HCU PHD CS MAY 2019
Question 1 
Consider the polynomial p(x)=c_{0} + c_{1}x + c_{2}x^2 + c_{3x}^3, where no coefficient is 0. The minimum number of multiplications required to evaluate p on an input x is
6  
4  
3  
8 
Question 1 Explanation:
Given,
p(x)=c0 + c1x + c2x^2 + c3 x^3
For minimum number of multiplications, lets modify above equation,
p(x)= c0 + x(c1 + c2x + c3 x^2)
=c0+x(c1+x(c2+c3x)
=c0+x*(c1+x*(c2+c3*x)
Hence minimum number of multiplications required is 3
For minimum number of multiplications, lets modify above equation,
p(x)= c0 + x(c1 + c2x + c3 x^2)
=c0+x(c1+x(c2+c3x)
=c0+x*(c1+x*(c2+c3*x)
Hence minimum number of multiplications required is 3
Question 2 
If S={x0 < x < 12}, M={x1 < x < 9} and N={x0 < x< 5}, find M' ∩ N'
{x9 ≤ x < 5}  
{x9 < x < 12}
 
{x0 < x < 12}  
{x5 < x < 9}

Question 2 Explanation:
S = Total range = {x 0
Now,
M = {x 1
M’ = {x 0
and
N = {x 0
N’ = {x 5≤x<12}
Now, clearly the intersection range of M’ and N’ is,
{x 9≤x<12}
M = {x 1
N = {x 0
Now, clearly the intersection range of M’ and N’ is,
{x 9≤x<12}
Question 3 
Let E, F and G be finite sets and let A = (E∩ F)  (F ∩ G) and B = (E  (E ∩ G))  (E  F).
Which one of the following is true?
A ⊂ B  
S ⊂ A  
A = B  
None of the above 
Question 3 Explanation:
Now,
A = (E∩F)  (F∩G)
= (2,5)  (5,6)
= {2}
Also,
B = (E  (E∩G))  (E  F)
= ({1,2,4,5}  {4,5})  (1,4)
= (1,2)  (1,4)
= {2}
Hence A = B
Question 4 
If the word FORGET is encoded as DPPHCU, then THINK is encoded as
VGKMM  
RIILI  
RIGOI  
RIGOR 
Question 4 Explanation:
Question 5 
Seven (distinct) road accidents occurred in a week. What is the probability that they all occurred
on the same day?
7^6
 
7^2  
2^7  
7^7 
Question 5 Explanation:
For every car accident we can choose a day in 7 ways. So total no. of ways in which 7 car accident can be assigned to 7 days = 7 × 7 × 7 × 7 × 7 × 7 × 7 = 7^{7}
Probability of accident happening on one day = 1/7^{7}
But there are 7 days in which we have to choose 1 day, in which all accidents are happening. Hence required probability is
^{7}C_{1}/7^{7 }= 7/7^{7} = 1/7^{6}
Probability of accident happening on one day = 1/7^{7}
But there are 7 days in which we have to choose 1 day, in which all accidents are happening. Hence required probability is
^{7}C_{1}/7^{7 }= 7/7^{7} = 1/7^{6}
Question 6 
What is the maximum number of different Boolean functions involving n Boolean variables?
n^2^n  
2^n  
2^2^n  
n^2 
Question 6 Explanation:
No. of rows possible with n boolean variables is 2^n, and each row can have two functions possible . Hence the total number of boolean functions possible is 2^(2^n).
Question 7 
Given below is a chart of rainfall amounts in Quinquinox city on a distant planet Quinox revolving around an equally distant Star. It has its own months and years. Year is, of course, the time takenin their own units of measurement to revolve once around their Star.
Examine the chart carefully and answer Question
How many months are there in a year on Quinox?
10  
20  
28  
Not possible from the data given 
Question 8 
Given below is a chart of rainfall amounts in Quinquinox city on a distant planet Quinox revolving around an equally distant Star. It has its own months and years. Year is, of course, the time taken in their own units of measurement to revolve once around their Star.
Examine the chart carefully and answer Question
If climate is classified into the following three categories,
QNd Seasonal rainfall with wet season being short
QNe Uniform rainfall throughout the year
QNm Seasonal rainfall with wet season being long
Which category describes the climate of Quinquinox?
QNm  
QNe  
QNd  
Not possible from the data given 
Question 9 
If the year on Quinox starts with MonOl (which is also the first data point), which month in a year is the wettest?
18  
12  
8  
5 
Question 10 
Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relations on S are
n^2 and n  
n^2 and 0  
n(n+1)/2 and n  
n(n+1)/2 and 0 
Question 10 Explanation:
For the relation to be equivalence ,it should be
>Reflexive
>Symmetric
>Transitive
The smallest equivalence relation is on size n, which contains all diagonal elements.
The largest equivalence relation is the maximum size of relation itself ,i.e. n^2.
>Reflexive
>Symmetric
>Transitive
The smallest equivalence relation is on size n, which contains all diagonal elements.
The largest equivalence relation is the maximum size of relation itself ,i.e. n^2.
Question 11 
Here is a puzzle: find a number x such that x leaves a remainder of 9 when divided by 10, a remainder of 8 when divided by 9, a remainder of 7 when divided by 8, ... , a remainder of 2 when divided by 3 and a remainder of 1 when divided by 2.
How many such numbers are there?
0  
Exactly 1  
2```  
Infinite 
Question 11 Explanation:
The lowest number divisible by all the numbers 1 to 10. So, for minimum value of N,
===>N+1=2520 (LCM of 1,2,3,....10)
or,N=2519
This property is satisfied by the number N=2520∗K−1, where K is a positive integer.
===>N+1=2520 (LCM of 1,2,3,....10)
or,N=2519
This property is satisfied by the number N=2520∗K−1, where K is a positive integer.
Question 12 
Car A goes 200 Kms at an average speed of 40 Kmph in one direction and returns to the starting point covering the distance of 200 Kms at an average speed of 50 Kmph. Another Car B goes 200 Kms at an average speed of 45 Kmph and does the return journey of 200 Kms also at an average speed of 45 Kmph. Which statement is TRUE about the two cars A and B?
Car A takes less time than Car B  
Car B takes less time than Car A  
Both Cars A and B take the same time  
Cannot be determined from the data given 
Question 12 Explanation:
Time taken by car A for complete journey = t_{1} + t_{2}
= 200/40 + 200/50
= 5 + 4
= 9 hr
Time taken by car B for complete journey = t _{1} + t_{2}
= 200/45 + 200/45
= 8.88 hr
Car B takes less time than car A.
= 200/40 + 200/50
= 5 + 4
= 9 hr
Time taken by car B for complete journey = t _{1} + t_{2}
= 200/45 + 200/45
= 8.88 hr
Car B takes less time than car A.
Question 13 
Which of the following is correctly represented by the Venn diagram above?
Elephants, Wolves, Animals  
Dogs, Cats, Pets  
Pigeons, Dogs, Birds  
Tables, Chairs, Furniture 
Question 13 Explanation:
Let’s check option wise,
A) Can’t be the answer because all Elephants and Wolves are animals hence the diagram would be,
B) Yes, True. Because there are some dogs which are pets and there are some cats which are pets. Not all of them are pets. So in the given diagram naming will be,
C)Can’t be the answer because Dogs are not selected to be pigeons and birds.
D)Can’t be the answer because all Tables and chairs are furniture. Hence diagram will be same like (A).
A) Can’t be the answer because all Elephants and Wolves are animals hence the diagram would be,
B) Yes, True. Because there are some dogs which are pets and there are some cats which are pets. Not all of them are pets. So in the given diagram naming will be,
C)Can’t be the answer because Dogs are not selected to be pigeons and birds.
D)Can’t be the answer because all Tables and chairs are furniture. Hence diagram will be same like (A).
Question 14 
Questions 14  16 are based on the Venn diagram below. S represents all integers between 1 and 30, P represents prime numbers between 1 and 30, M represents multiples of 3 between 1 and 30, and F represents all factors of 30.
If G = P ∩ M ∩ F, then
G = {3}
 
