HCU PHD CS MAY 2017
Question 1 
Two motorists set out at the same time from A to B, a distance of 100 miles. They both followed the same route and travelled at different though uniform speeds of integral number of miles /hour. The difference in their speeds was a prime number of miles/hour. After they had been driving for 2 hrs, the distance of the slower car from A was five times that of the faster car from B. How fast did the motorists drive?
30 and 37 miles/hour  
40 and 42 miles/hour  
47 and 49 miles/hour  
None of the above 
Question 1 Explanation:
The two motorists:
Let d=the distance the faster car has traveled. Then it still has 100d miles to go, and the slow car has, therefore, gone 5005d miles. Let A and B be the rates of the fast and slow cars in mph. Then d/A = (5005d)/B = 2
We get B=2505B
Then AB=6f250
=(3A125).
But since AB is prime 3A125=1
hence A=42mph and B=40 mph
Let d=the distance the faster car has traveled. Then it still has 100d miles to go, and the slow car has, therefore, gone 5005d miles. Let A and B be the rates of the fast and slow cars in mph. Then d/A = (5005d)/B = 2
We get B=2505B
Then AB=6f250
=(3A125).
But since AB is prime 3A125=1
hence A=42mph and B=40 mph
Question 2 
A job is done by M men in D days. Then M + N men can do the same job in
(MD)/M+N days  
D/M((M +N) days  
D(D/M)*N days  
D(M/D)*N days 
Question 2 Explanation:
let's assume 1 man will take m time to do the same job, so rate of working for i man is: 1(job)/d*m(days)= 1/d*m
More man means job will done faster so the new rate will be: (m+n)*(rate of 1 man) = m+n/d*m
Now convert this to m+r men by dividing top and bottom will take d*m/m+n
More man means job will done faster so the new rate will be: (m+n)*(rate of 1 man) = m+n/d*m
Now convert this to m+r men by dividing top and bottom will take d*m/m+n
Question 3 
An academic institute starts a class at 10:00 A.M. and ends at 1:47 P.M. It has 4
periods of equal distribution of time. After each period there is a gap of 5 minutes to
start another period. What is the exact duration of the period?
51  
52  
53  
57 
Question 3 Explanation:
let’s count total academic minutes in a day from 10:00 am to 1:47 pm i.e 227 minutes.
Total period is =4
Time gap after each period is = 5 minutes. First class starts at 10:00 am so total gap will be 5*3=15 minutes. Deduct gap from total academic minutes = 227 15=212
Total 4 periods we have given in the question so, 212/4= 53 minutes.
Total period is =4
Time gap after each period is = 5 minutes. First class starts at 10:00 am so total gap will be 5*3=15 minutes. Deduct gap from total academic minutes = 227 15=212
Total 4 periods we have given in the question so, 212/4= 53 minutes.
Question 4 
A contractor estimated that one of his bricklayers would take 9 hrs to build a certain
wall and the other 10 hours. However, he knew from experience that when they worked
together, 10 fewer bricks laid per hour. Since he was in a hurry, he put both men
on the job and found it took exactly 5 hours to build the wall. How many bricks did
it contain?
18  
90  
900  
It can not be determined from the given data 
Question 5 
The number of ways in which 3 men and 2 women can sit in a row so that no two men
are adjacent is
12  
24  
72  
19 
Question 5 Explanation:
The only possibility is
M W M W M
Where M represents men and W represents women.
Now three men can be arranged among themselves in 3! Ways and two women can be arranged in 2! ways.Hence the answer is 3! * 2! =12
M W M W M
Where M represents men and W represents women.
Now three men can be arranged among themselves in 3! Ways and two women can be arranged in 2! ways.Hence the answer is 3! * 2! =12
Question 6 
Given the statement, "I always cut the topright corner of a milk packet for opening it", a milk packet with its topright corner cut is
a necessary condition for the packet to have been opened by me  
a sufficient condition for the packet to have been opened by me  
both Ii necessary and a sufficient condition for the packet to have been opened by
me
 
sometimes a necessary condition and sometimes a sufficient condition for the
packet to have been opened by me

Question 6 Explanation:
The given statement is necessary condition that the packet was opened by me but it is not sufficient condition, because some other person also might open the milk packet in same way. But if it was opened by me then it has to be cut from top right corner ,hence nessecary condition.
