GATE Computer Science & IT 2014 — GATE 2014 · CS · Set 1

Consider the statement

“Not all that glitters is gold”

Predicate $glitters(x)$ is true if $x$ glitters and predicate $gold(x)$ is true if $x$ is gold. Which one of the following logical formulae represents the above statement?

Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .

Let $G=(V,E)$ be a directed graph where $V$ is the set of vertices and $E$ the set of edges. Then which one of the following graphs has the same strongly connected components as $G$ ?

Consider the following system of equations:

3x + 2y = 1

4x + 7z = 1

x + y + z = 3

x – 2y + 7z = 0

The number of solutions for this system is __________________

The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a 4-by-4 symmetric positive definite matrix is _____________________.

Let the function

$f(\theta) = \begin{vmatrix} \sin\theta & \cos\theta & \tan\theta \\ \sin(\frac{\pi}{6}) & \cos(\frac{\pi}{6}) & \tan(\frac{\pi}{6}) \\ \sin(\frac{\pi}{3}) & \cos(\frac{\pi}{3}) & \tan(\frac{\pi}{3}) \end{vmatrix}$

where $\theta \in \left[ \frac{\pi}{6},\frac{\pi}{3} \right]$ and  $f'(\theta)$ denote the derivative of $f$ with respect to $\theta$. Which of the following statements is/are TRUE?

I. There exists $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta) = 0$

II.  There exists $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta)\neq 0$

Consider the following Boolean expression for $F$:

$F(P,Q,R,S)= PQ + \bar{P}QR + \bar{P}Q\bar{R}S$

The minimal sum-of-products form of $F$ is

The base (or radix) of the number system such that the following equation holds is____________.

$\frac {312} {20} = 13.1$

A machine has a 32-bit architecture, with 1-word long instructions. It has 64 registers, each of which is 32 bits long. It needs to support 45 instructions, which have an immediate operand in addition to two register operands. Assuming that the immediate operand is an unsigned integer, the maximum value of the immediate operand is ____________.

Consider the following program in C language:

#include <stdio.h>
main()
{
    int i;
    int *pi = &i;
    scanf("%d",pi);
    printf("%d\n", i+5);
}

Which one of the following statements is TRUE?

Let $G$ be a graph with $n$ vertices and $m$ edges. What is the tightest upper bound on the running time of Depth First Search on $G$, when $G$ is represented as an adjacency matrix?

Consider a rooted $n$ node binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having exactly 4 nodes is $O(n^a\log^bn)$. Then the value of $a + 10b$ is __________.

Consider the directed graph below given. 

Which one of the following is TRUE?

Let $P$ be quicksort program to sort numbers in ascending order using the first element as the pivot. Let $t_1$ and $t_2$ be the number of comparisons made by $P$ for the inputs  [1 2 3 4 5] and [4 1 5 3 2] respectively. Which one of the following holds?

Which one of the following is TRUE?

Consider the finite automaton in the following figure.

What is the set of reachable states for the input string 0011 ?

Which one of the following is FALSE?

Match the following software process models with their characteristics.

Models

1) Waterfall model

2) Evolutionary model

3) Component-based software engineering

4) Spiral development

Characteristics

a) Specifications can be developed incrementally

b) Requirements compromises are inevitable

c) Explicit recognition of risk

d) Inflexible partitioning of the project into stages

Suppose a disk has 201 cylinders, numbered from 0 to 200. At some time, the disk arm is at cylinder 100, and there is a queue of disk access requests for cylinders 30, 85, 90, 100, 105, 110, 135 and 145. If Shortest-Seek Time First (SSTF) is being used for scheduling the disk access, the request for cylinder 90 is serviced after servicing ____________ number of requests.

Which one of the following is FALSE?

Consider the relation scheme $R = (E, F, G, H, I, J, K, L, M, N)$ and the set of functional dependencies

$\left\{ \{E, F \} \to \{G\}, \{F\} \to \{I, J\}, \{E, H\} \to \{K, L\}, \ \{K\} \to \{M\}, \{L\} \to \{N\}\right\}$

on $R$. What is the key for $R$?

Given the following statements:

S1: A foreign key declaration can always be replaced by an equivalent check  assertion in SQL. 

S2: Given the table $R(a,b,c)$ where $a$ and $b$ together form the primary key, the following is a valid table definition.

CREATE TABLE S (
    a INTEGER,
    d INTEGER,
    e INTEGER,
    PRIMARY KEY (d),
    FOREIGN KEY (a) references R)

Which one of the following statements is CORRECT?

Consider the following three statements about link state and distance vector routing protocols, for a large network with 500 network nodes and 4000 links.

[S1] The computational overhead in link state protocols is higher than in distance vector protocols.

[S2] A distance vector protocol (with split horizon) avoids persistent routing loops, but not a link state protocol.

[S3] After a topology change, a link state protocol will converge faster than a distance vector protocol.