G = {3.5}  
G = {1}  
G={1,3,5} 
Question 14 Explanation:
S = 1, 2, 3, 4, …, 30
P = 2,3,5,7,11,13,17,19,23,29
M = 3,6,9,12,15,18,21,24,27,30
F = 1,2,3,5,6,10,15,30
P∩M∩F = {3}
P = 2,3,5,7,11,13,17,19,23,29
M = 3,6,9,12,15,18,21,24,27,30
F = 1,2,3,5,6,10,15,30
P∩M∩F = {3}
Question 15 
Questions 14  16 are based on the Venn diagram below. S represents all integers between 1 and 30, P represents prime numbers between 1 and 30, M represents multiples of 3 between 1 and 30, and F represents all factors of 30.
What are the numbers in F but not in P or M?
1, 10  
Only 1  
Only 10  
1,3,10 
Question 15 Explanation:
S = 1, 2, 3, 4, …, 30
P = 2,3,5,7,11,13,17,19,23,29
M = 3,6,9,12,15,18,21,24,27,30
F = 1,2,3,5,6,10,15,30
F  (P∪M) = {1,2,3,5,6,10,15,30}  {2,3,5,6,7,9,11,12,13,15,17,18,19,21,23,24,27,29,30} = {1,10}
P = 2,3,5,7,11,13,17,19,23,29
M = 3,6,9,12,15,18,21,24,27,30
F = 1,2,3,5,6,10,15,30
F  (P∪M) = {1,2,3,5,6,10,15,30}  {2,3,5,6,7,9,11,12,13,15,17,18,19,21,23,24,27,29,30} = {1,10}
Question 16 
Questions 14  16 are based on the Venn diagram below. S represents all integers between 1 and 30, P represents prime numbers between 1 and 30, M represents multiples of 3 between 1 and 30, and F represents all factors of 30.
What is the cardinality of P ∩ F?
1  
2  
3  
4 
Question 16 Explanation:
S = 1, 2, 3, 4, …, 30
P = 2,3,5,7,11,13,17,19,23,29
M = 3,6,9,12,15,18,21,24,27,30
F = 1,2,3,5,6,10,15,30
P∩F = {2,3,5}
Hence cardinality of P∩F = 3
P = 2,3,5,7,11,13,17,19,23,29
M = 3,6,9,12,15,18,21,24,27,30
F = 1,2,3,5,6,10,15,30
P∩F = {2,3,5}
Hence cardinality of P∩F = 3
Question 17 
Read the paragraphs below and answer Question.
When looking back on any kind of movement or revolution, one always likes to point to a beginning: "It began right there  it all started with soandso's famous speech ... " If structured
programming can be thought of as a revolution, then surely Dijkstra's landmark paper, "Programming Considered as a Human Activity," published in 1965, marks its beginning. Virtually
the entire gospel of structured programming is contained in a few short pages: the arguments
against goto statements, the notion of topdown design, the emphasis on program correctness
and quality (or "elegance," as Dijkstra prefers to call it), and the strong argument against programs that modify themselves.
In addition to these fundamental concepts, there are some rather classic phrases that first appeared in this paper, and that have poppedup in dozens of subsequent articles and books. For
example, when discussing the "divide and conquer" approach characterizing topdown design,
Dijkstra admits, "I have only a very small head, ,and must live with it." What seems obvious to us today was a rather novel idea in 1965: the idea that while computers were  and still are
 getting faster and more powerful, human beings weren't.
This theme is repeated again and again, and is essentially the entire subject matter of Dijkstra's
1972 speech, "The Humble Programmer." ... Once you do read it, you can see why Dijkstra has
the reputation he does. His writing is succinct and yet convincing. Reading Dijkstra, someone
said, has been compared to eating marzipan  it's best to take very small bites, chew slowly,
and digest the mouthful before moving on to the next bite.
What is said to have begun with Dijkstra's landmark paper, "Programming Considered as a Human Activity" in 1965?
Structured programming  
Programs which modify themselves that eventually led to viruses  
High salaries to programmers
 
