# RESEARCH METHODOLOGY FOR ENGINEERING

**Q1: A pot is fully filled (upto brims) with water. A cube of ice floating in it is partially submerged and partially seen above the water level. As the ice cube fully melts, what will happen to the level of water ?**

(A) The water spills over

(B) The water level decreases

(C) The water level remains the same

(D) The water level increases

Ans: (C) The water level remains the same

Solution: The water level will not change. As the mass of ice before and after melting will remain same. When the ice was floating, the volume of water displaced has the mass equal to that of ice. After melting, that mass of ice has been converted into water. Thus there is no net change in level.

**Q2: Suppose a 2-dimensional graph is to be plotted, with ‘s’ as independent variable, ‘p’ as dependent variable and also showing the impact of a 3rd variable, ‘q’, on the ‘p’ variable, then : **

(A) independent variable, ‘s’, is plotted along the x-axis; dependent variable, ‘p’, is plotted along y-axis holding ‘q’ constant, then other plots of ‘s’ vs. ‘p’ are done, each for a different value of ‘q’ held constant.

(B) ‘p’ is plotted along x-axis; ‘s’ is plotted along y-axis holding ‘q’ constant, then other plots of ‘s’ vs. ‘p’ are done, each for a different value of ‘q’ held constant.

(C) ‘s’ is plotted along x-axis; ‘q’ is plotted along y-axis holding ‘p’ constant, then other plots of ‘q’ vs. ‘s’ are done, each for a different value of ‘p’ held constant.

(D) ‘p’ is plotted along the x-axis; ‘q’ is plotted along the y-axis holding ‘s’ constant, then other plots of ‘q’ vs. ‘p’ are done, each for a different value of ‘s’ held constant.

Ans: (A) independent variable, ‘s’, is plotted along the x-axis; dependent variable, ‘p’, is plotted along y-axis holding ‘q’ constant, then other plots of ‘s’ vs. ‘p’ are done, each for a different value of ‘q’ held constant.

**Q3: In a laboratory experiment, while plotting a graph, **

(A) generally, 10 readings are taken, and a graph is plotted by connecting all the points plotted, even if it results in a zig-zag line.

(B) generally, 25 readings are taken, and a graph is plotted by connecting all the points plotted, even if it results in a zig-zag line.

(C) generally, 6 to 8 readings are taken, and a graph is plotted by connecting all the points plotted, even if it results in a zig-zag line.

(D) generally, 6 to 8 readings are taken, and a graph is plotted by drawing a smooth curve passing close to all points but may not touch all/several points.

Ans: (D) generally, 6 to 8 readings are taken, and a graph is plotted by drawing a smooth curve passing close to all points but may not touch all/several points.

**Q4: The distinction between parameter and variable is :**

(A) Parameter is an intrinsic property of the system and exists even if no input is applied to a system, while variable shows up only in response to applied input(s).

(B) Parameter is a fixed property of the system and exists even if no input is applied to a system, while variable is a variable quantity that shows up only in response to applied input(s).

(C) Parameter is a variable property of the system, while variable is a fixed property of the system.

(D) Parameter is a fixed property of the system and exists only if input is applied to a system, while variable is a variable property that shows up even if no input(s) is (are) applied.

Ans: (B) Parameter is a fixed property of the system and exists even if no input is applied to a system, while variable is a variable quantity that shows up only in response to applied input(s).

**Q5: In a class, the ratio of number of boys to girls is 5 : 3. What percentage of the students in the class are girls ?**

