Mock CAT - 2 Test Booklet Serial Number: 7 7 0 3 6 0

INSTRUCTIONS
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How to answer:
1. This test has three sections which examine various abilities. These 3 sections have 90 questions in all with
each section having 30 questions. You will be given two and half hours to complete the test. In distributing
the time over the three sections, please bear in mind that you need to demonstrate your competence in all
three sections.
2. Directions for answering the questions are given before some of the questions wherever necessary. Read
these directions carefully and answer the questions by darkening the appropriate circles on the Answer
Sheet. There is only one correct answer to each question.
3. Each section carries 100 marks. Each section is divided into two sub-sections, A and B. All Questions in
sub-sections I-A, II-A and III-A carry two marks each. All Questions in sub sections I-B, II-B and III-B
carry four marks each. Wrong answers will attract a penalty of one-fourth the marks allotted to the questions.
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Candidates giving assistance or seeking/receiving help from any source in answering questions or copying
in any manner in the test will have their Answer Sheets cancelled.

MCT-0006/08 Test Form Number: 002

 SECTION – I

Sub-section I-A: Number of Questions = 10

Note: Questions 1 to 10 carry 2 marks each.

DIRECTIONS for questions 1 to 3: Answer the questions on the basis of the information given below.
The following table provides information about twenty Presidents of United States of America. They belong
to one out of the three different parties namely Democrat (D), Whig (W) and Republic (R). The table also
provides information about the tenure of their Presidentship and the state which they belong to.
The dates in the “Duration of Service” should be read as Year – Month – Date.
For example, 1841 – 04 – 06 should be read as 6th of April in the year 1841.

S.No. Persons Party Duration of Service (Both Inclusive) State

1 John Tyler W 1841-04-06 to 1845-03-03 Virginia
2 James K. Polk D 1845-03-04 to 1849-08-01 Tennessee
3 Zachary Taylor W 1849-08-02 to 1850-07-09 Louisiana
4 Millard Fillmore W 1850-07-10 to 1853-11-03 New York
5 Franklin Pierce D 1853-11-04 to 1857-03-03 New Hampshire
6 James Buchanan D 1857-03-04 to 1861-09-03 Pennsylvania
7 Abraham Lincoln R 1861-09-04 to 1865-04-15 Illinois
8 Andrew Johnson R 1865-04-16 to 1869-03-03 Tennessee
9 Ulysses S. Grant R 1869-03-04 to 1877-12-30 Illinois
10 Rutherford B. Hayes R 1877-12-31 to 1881-03-03 Ohio
11 James Garfield R 1881-03-04 to 1881-09-19 Ohio
12 Chester A. Arthur R 1881-09-20 to 1886-03-03 New York
13 Grover Cleveland D 1886-03-04 to 1889-03-03 New York
14 Benjamin Harrison R 1889-03-04 to 1893-03-03 Indiana
15 Grover Cleveland D 1893-03-04 to 1898-03-03 New York
16 William McKinley R 1898-03-04 to 1901-09-13 Ohio
17 Theodore Roosevelt R 1901-09-14 to 1909-03-03 New York
18 William Howard Taft R 1909-03-04 to 1913-03-03 Ohio
19 Woodrow Wilson D 1913-03-04 to 1921-03-03 New Jersey
20 Warren G. Harding R 1921-03-04 to 1927-03-09 Ohio

1. Among the following, who was the President of United States of America for the maximum duration?
(1) Grover Cleveland (2) Theodore Roosevelt (3) Woodrow Wilson
(4) Ulysses S. Grant (5) None of these

2. How many of these persons belonged to the Republic party and were the President of United States of
America for a tenure ranging from 2 to 5 years?
(1) Five (2) Six (3) Seven (4) Eight (5) Nine

3. A group out of these persons is formed in which, for every person in the group there is at least one more
person who belonged to the same party and the same state as him/her. The number of Presidents in this
group cannot exceed
(1) 9 (2) 10 (3) 14 (4) 12 (5) 11