Computer revolution 
Question 17 Explanation:
From the line
“ If structured programming can be thought of as a revolution, then surely Dijkstra's landmark paper, "Programming Considered as a Human Activity," published in 1965, marks its beginning. ” , clearly the answer is (A) .
“ If structured programming can be thought of as a revolution, then surely Dijkstra's landmark paper, "Programming Considered as a Human Activity," published in 1965, marks its beginning. ” , clearly the answer is (A) .
Question 18 
Read the paragraphs below and answer Question.
When looking back on any kind of movement or revolution, one always likes to point to a beginning: "It began right there  it all started with soandso's famous speech ... " If structured
programming can be thought of as a revolution, then surely Dijkstra's landmark paper, "Programming Considered as a Human Activity," published in 1965, marks its beginning. Virtually
the entire gospel of structured programming is contained in a few short pages: the arguments
against goto statements, the notion of topdown design, the emphasis on program correctness
and quality (or "elegance," as Dijkstra prefers to call it), and the strong argument against programs that modify themselves.
In addition to these fundamental concepts, there are some rather classic phrases that first appeared in this paper, and that have poppedup in dozens of subsequent articles and books. For
example, when discussing the "divide and conquer" approach characterizing topdown design,
Dijkstra admits, "I have only a very small head, ,and must live with it." What seems obvious to us today was a rather novel idea in 1965: the idea that while computers were  and still are
 getting faster and more powerful, human beings weren't.
This theme is repeated again and again, and is essentially the entire subject matter of Dijkstra's
1972 speech, "The Humble Programmer." ... Once you do read it, you can see why Dijkstra has
the reputation he does. His writing is succinct and yet convincing. Reading Dijkstra, someone
said, has been compared to eating marzipan  it's best to take very small bites, chew slowly,
and digest the mouthful before moving on to the next bite.
Which of the following is NOT a part of structured programming?
Elimination of goto statements
 
Topdown design  
Selfmodifying code  
Emphasis on elegance 
Question 18 Explanation:
From the line
“Virtually the entire gospel of structured programming is contained in a few short pages: the arguments against goto statements, the notion of topdown design, the emphasis on program correctness and quality (or "elegance," as Dijkstra prefers to call it), and the strong argument against programs that modify themselves. ”
Option (C) is wrong, because we can see that it is saying that argument against programs that modify themselves, means not favouring the self modifying code.Hence option C is wrong.
“Virtually the entire gospel of structured programming is contained in a few short pages: the arguments against goto statements, the notion of topdown design, the emphasis on program correctness and quality (or "elegance," as Dijkstra prefers to call it), and the strong argument against programs that modify themselves. ”
Option (C) is wrong, because we can see that it is saying that argument against programs that modify themselves, means not favouring the self modifying code.Hence option C is wrong.
Question 19 
Read the paragraphs below and answer Question.
When looking back on any kind of movement or revolution, one always likes to point to a beginning: "It began right there  it all started with soandso's famous speech ... " If structured
programming can be thought of as a revolution, then surely Dijkstra's landmark paper, "Programming Considered as a Human Activity," published in 1965, marks its beginning. Virtually
the entire gospel of structured programming is contained in a few short pages: the arguments
against goto statements, the notion of topdown design, the emphasis on program correctness
and quality (or "elegance," as Dijkstra prefers to call it), and the strong argument against programs that modify themselves.
In addition to these fundamental concepts, there are some rather classic phrases that first appeared in this paper, and that have poppedup in dozens of subsequent articles and books. For
example, when discussing the "divide and conquer" approach characterizing topdown design,
Dijkstra admits, "I have only a very small head, ,and must live with it." What seems obvious to us today was a rather novel idea in 1965: the idea that while computers were  and still are
 getting faster and more powerful, human beings weren't.
This theme is repeated again and again, and is essentially the entire subject matter of Dijkstra's
1972 speech, "The Humble Programmer." ... Once you do read it, you can see why Dijkstra has
the reputation he does. His writing is succinct and yet convincing. Reading Dijkstra, someone
said, has been compared to eating marzipan  it's best to take very small bites, chew slowly,
and digest the mouthful before moving on to the next bite.
Reading Dijkstra should be like eating marzipan  what does this mean?
His prose is very difficult to read like marzipan which should be eaten slowly to appreciate
its taste
 
His prose is so good that it should be read slowly to enjoy and understand it just like marzipan which should be eaten slowly to really enjoy its taste  
His prose is difficult and we cannot read it quickly just like eating marzipan whose taste is
so nasty that we can only eat small pieces
 
His prose is so good that it should be read all at once like swallowing something tasty 
Question 20 
Two cards are drawn together from a pack of 52 cards (a set of traditional playing cards) at random. What is the probability that one is a spade and qne is a heart?
13/102
 
3/20  
47/100  
29/342 
Question 20 Explanation:
In a pack of 52 cards there are 13 spades and 13 hearts out of which one spade and one heart should be selected.
Hence required probability,
^{13}C_{1}×^{13}C_{1}/^{52}C_{2} = 13/102
Hence required probability,
^{13}C_{1}×^{13}C_{1}/^{52}C_{2} = 13/102
Question 21 
The ratio of the number of boys and girls in a class is 4:3. If 100% of the boys and 20% of the girls are scholarship holders, what is the percentage of students who do not get scholarships?
76  
75*(5/7)
 