(A) 37.5 %

(B) 50 %

(C) 60 %

(D) 62.5 %

Ans: (A) 37.5 %

Solution: percenatge= (3/8 )*100 = 37.5 %

**Q6: If 25% of 260 equals 6.5% of P, what is P ?**

(A) 65

(B) 100

(C) 130

(D) 1000

Ans: (D) 1000

Solution: 25 % of 260 = 260/4 = 65

6.5 % of P = (6.5 x p )/ 100 = 65

So, P= 1000

**Q7: How many different arrangements are there of the letters A, B, C and D ?**

(A) 6

(B) 12

(C) 24

(D) 18

Ans: (C) 24

Solution: Possible arrangements with 4 objects= 4! = 4x3x2x1 =24

**Q8: In the figure below, a square of perimeter 24 is inscribed in a circle. What is the area of shaded region ?**

(A) 18π – 24

(B) 18π – 36

(C) 12π – 36

(D) 9π – 36

Ans: (D) 9π – 36

Solution: Perimeter of square= 4 x side = 24

So Side of square = 24/4 =6, which is the diameter of circle

So, radius of Circle= 6/2 = 3

Area of square = side x side = 6×6 = 36

Area of circle= π r^{2} = π x3x3 = 9π

Area of shaded region =Area of circle – Area of square = 9π – 36

**Q9: MULTAN : OUOTEN :: PURIFY: _**

(A) RUUIJY

(B) OQTVQS

(C) QVSJEZ

(D) None of these

Ans: (A) RUUIJY

Solution: MULTAN—->OUOTEN

M + 2= O

U = U

L + 3 = O

T = T

A + 4 = E

N =N

So PURIFY = RUUIJY as

P + 2= R

U=U

R + 3= U

I =I

F + 4= J

Y=Y

**Q10: If word PLAYER is coded as AELPRY, then word MANAGER is coded as :**

(A) AEAGMNR

(B) AAGEMNR

(C) AAEGMNR

(D) AAEGNMR

Ans: (C) AAEGMNR

Solution: The letters (Firstly, vowels and then consonants) of the word are arranged alphabetically.

**Q11: In the sequence below, some letters are missing. From the choices, select the choice that gives the letters that can fill the blanks in the sequence : a _ b _ _ _ a a _ b c _.**

(A) abcabc

(B) abccba

(C) abccbc

(D) ababcc

Ans: (C) abccbc

Solution: Inserting the letters of choice (3), in place of the blanks, we get a series which is a a b b c c a a b b c c.

Hence, the missing letters in the sequence are abccbc.

**Q12: The entropy of the universe is :**

(A) decreasing

(B) increasing

(C) constant

(D) getting halved every year

Ans: (B) Increasing

Solution: Total energy = Available energy( from which we can actually extract work ) + Unavailable energy (from which we cannot extract any useful work ).

Every time we try to extract useful work from Total energy(TE), some part eventually transforms into Unavailable energy(UAE). Which means Unavailable energy is increasing continuously.

Entropy is directly proportional to UAE. So as UAE increases, Entropy increases but Total Energy remains constant.

**Q13: How many 9’s are there in the following sequence which are either immediately followed by 9 or immediately preceded by 9 :793992896793579975**

(A) Four

(B) Two

(C) Three

(D) One

Ans: (A) Four

Solution: 793992896793579975

**Q14: What is the next letter in the series ?B, D, G, K, P, __**

(A) S

(B) V

(C) W

(D) X

Ans: (B) V

B + 2= D

D + 3 = G

G + 4= K

K + 5 =P

P + 6 = V

**Q 15: True value of a quantity can be practically obtained by : **

(A) mean of squares of a number of readings taken under no bias conditions such that positive deviations cancel out negative deviations.

(B) mean of a large number of readings taken under no bias conditions such that positive deviations cancel out negative deviations.

(C) whatever is measured by a laboratory or industrial meter.

(D) the actual value obtained after removing parallax error.

Ans: (D) the actual value obtained after removing parallax error.

**Q16: The sum, s, of probabilities of all outcomes of an event or a statistical experiment is : **

(A) zero

(B) 0 < s < 1

(C) 0 ≤ s ≤ 1

(D) 1

Ans: (D) 1

Solution: In an experiment ,the sum of probabilities for all possible outcomes is equal to one.

This means, for example, that if an experiment can have three possible outcomes (A, B, and C),

then P(A) + P(B) + P(C) = 1.

**Q17: If ‘+’ stands for ‘–’, ‘–’ stands for ‘×’, ‘×’ stands for ‘÷’, and ‘÷’ stands for ‘+’,then evaluate : 56 × 7 ÷ 13 – 11 + 15 – 8 ÷ 2 – 7**

(A) 30

(B) 45

(C) 60

(D) 90

Ans: (B) 45

Solution :56 × 7 ÷ 13 – 11 + 15 – 8 ÷ 2 – 7 means to calculate

56 ÷ 7 + 13 x 11 – 15 x 8 + 2 x 7

= 8 + 143 – 120 + 14

=45

**Q18: An engineer starts from home and travels 10 m towards West, then turns right and travels 40 m. He then travels 25 m East followed by 50 m towards the South to reach his factory. What is the approximate distance between his home and factory ?**

(A) 18 m

(B) 125 m

(C) 25 m

(D) 105 m

Ans: (A) 18 m

**Q19: A compass was damaged and its needle twisted / turned in such a manner that the pointer which was showing East, now showed North. A man went towards West as per the above mentioned compass. In which direction did he actually go ?**

(A) South-West

(B) South

(C) North-East

(D) North

Ans: (B) South

**Q 20: One evening, a person was facing a pole. The shadow of the pole fell to his right. Which direction he was facing ?**

(A) East

(B) West

(C) North

(D) South

Ans:(C) North

Solution: We know that the sun rises in the east and sets in the west. If the shadow of the pole fell exactly to his right, then the sun must be to his left. If the sun is to his left, then that direction must be the **west** direction. If the west direction lies to his left then he must be facing the **north** direction.

