C program?

void count(int n) {
    static int d = 1;

    printf("%d ", n);
    printf("%d ", d);

    d++;

    if (n > 1)
        count(n - 1);

    printf("%d ", d);
}

void main() {
    count(3);
}

Consider the following two-phase locking protocol.

Suppose a transaction $T$ accesses, for read or write operations, a certain set of objects:

This is done in the following manner:

Step 1. $T$ acquires exclusive locks to $O_1,\ldots,O_k$ in increasing order of their addresses.

Step 2. The required operations are performed.

Step 3. All locks are released.

This protocol will:

Consider a computer system with ten physical page frames.

The system is provided with an access sequence:

where each $a_i$ is a distinct virtual page number.

The difference in the number of page faults between the last-in-first-out page replacement policy and the optimal page replacement policy is __________.

Let $X$ be a recursive language and $Y$ be a recursively enumerable but not recursive language.

Let $W$ and $Z$ be two languages such that $\overline{Y}$ reduces to $W$, and $Z$ reduces to $\overline{X}$, where reduction means the standard many-one reduction.

Which one of the following statements is TRUE?

The attributes of three arithmetic operators in some programming language are given below.

The value of the expression

in this language is __________.

A sender uses the Stop-and-Wait ARQ protocol for reliable transmission of frames.

Frames are of size 1000 bytes and the transmission rate at the sender is 80 Kbps, where $1\text{ Kbps}=1000$ bits/second.

The size of an acknowledgement is 100 bytes and the transmission rate at the receiver is 8 Kbps.

The one-way propagation delay is 100 milliseconds.

Assuming no frame is lost, the sender throughput is __________ bytes/second.

Consider that $B$ wants to send a message $m$ that is digitally signed to $A$.

Let the pair of private and public keys for $A$ and $B$ be denoted by $K_x^-$ and $K_x^+$ for $x=A,B$, respectively.

Let $K_x(m)$ represent the operation of encrypting $m$ with a key $K_x$, and $H(m)$ represent the message digest.

Which one of the following indicates the CORRECT way of sending the message $m$ along with the digital signature to $A$?

An IP datagram of size 1000 bytes arrives at a router.

The router has to forward this packet on a link whose MTU, maximum transmission unit, is 100 bytes.

Assume that the size of the IP header is 20 bytes.

The number of fragments that the IP datagram will be divided into for transmission is __________.

For a host machine that uses the token bucket algorithm for congestion control, the token bucket has a capacity of 1 megabyte and the maximum output rate is 20 megabytes per second.

Tokens arrive at a rate to sustain output at a rate of 10 megabytes per second.

The token bucket is currently full and the machine needs to send 12 megabytes of data.

The minimum time required to transmit the data is __________ seconds.

Consider the transition diagram of a PDA given below with input alphabet $\Sigma=\{a,b\}$ and stack alphabet $\Gamma=\{X,Z\}$. $Z$ is the initial stack symbol. Let $L$ denote the language accepted by the PDA.

Which one of the following is TRUE?

Consider the following proposed solution for the critical section problem. There are $n$ processes: $P_0,\ldots,P_{n-1}$.

In the code, function pmax returns an integer not smaller than any of its arguments. For all $i$, $t[i]$ is initialized to zero.

Code for $P_i$:

do {
    c[i] = 1;
    t[i] = pmax(t[0], ..., t[n-1]) + 1;
    c[i] = 0;

    for every j != i in {0, ..., n-1} {
        while (c[j]);
        while (t[j] != 0 && t[j] <= t[i]);
    }

    Critical Section;

    t[i] = 0;

    Remainder Section;
} while (true);

Which one of the following is TRUE about the above solution?

Consider the following Syntax Directed Translation Scheme (SDTS), with non-terminals $\{S,A\}$ and terminals $\{a,b\}$.

Using the above SDTS, the output printed by a bottom-up parser for the input aab is:

Consider a disk queue with requests for I/O to blocks on cylinders:

The C-LOOK scheduling algorithm is used. The head is initially at cylinder number 63, moving towards larger cylinder numbers on its servicing pass. The cylinders are numbered from 0 to 199.

The total head movement, in number of cylinders, incurred while servicing these requests is __________.

Consider a computer system with 40-bit virtual addressing and page size of sixteen kilobytes.

If the computer system has a one-level page table per process and each page table entry requires 48 bits, then the size of the per-process page table is __________ megabytes.