85*(5/7)  
86 
Question 21 Explanation:
Since the ratio of boys and girls = 4/3
So, let the no. of boys = 4x
No. of girls = 3x
So, total no. of students = 7x
Now no. of boys who got scholarship = 0.1 × 4x = 0.4x
No. of girls who got scholarship = 0.2 × 3x = 0.6x
So no. of students who got scholarship = 0.4x + 0.6x = x
∴ No. of students who do not got scholarship = 7x  x = 6x
Hence the required percentage is,
6/7 × 100 = 85 (5/7)%
So, let the no. of boys = 4x
No. of girls = 3x
So, total no. of students = 7x
Now no. of boys who got scholarship = 0.1 × 4x = 0.4x
No. of girls who got scholarship = 0.2 × 3x = 0.6x
So no. of students who got scholarship = 0.4x + 0.6x = x
∴ No. of students who do not got scholarship = 7x  x = 6x
Hence the required percentage is,
6/7 × 100 = 85 (5/7)%
Question 22 
How many squares are there in the following figure?
14  
15  
17  
18 
Question 22 Explanation:
For straight squares,
No. of 1 box square = 10
No. of 4 box square = 3
For cross squares,
No. of 1 box square = 4
No. of 4 box square = 1
Hence, total no. of squares = 10 + 3 + 4 + 1 = 18
No. of 1 box square = 10
No. of 4 box square = 3
For cross squares,
No. of 1 box square = 4
No. of 4 box square = 1
Hence, total no. of squares = 10 + 3 + 4 + 1 = 18
Question 23 
Two candidates were contesting for the post of the chairperson of a committee, 3/4th of the members voted for A and 3/5th for B, 30 members voted in favour of both the candidates and 9 members did not cast their vote. Find the total number of members who cast their votes.
60  
80  
57  
51 
Question 23 Explanation:
Let the total no. of members be x.
Now,
No. of members who casted votes + no. of members who not casted votes = x
(3x/4 + 3x/5  30) + 9 = x
27x/20  21 = x
7x/20 = 21
X = 60
Hence total no. of members who casted their votes
= 3x/4 + 3x/5  30
= 3/4 × 60 + 3/5 × 60  30
= 45 + 36  30
= 51
Now,
No. of members who casted votes + no. of members who not casted votes = x
(3x/4 + 3x/5  30) + 9 = x
27x/20  21 = x
7x/20 = 21
X = 60
Hence total no. of members who casted their votes
= 3x/4 + 3x/5  30
= 3/4 × 60 + 3/5 × 60  30
= 45 + 36  30
= 51
Question 24 
Answer Questions 24  26 based on the following information.
A, 'B, C, D, E and Fare 6 relatives. Their relationships are:
(a) B is the son of C, but C is not the mother of B
(b) D is the daughter of A
(c) F is the brother of B
(d) A and C are a married couple
(e) E is the brother of C
Who is the mother of B?
F  
E  
D  
A 
Question 24 Explanation:
Let’s connect given information,
B is the son of C, but C is not the mother of B, means C is the father of B.
A and C are married couples, so since C is father of B, then definitely A is mother of B.
D is daughter of A, means B is brother of D or D is sister of B.
F is brother of B. So in total there are three children of A and C.
E is the brother of C. Means E is uncle of B, D and F.
Clearly, A is the mother of B.
B is the son of C, but C is not the mother of B, means C is the father of B.
A and C are married couples, so since C is father of B, then definitely A is mother of B.
D is daughter of A, means B is brother of D or D is sister of B.
F is brother of B. So in total there are three children of A and C.
E is the brother of C. Means E is uncle of B, D and F.
Clearly, A is the mother of B.
Question 25 
Answer Questions 24  26 based on the following information.
A, 'B, C, D, E and Fare 6 relatives. Their relationships are:
(a) B is the son of C, but C is not the mother of B
(b) D is the daughter of A
(c) F is the brother of B
(d) A and C are a married couple
(e) E is the brother of C
How many children does A have?
1  
2  
3  
4 
Question 25 Explanation:
Let’s connect given information,
B is the son of C, but C is not the mother of B, means C is the father of B.
A and C are married couples, so since C is father of B, then definitely A is mother of B.
D is daughter of A, means B is brother of D or D is sister of B.
F is brother of B. So in total there are three children of A and C.
E is the brother of C. Means E is uncle of B, D and F.
A have total three children,
D, B, F
B is the son of C, but C is not the mother of B, means C is the father of B.
A and C are married couples, so since C is father of B, then definitely A is mother of B.
D is daughter of A, means B is brother of D or D is sister of B.
F is brother of B. So in total there are three children of A and C.
E is the brother of C. Means E is uncle of B, D and F.
A have total three children,
D, B, F
Question 26 
Answer Questions 24  26 based on the following information.
A, 'B, C, D, E and Fare 6 relatives. Their relationships are:
(a) B is the son of C, but C is not the mother of B
(b) D is the daughter of A
(c) F is the brother of B
(d) A and C are a married couple
(e) E is the brother of C
Which of the following statements is/are TRUE?
E is D's uncle  
E is D's daughter  
F is E's son  
D and F are sisters 
Question 26 Explanation:
Let’s connect given information,
B is the son of C, but C is not the mother of B, means C is the father of B.
A and C are married couples, so since C is father of B, then definitely A is mother of B.
D is daughter of A, means B is brother of D or D is sister of B.
F is brother of B. So in total there are three children of A and C.
E is the brother of C. Means E is uncle of B, D and F.
P∩F = {2,3,5}
Hence cardinality of P∩F = 3.
B is the son of C, but C is not the mother of B, means C is the father of B.
A and C are married couples, so since C is father of B, then definitely A is mother of B.
D is daughter of A, means B is brother of D or D is sister of B.
F is brother of B. So in total there are three children of A and C.
E is the brother of C. Means E is uncle of B, D and F.
P∩F = {2,3,5}
Hence cardinality of P∩F = 3.
Question 27 
Words are sorted according to the following two rules applied in order: (a) nouns come before verbs, verbs come before adjectives, adjectives come before adverb; (b) a letter with less number of straight line segments comes before one with more straight lines, e.g., V (2 straight lines) comes before E (4 straight lines).
Given the words, ACADEMY, NEST, SUPERB. SUNDAY, NOTING, the correct ascending order is
NEST, SUNDAY, SUPERB, ACADEMY, NOTING  
SUNDAY, ACADEMY, NEST, NOTING, SUPERB  
SUNDAY, SUPERB, ACADEMY, NEST, NOTING
 
ACADEMY, NEST, NOTING, SUNDAY, SUPERB 
Question 27 Explanation:
According to the rules given in the question ,The correct answer is SUNDAY, ACADEMY, NEST, NOTING, SUPERB
Question 28 
A shelf has between 75 and 100 books. 1/6th of them are novels and 12.5% of them are biographies_ .Find the number of books.
76  
88  
96  
None of the Above 
Question 29 
A box contains 4 black 3 red and 5 green balls, 2 balls are drawn from the box at random. What is the probability that both the balls are of the same color?
1/6
 