**Q21: When a watch shows 3 : 45, the minute hand points towards East. When the watch shows 6 O’clock, in what direction will the hour hand point ?**

(A) North

(B) South

(C) East

(D) West

Ans: (A) North

**Q22: A is the husband of B. E is the daughter of C. A is the father of C. How is B related to E ?**

(A) Mother

(B) Grandmother

(C) Aunt

(D) Cousin

Ans: (B) Grandmother

**Q23: If we take the union and intersection respectively of a crisp/classical set with its compliment, what is the resultant in each case ?**

(A) 1 and 0 respectively.

(B) 0 and 1 respectively.

(C) Universal set, X, and Null set, ø, respectively.

(D) Null set, ø, and Universal set, X, respectively.

Ans: (C) Universal set, X, and Null set, ø, respectively.

**Q24: If P, Q and R are matrices, and if PQ = PR, then it :**

(A) does not imply that Q = R, except if P is non-singular.

(B) always implies that Q = R.

(C) never implies that Q = R.

(D) implies that Q and R are commutative under multiplication

Ans: (A) does not imply that Q = R, except if P is non-singular.

**Q25: If P and Q are matrices, then :**

(A) order of PQ is always the same as that of QP

(B) PQ = QP provided that matrices are conformable for multiplication in both cases

(C) in general, PQ may or may not be equal to QP

(D) both “A” and “B”

Ans: (C) in general, PQ may or may not be equal to QP

**Q26: How many negative integers satisfy | ** **x + 4 | + | x – 7 | = 13 ?**

(A) 2

(B) 3

(C) 4

(D) 5

Ans:

**Q27: If x∈R, the greatest value that x ^{4} / (1 + x^{8}) attains is :**

(A) 2/5

(B) 1/3

(C) 3/4

(D) 1/2

Ans: (D) 1/2

Solution: x∈R i.e. may be positive or negative, but x^{4} and x^{8} are both always positive, being the even powers.

Consider x^{4} = t

x^{4} / (1 + x^{8})= t/(1+ t^{2})

Smallest value of t =0 and 0 / (1+ 0) = 0

Next value of t= 1 and 1/(1 + 1) = 1/2

Next value of t= 2 and 2/(1 + 4) = 2/5

Next value of t= 3 and 3/(1 + 9) = 3/10

and so on.

We can see values are decreasing. and max value is 1/2

**Q28: Researcher S’s teaching experience (in years) is twice that of researcher M. But 2 years back, S’s teaching experience was thrice that of M. How many years S has been teaching ?**

(A) 8 years

(B) 10 years

(C) 12 years

(D) 16 years

Ans: (A) 8 years

Solution: Let experience of M = x years

So, experience of S = 2x years

2 Years Back, experience of M = x-2 years

and, experience of S = (2x -2) years

Given, (2x-2) = 3(x-2) = 3x – 6

6-2 = 3x – 2x

So, x=4

And, experience of S = 2x years = 8 years

**Q29: If you add three quarters of the number of Labs I have, to three quarters of a Lab., you will get the number of Labs I have. How many labs do I have ?**

(A) 3

(B) 4

(C) 6

(D) 9

Ans: (A) 3

Solution: let no of labs I have= x

ATQ, 3x/4 + 3/4 =x

3x + 3 =4x

x=3

**Q30: A Ph.D. entrance test had 60 questions. A student scores 1 mark for a correct answer, –1/2 for a wrong answer and –1/4 for not attempting a question. A candidate attempted 48 questions and got a net score of 33 marks. How many questions did he attempt wrongly ?**