002 1
DIRECTIONS for Questions 4 to 7: Answer the questions on the basis of the information given below.
MS, MBA, LLB, MD and MHM are the five most sought after professional degree programmes in each of the
five countries viz. India, US, UK, Austrailia, and Singapore. To complete any of these degrees, students can
choose to study in any of these five countries. After the completion of their degrees, these students become
professionals employable in all the five countries. The following table lists the total Expenses Incurred (EI) on
these professional degrees and the Annual Incomes (AI) earned by the professionals, in their first job after the
completion of their degrees, in each of these five countries in the local currencies.

Expenses Incurred(EI) and Annual Incomes (AI)

Degree India (INR) US (USD) UK (GBP) Austrailia (AUD) Singapore (SGD)
EI AI EI AI EI AI EI AI EI AI
MS 50000 600000 36500 40000 30000 20000 35000 30000 50000 60000
MBA 400000 800000 45000 30000 28000 10000 40000 60000 55000 90000
LLB 300000 500000 35000 50000 20000 40000 32000 40000 42000 120000
MD 1500000 2000000 62000 60000 25000 80000 28000 70000 40000 100000
MHM 180000 240000 50000 70000 70000 90000 20000 25000 40000 60000

Using the following table, the EI and the AI figures of different countries can be compared.

Exchange Rates
Currency Equivalent to INR
One USD 39.8
One GBP 79
One AUD 35.9
One SGD 28.7

Assume that the data given in the above two tables is valid for every year. Also assume that professionals
receive no increment in their salaries, unless specified.

4. Studying in which of these five countries, a student gets the best return on the expense incurred by him,
at the end of one year, if he completes MHM degree and works in the same country ?
(1) India (2) US (3) UK
(4) Australia (5) Singapore

5. Mr. Smith works in Australia for an Australian company. The company sponsors him an interest free
loan of 75% of the total expense on his MBA degree in UK. In return, Mr. Smith has to serve the
company for three consecutive years in Australia after completing his MBA. The salary net of deductions
that the company can pay Mr. Smith, when employing him again, for full recovery of the loan amount
over the period of three years cannot be more than
(1) 44600 AUD (2) 25600 AUD (3) 15400 AUD
(4) 18400 AUD (5) None of these

2 002
6. Mr. H. Gopal Shastry lives in India. In a few days, he will leave for UK to pursue a one year MBA
degree. Airfare from India to UK is INR 16500 and that from UK to India is GBP 386. Before completing
his degree, he wishes to visit India. Before allocating money for his expense on his MBA degree in UK,
his total Budget for tuition and travel is INR 2340000 only. How many times, from UK, can he make a
return trip to India ?
(1) Only Once (2) Only Twice (3) Only Thrice
(4) Only Four Times (5) Only Five Times

7. Amol and Bimal completed their MS degrees in Singapore and in US respectively funded through a
zero interest loan. After completion of their degrees, Amol started working in US and Bimal started
working in Singapore. Taking into account, their expenditures on degrees and their salaries only, the
difference in the income available to be spent for Amol and Bimal after repaying their study loans, at
the end of first year of their jobs is approximately
(1) 2820 USD (2) 3055 USD (3) 3925 USD
(4) 4300 USD (5) 10700 USD

DIRECTIONS for Questions 8 to 10: Answer the questions on the basis of the information given below.
The result of AIEEE 2008 for 17 Indian states is given below. The table provides both State Rank and All
India rank for a certain set of people. For example there are 200 students in Haryana who had a state rank
ranging from 800 to 1600 and an All India Rank ranging from 4000 to 5000. No two students can have same
All India Rank, or even same state rank from the same state.