19/66  
47/66  
2/11 
Question 29 Explanation:
Required probability = P(both the balls are black) + P(both the balls are red) + P(both the balls are green)
= ^{4}C2/^{12}C2 + ^{3}C2/^{12}C2 + ^{5}C2/^{12}C2
= 19/66
= ^{4}C2/^{12}C2 + ^{3}C2/^{12}C2 + ^{5}C2/^{12}C2
= 19/66
Question 30 
What is the first letter of a meaningful English word formed from the 1st, 4th, 7th and 11th letters of "SUPERFLUOUS"?
E  
L  
R  
S 
Question 30 Explanation:
The 1st ,4th ,7th, and 11th letters are S,E,L,S and the meaningful words formed from these letters are ELSE. And the first letter of this word is E.
Question 31 
The following figure shows a ring containing 105 teeth inside which is a wheel with 80 teeth. The black dots  one on the wheel and one on the ring are initially aligned as shown. The wheel is now rotated anticlockwise along the ring with no slippage.After how many revolutions of the wheel will it return to the initial alignment?
5  
15  
21  
26 
Question 32 
What is the cardinality of the power set of {a, b, {a, b} }?
8  
16  
9  
15 
Question 32 Explanation:
Since in the set there are 3 elements .Hence the no. of elements in the power set of given set is 2^3 = 8
Question 33 
In Research Methodology, what does the word Ontology refer to?
Concepts and categories, their properties and relationships
 
Research papers and journals, their citation indices and impact factors  
Cancers, diseases their treatments and hospitals  
A word indexing method 
Question 33 Explanation:
Ontology is the philosophical study of being. More broadly, it studies concepts that directly relate to being, in particular becoming, existence, reality, as well as the basic categories of being and their relations.
Question 34 
Which of the following is given as a classic example of proof by contradiction?
If a, b, e are positive integers, then a^n + b^n noteq c^n for any n > 2  
The number of primes is infinite  
The sum of first n integers is n(n+1)/2
 
If a, b, c are the sides of a rightangled triangle and c is its hypotenuse, then a^2 + b^2 = c^2 
Question 34 Explanation:
Proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction
Question 35 
Some possible reasons for Literature Review in research are given below. Read them and answer the question given below.
I. Show the state·oftheart so that the significance of the solution proposed is clear to the reader.
II. Give a correct context to the scope of the work proposed in the thesis.
III. Demonstrate the scholarliness of the thesis writer.
IV. FiJI the minimum page requirement for a thesis.
Which of the above statements are VALID reasons?
I and II
 
I and III  
II and III
 
None of the Above

Question 35 Explanation:
Both statement I and II are valid
Question 36 
What is the language of the Nondeterministic Finite Automaton(NFA) on Σ={a,b} given below?
a* b*  
a· b'
 
a + b'
 
(ab)'  
None of the above 
Question 36 Explanation:
Let's check option wise:
A) The given expression generates ε , which is not generated by given automata.
B) The given automata can generate only b , which is not generated by the given regular expression.
C) The given automata can generate string ab which is not generated by given regular expression.
D) The given automata generates abab which cannot be generated by given automata.
A) The given expression generates ε , which is not generated by given automata.
B) The given automata can generate only b , which is not generated by the given regular expression.
C) The given automata can generate string ab which is not generated by given regular expression.
D) The given automata generates abab which cannot be generated by given automata.
Question 37 
The language of the following CFG on Σ= {a, b} given by
S → aSb I SS I ε
with n^{a} (w) denoting the number of a's present in w is
{a^nb^n : n ≥ 0}  
{w: n_{a}(w) = n_{b}(w) and n_{a}(v) >= n_{b}(v) where v is any prefIx of w}  
{w: n_{a}(w) ≠ n_{b}(w)}  
{w: n_{a}(w) = n_{b}(w)} 
Question 37 Explanation:
The given grammar generates the strings with “no. of a’s = no. of b’s”
Question 38 
Consider the ultimate software verification problem: A software that can verify any program submitted as input to check if it is correct or not. This problem is
Undecidable  
Decidable  
Context Free  
NPHard 
Question 38 Explanation:
An undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yesorno answer
Question 39 
Which of the following statements is FALSE?
For every Nondeterministic PDA there exists an equivalent DPDA
 
For every Nondeterministic TM there exists an equivalent deterministic TM  
For every regular expression there exists an equivalent NFA  
For every NFA there exists an equivalent DFA 
Question 39 Explanation:
A) False because NPDA is more powerful than DPDA.
B) True because Non deterministic TM has the same power as Deterministic TM.
C) True because regular expressions have the same power as NFA.
D) True because NFA and DFA are equivalent in power.
B) True because Non deterministic TM has the same power as Deterministic TM.
C) True because regular expressions have the same power as NFA.
D) True because NFA and DFA are equivalent in power.
Question 40 
A randomaccess read/write semiconductor memory chip is organized into 128 words of 8 bits
each. A larger memory of 4K words of 16 bits each (K = 1024) may be obtained by connecting
32 chips in a 16 x 2 array  
32 chips in a 32 x 1 array  
64 chips in a 32 x 2 array
 
64 chips in a 8x8 array 
Question 41 
A certain computer represents floating point numbers by means of a signed magnitude fractional
mantissa and an excess16 base 4 exponent. The floating point format number is 110010111000.
What is its decimal value?
3.5  
14  
7/8  
2 
Question 42 
Which of the following is true of interrupts?
They are generated when memory cycles are "stolen".  
They are used in place of data channels  
They can indicate completion of an I/O operation  
They cannot be generated by arithmetic operations. 
Question 42 Explanation:
An interrupt is the automatic transfer of software execution in response to a hardware event that is asynchronous with the current software execution. This hardware event is called a trigger.
The hardware event can either be a busy to ready transition in an external I/O device (like the UART input/output) or an internal event (like bus fault, memory fault, or a periodic timer). When the hardware needs service, signified by a busy to ready state transition, it will request an interrupt by setting its trigger flag.
The hardware event can either be a busy to ready transition in an external I/O device (like the UART input/output) or an internal event (like bus fault, memory fault, or a periodic timer). When the hardware needs service, signified by a busy to ready state transition, it will request an interrupt by setting its trigger flag.
Question 43 
The following assembly language program fragment was written for a singleaddress computer with one accumulator register. What is stored in z?
LOAD b
MULT c
STORE t1
ADD a
STORE t2
MULT t2
ADD tl
STORE z
(a+bc)^2 +bc  
t1(bc  a)  t2  
2bc + a^2
 