Question 7 
A common problem in Computer Science research is to minimise an equation of the Form
where λ is a parameter, E_{t} , E_{m} and E_{d} are the total, model and data errors. Model
error reflects the mismatch between predicted and actual values, while data error is
the error due to noise in the data. For noisy data, the value of λ should be
Close to 0  
Close to 1  
Close to 0.5  
None of the above 
Question 8 
Using general knowledge about Computer Science and by reading the following paragraph carefully, answer the Questions 8  12 below:
Princeton asked me to develop a course in automata theory. Since there were no courses or books on the subject, I asked McCluskey to recommend some materials for a course on automata theory. He gave me a list of six papers and told me that the material would probably give students a good background in automata theory. McCluskey'S list included works by Warren McCulloch and Walter Pitts, Michael Rabin and Dana Scott, John Backus and Peter Naur, Noam Chomsky, Juris Hartmanis and RichardStearns, and, of course, Alan Turing.
In 1943 McCulloch and Pitts, working in neurophysiology, published a paper on a logical calculus for describing events in neuron nets. The paper had a notation for describing how these strings of zeros and ones combine in neurons to produce new strings of zeros and ones. This notation was subsequently developed into the language of regular expressions for describing sets of strings. Rabin and Scott were mathematicians who developed a model of a computer with a finite amount of memory. They called this model the finitestate automaton, and showed that the possible behaviors of finitestate automata were precisely those behaviors that could be described by the regular expressions that grew out of the work of McCulloch and Pitts. ...... The work of Hartmanis and Stearns attracted researchers and focused· attention on the topic of complexity. Among the more significant advances that resulted were the classification of the complexity of most major mathematical theories, the reducibility of many combinatorial problems, the concept of NPcompleteness, and a deeper understanding of concepts such as randomness. Also, through this course I met Jeffrey Ullman and Alfred Aho, with whom I subsequently collaborated for many years. Formal Languages and Automata Theory, which I wrote with Ullman, also evolved from this course.
Who is the ’I’, in the passage?
McCluskey·  
Jeffrey Ullman  
John Hopcroft  
Edsger Dijkstra 
Question 9 
Using general knowledge about Computer Science and by reading the following paragraph carefully, answer the Questions 8  12 below:
Princeton asked me to develop a course in automata theory. Since there were no courses or books on the subject, I asked McCluskey to recommend some materials for a course on automata theory. He gave me a list of six papers and told me that the material would probably give students a good background in automata theory. McCluskey'S list included works by Warren McCulloch and Walter Pitts, Michael Rabin and Dana Scott, John Backus and Peter Naur, Noam Chomsky, Juris Hartmanis and RichardStearns, and, of course, Alan Turing.
In 1943 McCulloch and Pitts, working in neurophysiology, published a paper on a logical calculus for describing events in neuron nets. The paper had a notation for describing how these strings of zeros and ones combine in neurons to produce new strings of zeros and ones. This notation was subsequently developed into the language of regular expressions for describing sets of strings. Rabin and Scott were mathematicians who developed a model of a computer with a finite amount of memory. They called this model the finitestate automaton, and showed that the possible behaviors of finitestate automata were precisely those behaviors that could be described by the regular expressions that grew out of the work of McCulloch and Pitts. ...... The work of Hartmanis and Stearns attracted researchers and focused· attention on the topic of complexity. Among the more significant advances that resulted were the classification of the complexity of most major mathematical theories, the reducibility of many combinatorial problems, the concept of NPcompleteness, and a deeper understanding of concepts such as randomness. Also, through this course I met Jeffrey Ullman and Alfred Aho, with whom I subsequently collaborated for many years. Formal Languages and Automata Theory, which I wrote with Ullman, also evolved from this course.
...... denotes some missing sentences in the passage. What are the most likely missing sentences?
Sentences about Hopcroft's early work in the course  
Sentences about work by Hartmanis and Stearns  
Sentences about work by Backus, Naur and Chomsky  
Sentences about Princeton university 
Question 9 Explanation:
The missing sentences was about Backus naur and Chomsky because the second paragraph contains all the names of the McCluskey'S list except these two names.