S.No. State State rank All India Rank Number of students

1 Kerala 1-400 2000-4000 250
2 Tamil Nadu 200 -400 3000-5000 100
3 Delhi 500-900 1000-2000 400
4 Andhra Pradesh 500-1000 4000-5000 250
5 Uttar Pradesh 600-1200 500-2500 150
6 Madhya Pradesh 1000-1500 3500-4500 300
7 Bihar 2000-2500 4000-5000 400
8 Rajasthan 100-300 500-1000 100
9 Haryana 800-1600 4000-5000 200
10 Himachal Pradesh 700-1000 3000-4000 100
11 Jharkhand 100-300 500-1000 150
12 Maharashtra 200-800 1000-2000 300
13 Karnataka 400-700 3000-3500 100
14 Orissa 500-1000 300-600 50
15 Uttaranchal 1000-1500 6000-7000 400
16 Punjab 300-800 2500-3000 200
17 West Bengal 400-1000 2000-3000 250

8. The number of students that have State Rank greater than 450 and an All India Rank less than or equal
to 2000 out of the students given in the table is atleast
(1) 500 (2) 450 (3) 900 (4) 350 (5) 499

002 3
9. TIIT Hyderabad has an admission criteria for its students which requires both state and All India rank to
be less than or equal to 1000 . If every student who qualifies this criteria gets admitted from these 17
states, the number of seats in TIIT, Hyderabad is atmost
(1) 550 (2) 450 (3) 400
(4) 300 (5) 451

10. Dali College of Engineering has admission criteria for every aspirant that he / she must have a state rank
less than or equal to 500 in their respective states. Which state has the maximum number of students in
Dali College of Engineering if every student applies there for admission?
(1) Kerala (2) Maharashtra (3) Punjab
(4) Jharkhand (5) Cannot be determined

4 002
 Sub-section I-B: Number of Questions = 20

Note: Questions 11 to 30 carry 4 marks each.

DIRECTIONS for Questions 11 to 14: Each question is followed by two statements, A and B. Answer each
question using the following instructions:

Mark (1) if the question can be answered by using the statement A alone but not by using the statement B
alone.
Mark (2) if the question can be answered by using the statement B alone but not by using the statement A
alone.
Mark (3) if the question can be answered by using either of the statements alone.
Mark (4) if the question can be answered by using both the statements together but not by either of the
statements alone.
Mark (5) if the question cannot be answered on the basis of the two statements.

11. Is b2 + 2ab − 48a 2 > 0

A: ax 2 + bx + 4a > 0, for every real x.
B: 2ax + 4bx + 3 = 0 for only one real x.

12. In a quadrilateral ABCD, BD = 10 cm, AB = 6 cm and CD = 8 cm. Determine the area of quadrilateral
ABCD?
A: M1 and M2 are midpoints AB and CD respectively. M1M2 = 5 cm and ∠BDC = 30°.
B: M1 and M2 are midpoints of AB and AD respectively. M1M2 = 5 cm and ∠ABD = 45°.

13. Ryan, Samar, Julie, Merissa, Sandy and Nicole are siblings. Sandy is younger than both Merissa and
Ryan. Julie is older than Samar. Merissa is younger than Samar but older than Nicole. Who is the oldest
among them?
A: The aggregate age of Samar and Ryan is less than the aggregate age of Nicole and Merissa.
B: The aggregate age of Julie and Merissa is less than the aggregate age of Ryan and Nicole.

14. Jerry, Sherry and Larry played one out of the three sports namely badminton, squash and table tennis .
Their respective opponents in these sports is one among the three persons namely Dhiru, Veeru and
Neeru. All games are played between exactly two people. Who is the opponent of Larry?
A: Veeru is not the opponent of Larry and Jerry did not play table tennis
B: Veeru did not play badminton and Dhiru played squash.

002 5
DIRECTIONS for Questions 15 to 18: Answer the questions on the basis of the information given below.
A car manufacturing company XYZ sold 10000 cars in the year 2007. Out of the twelve months in the year,
the number of months in which the company sold more than 1000 cars is five and each of these five months
is termed “Productive” by the company. The company formed 12 groups of months such that each group had
six months each. Out of the 12 groups, there is only 1 group in which there are no “Productive” month and 1
group in which there are exactly 5 “Productive” months. The group in which there are exactly 5 “Productive”
months is Group 7.