(a+bc)+bc 
Question 43 Explanation:
LOAD b // b is loaded in accumulator
MULT c //c is multiplied to b and then bc is loaded back to accumulator
STORE tl // bc is stored in temporary variable t1
ADD a // a is added to value stored in accumulator .So now accumulator contains a+bc
STORE t2 // a+bc is stored in variable t2
MULT t2 // t2 is multiplied by the value of accumulator ,i.e. a+bc is multiplied to a+bc ,and loaded back to accumulator.Now the value in the accumulator is (a+bc)^2
ADD tl // value in accumulator is added to value in t1 ,i.e. ,(a+bc)^2+bc is now loaded in accumulator.
STORE z // The final value in accumulator ,i.e. ,(a+bc)^2+bc is stored in z.
MULT c //c is multiplied to b and then bc is loaded back to accumulator
STORE tl // bc is stored in temporary variable t1
ADD a // a is added to value stored in accumulator .So now accumulator contains a+bc
STORE t2 // a+bc is stored in variable t2
MULT t2 // t2 is multiplied by the value of accumulator ,i.e. a+bc is multiplied to a+bc ,and loaded back to accumulator.Now the value in the accumulator is (a+bc)^2
ADD tl // value in accumulator is added to value in t1 ,i.e. ,(a+bc)^2+bc is now loaded in accumulator.
STORE z // The final value in accumulator ,i.e. ,(a+bc)^2+bc is stored in z.
Question 44 
The logic circuit given below is used to compare two unsigned 2bit numbers, X_{1}X_{0 }= X and
Y_{1} Y_{0} = Y, where X_{o} and Y_{o }are the least significant bits. (A small circle on any line in a logic
diagram indicates logical NOT). Which of the following always makes the output Z have the
value 1?
X >Y  
X < Y  
X =Y  
X ≥ Y

Question 44 Explanation:
So from the above table we can clearly see that, for X>Y the value of Z is 1.
Question 45 
The constraint that specifies the number of entities to which another entity can be associated via
a relationship set in ER model is referred as
Mapping cardinality  
Entity integrity  
Domain integrity  
Assertion 
Question 45 Explanation:
In a Relationship, Participation constraint specifies the existence of an entity when it is related to another entity in a relationship type. It is also called minimum cardinality constraint. This constraint specifies the number of instances of an entity that can participate in a relationship type
Question 46 
An attribute "Address" is divided into Street, City, state, Zip and Country. The attribute "Address"
is referred as
Single valued attribute  
Multivalued attribute  
Composite attribute  
Derived attribute 
Question 46 Explanation:
Composite attribute is an attribute where the values of that attribute can be further subdivided into meaningful subparts. Here the address is divided into Street, City, state, Zip and Country.
Question 47 
The relationship associating the weak entity set with the identifying set is called
Partial entity set  
Identifying relationship  
Aggregation  
ISA relationship 
Question 47 Explanation:
The relationship associating the weak entity sets with the identifying entity set is called as an Identifying relationship. An identifying set is a many to one from the weak entity set to the identifying entity set.
Question 48 
If E1 and E2 are relational algebra expressions then which of the following is NOT a relational
algebra expression
E1 U E2  
El X E2  
E1  E2  
E1 / E2 
Question 48 Explanation:
Six basic operators in relational algebra:
Select σ selects a subset of tuples from reln
Project π deleted unwanted columns from reln
Cartesian Product × allows to combine two relations
Setdifference  tuples in reln. 1, but not in reln. 2
Union ∪ tuples in reln 1 plus tuples in reln 2
Rename ρ renames attribute(s) and relation
Select σ selects a subset of tuples from reln
Project π deleted unwanted columns from reln
Cartesian Product × allows to combine two relations
Setdifference  tuples in reln. 1, but not in reln. 2
Union ∪ tuples in reln 1 plus tuples in reln 2
Rename ρ renames attribute(s) and relation
Question 49 
The set of statements that are executed automatically as a side effect of a modification to the
database is a
Function  
Procedure  
Package  
Trigger 
Question 49 Explanation:
Statement executed automatically by the system as a side effect of modification to database  Trigger. A database trigger is what is executed automatically in response to certain events on a particular table or view in a database.
Question 50 
A digital signaling system is required to operate at 9600 bps. If a signal element encodes a 4bit
word, what is the minimum required bandwidth of the channel?
1200Hz  
4800Hz  
19200Hz  
1900Hz 
Question 50 Explanation:
Using Nyquist's equation: C = 2B log_{2}M
We have C = 9600 bps a. log_{2}M = 4, because a signal element encodes a 4bit word Therefore,
C = 9600 = 2B x 4, and B = 1200 Hz
We have C = 9600 bps a. log_{2}M = 4, because a signal element encodes a 4bit word Therefore,
C = 9600 = 2B x 4, and B = 1200 Hz
Question 51 
Host 130.37.56.201 is on a Class Network.
A  
B  
C  
D 
Question 51 Explanation:
The range of different classes are
Class A > 1126
Class B > 128191
Class C > 192223
Clearly 130 is in the range of 128191.
Class A > 1126
Class B > 128191
Class C > 192223
Clearly 130 is in the range of 128191.
Question 52 
A TCP segment consisting of 1500 bits of data and 160 bits of header is sent to the IP layer,
which appends another 160 bits of header. This is then transmitted through two networks, each
of which uses a 24bit packet header. The destination network has a maximum packet size of
800 bits. How many bits, including headers, are delivered to the network layer protocol at the
destination?
1820  
1844  
1868  
1892 
Question 53 
A slotted LAN has m stations. The probability for an individual station to transmit is t in a time slot.
What shall be the probability that in a given time slot ONLY one station transmits?
mt(1  t)^m1
 
(1  t)^m1  
t(1  t)^m1  
1  (1  t)^m1 
Question 53 Explanation:
We will use the Binomial distribution formula here.
Hence required probability,
= ^{m}C_{1} (t)’(1  t)m1
= mt(1  t)^{m1}
Hence required probability,
= ^{m}C_{1} (t)’(1  t)m1
= mt(1  t)^{m1}
Question 54 
Two systems S1 and S2 are configured with the following IP address:
S1: 203.197.2.53; netmask 255.255.128.0
S2: 203. 197.75.201;netmask 255.255.192.0
Which one of the following statements is true?
S1 assumes S2 is on same network, but S2 assumes S1 is on a different network  
S2 assumes S1 is on same network, but S1 assumes S2 is on a different network  
S1 and S2 both assume they are on the same network  
S1 and S2 both assume they are on different networks 
Question 54 Explanation:
For S1,
IP address  203.197.2.53
So Netmask  255.255.128.0
For S2,
IP address  203.197.75.201
Netmask  255.255.192.0
Now first let’s check for S1,
Network ID according to S1 for itself,
203.197.2.53
AND 255.255.128.0