Question 10 
Using general knowledge about Computer Science and by reading the following paragraph carefully, answer the Questions 8  12 below:
Princeton asked me to develop a course in automata theory. Since there were no courses or books on the subject, I asked McCluskey to recommend some materials for a course on automata theory. He gave me a list of six papers and told me that the material would probably give students a good background in automata theory. McCluskey'S list included works by Warren McCulloch and Walter Pitts, Michael Rabin and Dana Scott, John Backus and Peter Naur, Noam Chomsky, Juris Hartmanis and RichardStearns, and, of course, Alan Turing.
In 1943 McCulloch and Pitts, working in neurophysiology, published a paper on a logical calculus for describing events in neuron nets. The paper had a notation for describing how these strings of zeros and ones combine in neurons to produce new strings of zeros and ones. This notation was subsequently developed into the language of regular expressions for describing sets of strings. Rabin and Scott were mathematicians who developed a model of a computer with a finite amount of memory. They called this model the finitestate automaton, and showed that the possible behaviors of finitestate automata were precisely those behaviors that could be described by the regular expressions that grew out of the work of McCulloch and Pitts. ...... The work of Hartmanis and Stearns attracted researchers and focused· attention on the topic of complexity. Among the more significant advances that resulted were the classification of the complexity of most major mathematical theories, the reducibility of many combinatorial problems, the concept of NPcompleteness, and a deeper understanding of concepts such as randomness. Also, through this course I met Jeffrey Ullman and Alfred Aho, with whom I subsequently collaborated for many years. Formal Languages and Automata Theory, which I wrote with Ullman, also evolved from this course.
Who invented the finite state automaton?
Hopcroft and Ullman  
Chomsky  
McCulloch and Pitts  
Rabin and Scott 
Question 10 Explanation:
From the line “Rabin and Scott were mathematicians who developed a model
of a computer with a finite amount of memory. They called this model the finitestate
Automaton” it is clear that the answer is Rabin and Scott.
Question 11 
Using general knowledge about Computer Science and by reading the following paragraph carefully, answer the Questions 8  12 below:
Princeton asked me to develop a course in automata theory. Since there were no courses or books on the subject, I asked McCluskey to recommend some materials for a course on automata theory. He gave me a list of six papers and told me that the material would probably give students a good background in automata theory. McCluskey'S list included works by Warren McCulloch and Walter Pitts, Michael Rabin and Dana Scott, John Backus and Peter Naur, Noam Chomsky, Juris Hartmanis and RichardStearns, and, of course, Alan Turing.
In 1943 McCulloch and Pitts, working in neurophysiology, published a paper on a logical calculus for describing events in neuron nets. The paper had a notation for describing how these strings of zeros and ones combine in neurons to produce new strings of zeros and ones. This notation was subsequently developed into the language of regular expressions for describing sets of strings. Rabin and Scott were mathematicians who developed a model of a computer with a finite amount of memory. They called this model the finitestate automaton, and showed that the possible behaviors of finitestate automata were precisely those behaviors that could be described by the regular expressions that grew out of the work of McCulloch and Pitts. ...... The work of Hartmanis and Stearns attracted researchers and focused· attention on the topic of complexity. Among the more significant advances that resulted were the classification of the complexity of most major mathematical theories, the reducibility of many combinatorial problems, the concept of NPcompleteness, and a deeper understanding of concepts such as randomness. Also, through this course I met Jeffrey Ullman and Alfred Aho, with whom I subsequently collaborated for many years. Formal Languages and Automata Theory, which I wrote with Ullman, also evolved from this course.
What was the difficulty in offering the course on Finite Automata Theory at Princeton?
There were no textbooks for the subject  
There were no teachers for the subject  
There were no students for the subject  
None of the above 
Question 11 Explanation:
From the line”Since there were no courses or books on the subject” it is clear that the answer is option A.