Which one of the following is correct about S1, S2, and S3 ?

Which of the following are used to generate a message digest by the network security protocols?

(P) RSA (Q) SHA-1 (R) DES (S) MD5

Identify the correct order in which the following actions take place in an interaction between a web browser and a web server.

1. The web browser requests a webpage using HTTP.

2. The web browser establishes a TCP connection with the web server.

3. The web server sends the requested webpage using HTTP.

4. The web browser resolves the domain name using DNS.

Consider a token ring network with a length of 2 km having 10 stations including a monitoring station. The propagation speed of the signal is 2 × 10⁸ m/s and the token transmission time is ignored. If each station is allowed to hold the token for 2 µsec, the minimum time for which the monitoring station should wait (in µ sec)before assuming that the token is lost is _______.

Let the size of congestion window of a TCP connection be 32 KB when a timeout occurs. The round trip time of the connection is 100 msec and the maximum segment size used is 2 KB. The time taken (in msec) by the TCP connection to get back to 32 KB congestion window is _________.

Consider a selective repeat sliding window protocol that uses a frame size of 1 KB to send data on a 1.5 Mbps link with a one-way latency of 50 msec. To achieve a link utilization of 60%, the minimum number of bits required to represent the sequence number field is ________.

Consider the following four schedules due to three transactions (indicated by the subscript) using $read$ and $write$ on a data item $x$, denoted by $r(x)$ and $w(x)$ respectively. Which one of them is conflict serializable?

Given the following two statements:
S1: Every table with two single-valued attributes is in 1NF, 2NF, 3NF and BCNF.
S2: AB → C, D → E, E → C is a minimal cover for the set of functional dependencies  AB→C, D→E, AB→E, E→C.
Which one of the following is CORRECT?

An operating system uses the Banker’s algorithm for deadlock avoidance when managing the allocation of three resource types X, Y, and Z to three processes P0, P1, and P2. The table given below presents the current system state. Here, the Allocation matrix shows the current number of resources of each type allocated to each process and the Max matrix shows the maximum number of resources of each type required by each process during its execution.

There are 3 units of type X, 2 units of type Y and 2 units of type Z still available. The system is currently in a safe state. Consider the following independent requests for additional resources in the current state:

REQ1: P0 requests 0 units of X, 0 units of Y and 2 units of Z

REQ2: P1 requests 2 units of X, 0 units of Y and 0 units of Z

Which one of the following is TRUE?

Consider the following set of processes that need to be scheduled on a single CPU. All the times are given in milliseconds.

$\small \begin{array}{|c|c|c|} \hline \textbf{Process Name} & \textbf{Arrival Time} & \textbf{Execution Time} \\\hline \text{A} & 0 & 6 \\\hline \text{B} & 3 & 2 \\\hline \text{C} & 5 & 4 \\\hline \text{D} & 7 & 6 \\\hline \text{E} & 10 & 3 \\\hline \end{array}$

Using the shortest remaining time first scheduling algorithm, the average process turnaround time (in msec) is ____________________.

Assume that there are 3 page frames which are initially empty. If the page reference string is 1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6, the number of page faults using the optimal replacement policy is__________.

A canonical set of items is given below

$S \to L .> R$

$Q \to R.$

On input symbol < the set has

Let $L$ be a language and $\overline L$ be its complement. Which one of the following is NOT a viable possibility?

Which of the regular expressions given below represent the following DFA?

I) 0*1(1+00*1)*

II) 0*1*1+11*0*1

III) (0+1)*1

There are 5 bags labeled 1 to 5. All the coins in a given bag have the same weight. Some bags have coins of weight 10 gm, others have coins of weight 11 gm. I pick 1, 2, 4, 8, 16 coins respectively from bags 1 to 5. Their total weight comes out to 323 gm. Then the product of the labels of the bags having 11 gm coins is ___.

Suppose a polynomial time algorithm is discovered that correctly computes the largest clique in a given graph. In this scenario, which one of the following represents the correct Venn diagram of the complexity classes P, NP and NP Complete (NPC)?

The minimum number of comparisons required to find the minimum and the maximum of 100 numbers is _________________.

Consider a hash table with 9 slots. The hash function is $h(k) = k \ mod \ 9$. The collisions are resolved by chaining. The following 9 keys are inserted in the order: 5, 28, 19, 15, 20, 33, 12, 17, 10. The maximum, minimum, and average chain lengths in the hash table, respectively, are

Consider the following C function in which size is the number of elements in the array E:

int MyX(int *E, unsigned int size)
{
    int Y = 0;
    int Z;
    int i, j, k;

    for(i = 0; i < size; i++)
        Y = Y + E[i];

    for(i = 0; i < size; i++)
        for(j = i; j < size; j++)
        {
            Z = 0;
            for(k = i; k <= j; k++)
                Z = Z + E[k];
            if (Z > Y)
                Y = Z;
        }
    return Y;
}

The value returned by the function MyX is the

Consider the following pseudo code. What is the total number of multiplications to be performed?