(A) 8

(B) 12

(C) 14

(D) 10

Ans: (A) 8

Solution: Total attempted = 48 questions

Let correct attempted = x questions and marks= x

then incorrect attempted= 48-x questions and marks = -(48-x)/2

Not attempted = 60 – 48 = 12 questions and marks =-12/4 = -3

ATQ, x – (48-x) /2 – 3 = 33

2x – 48 + x – 6 = 66

3x= 120

x= 40

wrong/ incorrect attempted= 48-x = 48-40 = 8 questions

**Q31: Among the visitors to a Lab., the ratio of the number of Professors to B.Tech. students was the same as that of B.Tech. students to Research Scholars. Greater number of visitors were Research Scholars who were attracted by research facilities in the Lab. One day, 7 B.Tech. students visited the said Lab. How many Research Scholars visited the Lab. that day ?**

(A) 44

(B) 49

(C) 52

(D) 57

Ans: (B) 49

Solution: Let no of Professor = x

No of BTech Students = 7

NO of Research Scholars = y

ATQ, x/7 = 7/y

xy = 49 = 1 x 49 or 7 x 7

But greater number no visitors were research scholars.

So, no of research scholars were 49 and Professor were= 1

**Q32: A dealer bought an equipment at 30% discount on the list price. He then sold it at a price which is 160% of the list price, thereby making a profit of Rs. 81. What is the list price of the equipment ?**(A) 100

(B) 90

(C) 80

(D) 240

Ans: (B) 90

Solution: Let list price = x

He bought at 30 % discount means at 70x/100

Sale Price SP = 160% of list price = 160x/100

Profit = 160x/100 – 70x/100 = 81

160x – 70x = 8100

90x = 8100

x = 90

**Q33: A researcher found that for the 1007 pages of his thesis, there were on an average 2 mistakes per page, while in the first 612 pages, there were only 434 mistakes, they seemed to increase for the latter pages. Find the average number of mistakes per page for the remaining pages :**

(A) 6

(B) 4

(C) 2

(D) 3

Ans: (B) = 4

Solution: Total mistakes = 1007 x 2 =2014

Mistakes in 612 pages = 434

Mistakes in remaining pages = 2014 – 434 = 1580

Remaining no of pages = 1007 – 612 = 395

Average no of mistakes in remaining pages = 1580 / 395 = 4

**Q34: After enjoying a feast at my college canteen with 12 friends, I paid Rs. 145 but my each friend paid an equal amount, say X. Later we found that the average sum paid by all of us was Rs. 5 more than what was originally paid by each of my friends. What amount did each friend pay ?**

(A) Rs. 120

(B) Rs. 100

(C) Rs. 95

(D) Rs. 80

Ans: (D) Rs 80

Solution: I paid = 145 Rs

Let each friend paid = x Rs

12 Friends paid = 12x Rs

Total amount = 12x + 145 Rs

Average = (12x + 145 )/13 Rs

ATQ, (12x + 145) / 13 = x + 5

12x + 145 = 13x + 65

x = 145-65 = 80 Rs

**Q35: A tank of 60000 litres capacity has three inlet taps P, Q and R which can individually fill the tank in 20, 15 and 12 hours respectively. It has an outlet pipe S which can supply water to 100 houses. If all the pipes are opened simultaneously, how much water enters the tank every hour ?**

(A) 8000 litres

(B) 9600 litres

(C) 11400 litres

(D) 12000 litres

Ans: (D) 12000 litres

Solution: ^{1}/_{20} + ^{1}/_{15} + ^{1}/_{12} = ^{12}/_{60} = ^{1}/_{5}

In 1 hour they can fill ^{1}/_{5} th tank = 60000 / 5 = 12000 litres

**Q36: In domestic installations, we get phase to ………. voltage which is about …… V while in industrial installations, we usually get phase to ……… voltage which is about ……. V:**

(A) neutral, 440, phase, 230 (B) neutral, 230, phase, 440

(C) neutral, 230, phase, 400 (D) phase, 230, neutral, 400

Ans:

Solution:

P, Q, R and S are motor wiremen. Working alone, wireman P can wire 1 motor

in 12 hours. Q is 20% faster P. R is 50% faster than P. S is twice as fast as P.

In how much time R alone can do wiring of 90 motors ?

(A) 720 hours (B) 600 hours

(C) 320 hours (D) 480 hours

P and Q run a closed circuit race. Besides leading just after start, P overtakes Q

twice per round. What is P’s speed compared to Q’s ?

(A) 4 times (B) 3 times

(C) 2 times (D) 5 times

An upstream journey of 18 km takes a motor boat 3 hours more than the same

distance downstream. If the motor boat speed in still water is twice the speed of

the stream, find the speed of the stream :

(A) 7.2 km/hr (B) 6 km/hr

(C) 4.5 km/hr (D) 4 km/hr

In the figure below, PQ = PR = PS and angle QRP = 30°. Find angle QSP.