Question 12 
Using general knowledge about Computer Science and by reading the following paragraph carefully, answer the Questions 8  12 below:
Princeton asked me to develop a course in automata theory. Since there were no courses or books on the subject, I asked McCluskey to recommend some materials for a course on automata theory. He gave me a list of six papers and told me that the material would probably give students a good background in automata theory. McCluskey'S list included works by Warren McCulloch and Walter Pitts, Michael Rabin and Dana Scott, John Backus and Peter Naur, Noam Chomsky, Juris Hartmanis and RichardStearns, and, of course, Alan Turing.
In 1943 McCulloch and Pitts, working in neurophysiology, published a paper on a logical calculus for describing events in neuron nets. The paper had a notation for describing how these strings of zeros and ones combine in neurons to produce new strings of zeros and ones. This notation was subsequently developed into the language of regular expressions for describing sets of strings. Rabin and Scott were mathematicians who developed a model of a computer with a finite amount of memory. They called this model the finitestate automaton, and showed that the possible behaviors of finitestate automata were precisely those behaviors that could be described by the regular expressions that grew out of the work of McCulloch and Pitts. ...... The work of Hartmanis and Stearns attracted researchers and focused· attention on the topic of complexity. Among the more significant advances that resulted were the classification of the complexity of most major mathematical theories, the reducibility of many combinatorial problems, the concept of NPcompleteness, and a deeper understanding of concepts such as randomness. Also, through this course I met Jeffrey Ullman and Alfred Aho, with whom I subsequently collaborated for many years. Formal Languages and Automata Theory, which I wrote with Ullman, also evolved from this course.
Which of the following did not grow out of the work by Hartmanis and Stearns?
Regular expressions  
Reducibility of combinatorial problems  
Classification of complexity  
NPCompleteness 
Question 12 Explanation:
From the line “The work of Hartmanis and Stearns attracted researchers
and focused· attention on the topic of complexity. Among the more significant advances
that resulted were the classification of the complexity of most major mathematical theories,
the reducibility of many combinatorial problems, the concept of NPcompleteness, and a
deeper understanding of concepts such as randomness” it is clear that regular expression was not grown out of the work by Hartmanis and Stearns.
Question 13 
Which plots show the relationship between two or three variables when comparing data
sets consisting of multiple observations?
Histograms  
Scatter Plots  
Probability Plots  
All the above 
Question 14 
Variability in groups of observations with widely differing means can be compared
using the following measure
Coefficient of variation  
Mean deviation
 
Measure of skewness  
None of the above 
Question 15 
Features / attributes of patterns, which can be measured, are called
Qualitative measure  
Data  
Variables  
All 
Question 16 
Find the sample variance, standard deviation and range of the following data: 572, 572, 573, 568, 569, 575, 565, 570
Variance =10, standard deviation = 3.162, range = 11  
Variance =13, standard deviation = 4.162, range = 10  
Variance =10, standard deviation = 3.162, range = 09  
Variance =10, standard deviation = 3.162, range = 10 
Question 17 
The president and treasurer are to be chosen from a student club consisting of 50
people. How many different choices of officers are possible if there are no restrictions?
2450  
2500  
1225  
1250 
Question 17 Explanation:
We are picking 2 out of a field of 50, and order does matter.So
answer is P(50,2) = 2450
answer is P(50,2) = 2450
Question 18 
In a college football training session, the defensive coordinator needs to have 10 players
standing in a row. Among these 10 players, there are 1 freshman, 2 sophomore, 4 juniors
and 3 seniors. How many different ways can they be arranged in a row if only their
class level will be distinguished?
14600  
12600  
12800  
None of the above

Question 18 Explanation:
Since only their class level will be distinguished. So 2 sophomore will be treated same, 4 juniors will be treated same, and 3 seniors will be treated same.
Hence the no. of ways they can be arranged in a row,
=12600
Hence the no. of ways they can be arranged in a row,
=12600
Question 19 
In how many ways can 5 different trees be planted in a circle?
24  
12  
6  
120 
Question 19 Explanation:
There are a total of 5! (=120) ways to plant five different trees. However, the trees are in a circle, in which each "way" is counted five times, due to rotations. This leaves us 5!/5 = 4! = 24 ways to plant five different trees in a circle.
There are 19 questions to complete.