D = 2
for i = 1 to n do
    for j = i to n do
        for k = j + 1 to n do
            D = D * 3

Consider a 6-stage instruction pipeline, where all stages are perfectly balanced.Assume that there is no cycle-time overhead of pipelining. When an application is executing on this 6-stage pipeline, the speedup achieved with respect to non-pipelined execution if 25% of the instructions incur 2 pipeline stall cycles is ______________________.

An access sequence of cache block addresses is of length $N$ and contains n unique block addresses. The number of unique block addresses between two consecutive accesses to the same block address is bounded above by $k$. What is the miss ratio if the access sequence is passed through a cache of associativity $A\geq k$ exercising least-recently-used replacement policy?

Consider the 4-to-1 multiplexer with two select lines $S_1$ and $S_0$ given below

The minimal sum-of-products form of the Boolean expression for the output $F$of the multiplexer is

The function $f(x) =x \sin x$ satisfies the following equation:

$f''(x) + f(x) +t \cos x = 0$

The value of $t$ is______.

A function $f(x)$ is continuous in the interval [0,2]. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true?

Four fair six-sided dice are rolled. The probability that the sum of the results being 22 is $X / 1296$. The value of $X$ is _______

A pennant is a sequence of numbers, each number being 1 or 2. An n-pennant is a sequence of numbers with sum equal to n. For example, (1,1,2) is a 4-pennant. The set of all possible 1-pennants is {(1)}, the set of all possible 2-pennants is {(2), (1,1)}and the set of all 3-pennants is {(2,1), (1,1,1), (1,2)}. Note that the pennant (1,2) is not the same as the pennant (2,1). The number of 10- pennants is ______________.

Let $S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set {0,1}. The value of $\log_2 \log_2N$ is _______.

Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $(a,b)$  and $(c,d)$ if $|a-c| \leq 1$ and $|b-d| \leq 1$. The number of edges in this graph is______.

An ordered $n$−tuple $(d_1, d_2,\ldots,d_n)$ with $d_1 \geq d_2 \geq \ldots \geq d_n$ is called graphic  if there exists a simple undirected graph with $n$ vertices having degrees $d_1,d_2,\ldots,d_n$  respectively. Which one of the following 6-tuples is NOT graphic?

Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE?

Given the following schema:

employees(emp-id, first-name, last-name, hire-date,
          dept-id, salary)
departments(dept-id, dept-name, manager-id, location-id)

You want to display the last names and hire dates of all latest hires in their respective departments in the location ID 1700. You issue the following query:

SQL>SELECT last-name, hire-date
    FROM employees
    WHERE (dept-id, hire-date) IN
    (SELECT dept-id, MAX(hire-date)
    FROM employees JOIN departments USING(dept-id)
    WHERE location-id = 1700
    GROUP BY dept-id);

What is the outcome?

Consider two processors $P_1$ and $P_2$ executing the same instruction set. Assume that under identical conditions, for the same input, a program running on $P_2$ takes 25% less time but incurs 20% more CPI (clock cycles per instruction) as compared to the program running on $P_1$. If the clock frequency of $P_1$ is 1GHZ, then the clock frequency of $P_2$ (in GHz) is ______.

Which of the following options is the closest in meaning to the phrase underlined in the sentence below?

It is fascinating to see life forms cope with varied environmental conditions.

Choose the most appropriate word from the options given below to complete the following sentence.

He could not understand the judges awarding her the first prize, because he thought that her performance was quite __________.

In a press meet on the recent scam, the minister said, "The buck stops here". What did the minister convey by the statement?

If $(𝑧 + 1/𝑧)^2$ = 98, compute $(𝑧^2 + 1/𝑧^2)$ .

The roots of $ax^2 + bx + c = 0$ are real and positive. $a$, $b$ and $c$ are real. Then $ax^2 + b|x| + c = 0$ has

The Palghat Gap (or Palakkad Gap), a region about 30 km wide in the southern part of the Western Ghats in India, is lower than the hilly terrain to its north and south. The exact reasons for the formation of this gap are not clear. It results in the neighbouring regions of Tamil Nadu getting more rainfall from the South West monsoon and the neighbouring regions of Kerala having higher summer temperatures.

What can be inferred from this passage?

Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses such as depression and schizophrenia, and consequently, that doctors will be able to eradicate these diseases through early identification and gene therapy.

On which of the following assumptions does the statement above rely?

Round-trip tickets to a tourist destination are eligible for a discount of 10% on the total fare. In addition, groups of 4 or more get a discount of 5% on the total fare. If the one way single person fare is Rs 100, a group of 5 tourists purchasing round-trip tickets will be charged Rs _____________ .

In a survey, 300 respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter?

When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? _____________