203.197.0.0
Network ID according to S1 for S2,
203.197.75.201
255.255.128.0

203.197.0.0
Since according to S1 NID of both S1 and S2 are the same, it assumes S2 to be in the same network.
Now let’s check for S2,
Network ID according to S2 for itself,
203.197.75.201
AND 255.255.192.0

203.197.264.0
Network ID according to S2 for S1,
203.197.2.53
255.255.192.0

203.197.0.0
Since according to S2 NID of both S1 and S2 are different, so it assumes S1 to be in a different network.
IP address  203.197.2.53
So Netmask  255.255.128.0
For S2,
IP address  203.197.75.201
Netmask  255.255.192.0
Now first let’s check for S1,
Network ID according to S1 for itself,
203.197.2.53
AND 255.255.128.0

203.197.0.0
Network ID according to S1 for S2,
203.197.75.201
255.255.128.0

203.197.0.0
Since according to S1 NID of both S1 and S2 are the same, it assumes S2 to be in the same network.
Now let’s check for S2,
Network ID according to S2 for itself,
203.197.75.201
AND 255.255.192.0

203.197.264.0
Network ID according to S2 for S1,
203.197.2.53
255.255.192.0

203.197.0.0
Since according to S2 NID of both S1 and S2 are different, so it assumes S1 to be in a different network.
Question 55 
Computer P sends 64 byte messages to Computer Q through a sliding window protocol. The
delay between P and Q is 160 ms and the bandwidth is 256 kbps. What is the optimal size of
the window for P to send messages?
40  
80  
320  
640  
None of the above

Question 55 Explanation:
Optimal window size = 2a
where a = T_{p}/T_{t}
T_{p} is given as 160ms
T_{t} = L/B = 64×8/256×103 = 29/28 ms = 2 ms
∴ Optimal window size = 2 × T_{p}/T_{t} = 2 × 160/2 = 160
where a = T_{p}/T_{t}
T_{p} is given as 160ms
T_{t} = L/B = 64×8/256×103 = 29/28 ms = 2 ms
∴ Optimal window size = 2 × T_{p}/T_{t} = 2 × 160/2 = 160
Question 56 
In the following process state transition diagram for a uniprocessor system, assume that there are always some processes in the ready state. Now, consider the following statements.
I. If a process makes a transition D, it would result in another process making transition A immediately
II. A process P2 in blocked state can make transition E while another process PI is in running state
III. The OS uses preemptive scheduling
IV. The OS uses nonpreemptive scheduling
Which of the above statements are TRUE?
I and II  
I and III  
II and III  
II and IV 
Question 56 Explanation:
S1 is false because If a process makes a transition D ,then it would result in another process making transition B immediately and not A.
S2 is true.
S3 is true due to the transition C, because transition C states that if a process is in running state it can be pulled out to a ready state when some high priority process comes in the ready state.
S4 is false ,since S3 is true.
S2 is true.
S3 is true due to the transition C, because transition C states that if a process is in running state it can be pulled out to a ready state when some high priority process comes in the ready state.
S4 is false ,since S3 is true.
Question 57 
Consider a disk pack with 16 surfaces, 128 tracks per surface and 256 sectors per track. 512
bytes of data are stored in a bit serial manner in a sector.· The capacity of the disk pack and the
number of bits required to specify a particular sector in the disk are respectively:
256 MB, 19b  
256MB,8b  
512 MB, 20b  
64 GB, 28b 
Question 57 Explanation:
Let first find capacity of disk,
16 surfaces × 128 tracks × 256 sectors/track × 512 bytes/sector
= 2^{4} × 2^{7 }× 2^{8 }× 2^{9}
= 2^{28}
= 256 MB
Now let's find no. of bits required to specify a particular sector,
16 surfaces × 128 tracks × 256 sectors/track
= 2^{4} × 2^{7} × 2^{8} = 2^{19}
Hence 19 bits.
16 surfaces × 128 tracks × 256 sectors/track × 512 bytes/sector
= 2^{4} × 2^{7 }× 2^{8 }× 2^{9}
= 2^{28}
= 256 MB
Now let's find no. of bits required to specify a particular sector,
16 surfaces × 128 tracks × 256 sectors/track
= 2^{4} × 2^{7} × 2^{8} = 2^{19}
Hence 19 bits.
Question 58 
Identify the correct order in which a server process must invoke the function calls accept, bind,
listen and recv according to UNIX socket API.
listen, accept, bind, recv  
bind, listen, accept, recv  
bind, accept, listen, recv  
accept, listen, bind, recv 
Question 58 Explanation:
The correct order in which a server process must invoke the function calls according to UNIX socket API is
socket() creates a new socket of a certain type, identified by an integer number, and allocates system resources to it.
bind() associates a socket with a socket address structure, i.e. a specified local IP address and a port number.
listen() causes a bound TCP socket to enter listening state.
accept() accepts a received incoming attempt to create a new TCP connection from the remote client, and creates a new socket associated with the socket address pair of this connection.
send(), recv(), sendto(), and recvfrom() are used for sending and receiving data.
socket() creates a new socket of a certain type, identified by an integer number, and allocates system resources to it.
bind() associates a socket with a socket address structure, i.e. a specified local IP address and a port number.
listen() causes a bound TCP socket to enter listening state.
accept() accepts a received incoming attempt to create a new TCP connection from the remote client, and creates a new socket associated with the socket address pair of this connection.
send(), recv(), sendto(), and recvfrom() are used for sending and receiving data.
Question 59 
Let f be a Boolean expression in 8 variables which has true value exactly for 4 combinations out of 2^8 possible combinations. Then f can be expressed as sum of minterms.
10  
8  
6  
4 
Question 59 Explanation:
No. of minterms is equal to the no. of combinations with true value.
Question 60 
One of the main limitations of Hierarchical databases is
Limited capacity  
Overheads associated with maintaining indices  
Limited flexibility in data access  
Poor performance 
Question 60 Explanation:
One of the main limitations of Hierarchical databases is limited flexibility in data access .
Question 61 
Consider a Relational schema R(A, B, C, D) and functional dependencies A → B and C → D.
Then the decomposition of R into R1 (A, B) and R2(C, D) is
dependency preserving and lossless join
 