(A) 30° (B) 40°

(C) 45° (D) 60°

- In the table below, Types of Research are given on left hand side. A few

Characteristics are given on the right hand side. Then in the further underneath

Table, possible matches are given; select the best choice :

Research Types Characteristics

(a) Fundamental research (i) Finding out the extent of perceived

impact of an intervention.

(b) Applied research (ii) Developing an effective foundation

through theory building.

(c) Action research (iii) Improving an existing situation

through the use of apt interventions.

(d) Evaluative research (iv) Exploring the possibility of a theory

for use in various situations.

(a) (b) (c) (d)

(A) (i) (ii) (iii) (iv)

(B) (ii) (iii) (iv) (i)

(C) (iii) (iv) (i) (ii)

(D) (ii) (iv) (iii) (i) - A researcher is asked, “What is the probability of finding an apple in the

refrigerator ?” The researcher had no idea, neither knowledge nor prior information

about an apple having been kept in the refrigerator. Yet he answers, without bias

or inclination, as follows; what is his best answer ?

(A) 1.0 (B) 0.75

(C) 0.5 (D) 0

M-PHD-CSE-A 12 - While writing a research paper, which one of the following statements is most

true ?

(A) The ‘Abstract’ contains a gist of the entire paper but has no citation of

references.

(B) The ‘Abstract’ contains a gist of the entire paper and has citation of

references cited in the ‘Abstract’ part alone.

(C) The ‘Future Directions’ section must cite the possible offshoots which the

authors perceive themselves as well as those perceived by previous

researchers.

(D) The ‘Materials and Methods’ section, if detailed in the paper, must carry out

a comprehensive analysis of results. - A chain has five links in it, each of which can individually carry a maximum

weight of 2.3 Kg, 1.7 Kg, 5.3 Kg, 2.7 Kg and 0.7 Kg. Then which statement is

most apt for this chain ?

(A) The strength of this chain is that of the strongest link in it

(B) The strength of this chain is that of the weakest link in it

(C) The strength of this chain is 12.7 Kg

(D) The strength of this chain is the average of the individual link strengths - What type of reasoning is used in the following statement ?

“Superiority of intellect depends on its power of concentration on one theme in

the same way as a convex lens collects all the rays that strike upon it, into one

point” :

(A) Psychological (B) Mathematical

(C) Deductive (D) Analogical

M-PHD-CSE-A 13 P.T.O. - In the context of publications, which statement is true for SCI ?

(A) Scientific Citation Index is a citation index originally produced by the

Institute for Scientific Information and created by Eugene Garfield.

(B) Super Citation Index is a citation index originally produced by the Institute

for Scientist’s Information and created by Bill Gates.

(C) Science Citation Index is a citation index originally produced by the Institute

for Scientific Information and created by Eugene Garfield.

(D) Science Common Index is a citation index originally produced by the Institute

for Scientific Information and created by Clarivate Analytics. - The term ICT usually refers to :

(A) An acronym that stands for Indian Classical Technologies

(B) Convergence of audio-visual and telephone networks with computer networks

through a single cabling or link system

(C) Unified communications and integration of telecommunications, computers,

enterprise software, middleware, audio-visual systems and storage

(D) Both “B” and “C” - With reference to a fixed frame of reference, your competitor moves forward with

a velocity of 9.8 m/second while you too move forward a velocity of 5.2 m/sec

with reference to the same frame. What is your velocity vis-à-vis that of your

competitor ?

(A) 15 m/sec in forward direction

(B) 4.6 m/sec in forward direction

(C) 7.5 m/sec in forward direction

(D) 4.6 m/sec in backward direction

49. In the following figure (not drawn to scale), angle DEF = 35°. Find the other

two angles of triangle DEF if DE and DF are the angle bisectors of angles ADB

and ADC respectively :

(A) 30° and 120°

(B) 65° and 80°

(C) 55° and 90°

(D) 70° and 75°

- A publisher publishes journals in two modes – Subscription mode, and Open

access mode. Which choice is most correct in the context of an open access

journal :

(A) It is a journal of which the subscription cost is borne by the subscriber.

(B) It is a journal of which the contents are freely accessible by anybody in the

world.

(C) It is a journal of which the subscription cost per paper is borne by the

respective author.

(D) “B” and “C”