lossless join but not dependency preserving  
dependency preserving but not lossless join  
neither dependency·preserving nor lossless join 
Question 61 Explanation:
R_{1}(A,B) contains FD A→B
R_{2}(C,D) contains FD C→D
So, yes dependency preserving.
But there is no common attribute between R_{1} and R_{2}, hence not lossless join.
R_{2}(C,D) contains FD C→D
So, yes dependency preserving.
But there is no common attribute between R_{1} and R_{2}, hence not lossless join.
Question 62 
What is the highest normal form of a relation R(A, B, C, D, E) with FD set?
{B → A, A → C, BC → D, AC→ BE}
2NF  
3NF  
BCNF  
4NF 
Question 62 Explanation:
B → A
A → C
BC → D
AC → BE
B^{+} = BACDE
A^{+} = ACBED
So A & B are Candidate key.
There is no partial dependency, so in 2NF.
But in the BC → D, neither BC is key nor D is prime attribute, hence not in 3NF.
Note: Official Key given optionC is correct.
A → C
BC → D
AC → BE
B^{+} = BACDE
A^{+} = ACBED
So A & B are Candidate key.
There is no partial dependency, so in 2NF.
But in the BC → D, neither BC is key nor D is prime attribute, hence not in 3NF.
Note: Official Key given optionC is correct.
Question 63 
Which of the following statements is TRUE about static variables in C?
Their lifetime is exactly the same as the lifetime of the program  
Their lifetime is exactly the same as a register variable  
Their lifetime is exactly the same as that of the function in which they are declared, but they
retain their value between calls
 
None of the Above 
Question 63 Explanation:
The lifetime of static variables is exactly the same as the lifetime of the program .
Question 64 
An array of integers is declared in C language as
int pat [32] [10] ;
Which of the following array elements are in adjacent locations in memory?
pat [31] [6], pat [0] [7]  
pat [28] [0], pat [28] [9]  
pat [15] [0], pat [16] [0  
None of the Above. 
Question 64 Explanation:
After pat[31][6] the next location will be pat[31][7].
After pat[28][0] the next location will be pat[28][1].
After pat[15][0] the next location will be pat[15][1].
After pat[28][0] the next location will be pat[28][1].
After pat[15][0] the next location will be pat[15][1].
Question 65 
A shop announces a grand 13th anniversary sale where every customer is allowed to take 1300 worth of goods from the items listed below (each weighs 5 Kg). A person wishes to take items totalling 15 Kg in weight because airlines allow only 15 Kg to be carried. Which type of algorithm gives the correct solution to the problem of picking up items satisfying both the weight and free gift amount constraints?
Item A: 100, Item B: 300, Item C: 600, Item D: 800, Item E: 750
Greedy based on cost/weight ratio  
DivideandConquer  
Dynamic Programming
 
None of the Above 
Question 65 Explanation:
Dynamic programming means simplifying a complicated problem by breaking it down into simpler subproblems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart recursively.We can solve the above problem by considering cost as well as weight. We can consider some items and not considered some items by taking cost as well as weight.
It is not greedy because greedy algorithm follows the problemsolving heuristic of making the locally optimal choice at each stage with the intent of finding a global optimum.
It is nor divideandconquer because divideandconquer algorithm works by recursively breaking down a problem into two or more subproblems of the same or related type, until these become simple enough to be solved directly. The solutions to the subproblems are then combined to give a solution to the original problem.
It is not greedy because greedy algorithm follows the problemsolving heuristic of making the locally optimal choice at each stage with the intent of finding a global optimum.
It is nor divideandconquer because divideandconquer algorithm works by recursively breaking down a problem into two or more subproblems of the same or related type, until these become simple enough to be solved directly. The solutions to the subproblems are then combined to give a solution to the original problem.
Question 66 
Consider the following statements:
I. SRAMs are made up of flipflops each storing 1 bit
II. SRAMs are slower than DRAMs because SRAMs need more transistors than DRAMs which
use a transistor and a capacitor
Ill. SRAMs are more expensive than DRAMs
Which of the above statements are TRUE?
I and II only  
I and III only  
II and III only  
All 
Question 66 Explanation:
S1 and S3 are true. But S2 is false because SRAM is faster than DRAM.
Question 67 
Processes PI and P2 use cri tical_flag in the following routine to achieve mutual exclusion.
Assume that critical_flag is initialized to FALSE in the main program.
get_exclusive_access ( )
{
}
if (critical _flag == FALSE) {
critical_flag = TRUE ;
critical_region () ;
critical_flag = FALSE;
}
Consider the following statements.
I. It is possible for both PI and P2 to enter the critical region concurrently.
II. It is possible for deadlock to occur.
Which of the following holds TRUE?
I is FALSE but II is TRUE  
I is TRUE but II is FALSE  
Both I and II are FALSE
 
Both I and II are TRUE 
Question 67 Explanation:
S1 is true. Suppose P1 executed if part and entered the loop and then got preempted and then P2 will execute the if part and even P2 will enter the loop since the value of critical_flag is not modified by P1,hence both can enter the critical section concurrently.
S2 is false , because there is no way for deadlock to occur.
S2 is false , because there is no way for deadlock to occur.
Question 68 
A Page Table is given below in a virtual memory system having a page size of 1024. Each virnal
address is in the form [p, d] where p and d are the page number and the displacement in that
page, respectively. A virtual address of [0, 514] maps to an actual address of
514  
1024  
2562  
3586 
Question 69 
Nodes in a Resource Allocation Graph are
Processes  
Resources  
Processes and Resources
 
Outstanding resource requests 
Question 69 Explanation:
Nodes in a resource allocation graph are resources and processes.
Question 70 
Which of the following page replacement algorithms DOES NOT suffer from Belady's Anomaly?
First Come First Serve  
LRU  
Most Recently Used
 
None of the Above 
Question 70 Explanation:
Generally, on increasing the number of frames to a process’ virtual memory, its execution becomes faster as less number of page faults occur. Sometimes the reverse happens, i.e. more number of page faults occur when more frames are allocated to a process. This most unexpected result is termed as Belady’s Anomaly.
There are 70 questions to complete.