The following table provides information about the composition of each of the 12 groups formed by the
company.

Month 1 Month 2 Month 3 Month 4 Month 5 Month 6

Group 1 November October January June March February
Group 2 June November July October September March
Group 3 January February March April July August
Group 4 June March October December November April
Group 5 August February November September July May
Group 6 December March January February April July
Group 7 January April September July May August
Group 8 June November May October March December
Group 9 December June March September July May
Group 10 February May August April January July
Group 11 November December March May October June
Group 12 February March June January December October

15. Which of the following months is not termed “Productive” by the company?
(1) January (2) May (3) September (4) April (5) August

16. How many groups have four “Productive” months?

(1) 5 (2) 1 (3) 2 (4) 3 (5) 4

17. Which of the following statements is/are NOT true?

A. There is only 1 group in which the number of months that are not termed “Productive” by the
company is 4.
B. There are exactly two pairs of consecutive months that are termed “Productive” by the company.
C. There are exactly four pairs of consecutive months that are not termed “Productive” by the company.
(1) Only A (2) Only C (3) Both B and C
(4) Both A and C (5) Neither A nor B nor C.

18. In how many groups the number of “Productive” months is not more than the number of months that
are not “Productive”?
(1) 9 (2) 8 (3) 7 (4) 10 (5) None of these

6 002
DIRECTIONS for Questions 19 to 22: Answer the questions on the basis of the information given below.
Many Asian countries including China, Japan, Kazakhstan, India, Singapore, Malaysia and Jordon participated
in one or more sporting events held at the 2006 Asian Games. In each sporting event at least three countries
participated. At the end of each sporting event, the country finishing at the first, the second and the third
positions were awarded a gold, a silver and a bronze medal respectively. The following bar graph shows
distribution of the three types of medals. In this graph, the parts marked by “Data Not Available” may have
belonged to one or more of all the participating countries.

100%
10.50%
90% 23.00% 31.00%
80% 14.50%
70% 12.50% 15.50%
10.00%
60% 10.00%
50% 20.50% 15.00%
15.50%
40%
12.50% 16.50%
30%
20% 18.00% 12.50%
37.50%
10%
10.50% 15.00%
0%
Gold Silver Bronze
China Japan Kazakhstan
India Singapore Malaysia
Jordon Data Not Available

19. Which of the following could not have been the sum of the number of silver and the number of bronze
medals won by Malaysia ?
(1) 142 (2) 164 (3) 213 (4) 284 (5) 355

20. What was the ratio of the number of gold medals won by Singapore to the number of silver medals won
by Jordon ?
(1) 21 : 31 (2) 4 : 5 (3) 31 : 33 (4) 29 : 31 (5) Cannot be determined

21. The total number of medals won by India was at least what percentage of the total number of medals
won by China?
(1) 31.12% (2) 75.80% (3) 62.24% (4) 39.50% (5) Cannot be determined

22. It is given that the parts of the graph marked as “Data Not Available” belonged to exactly one of the
seven countries that are mentioned above but was not included in the respective bar in the graph. When
arranged in an ascending order of the total number of medals won, which of the following will never be
a possible case ?
(1) Jordon, Japan, Kazakhstan (2) Malaysia, India, Singapore
(3) Japan, China, Singapore (4) Japan, Singapore, Jordon
(5) Malaysia, India, Kazakhstan

002 7
DIRECTIONS for Questions 23 to 26: Answer the questions on the basis of the information given below.
A public poll was conducted to find the most popular sportsman in the year 2007. The public poll was
conducted in five rounds namely Round I, Round II, Round III ,Round IV and Round V in that particular
order. The same group of 200 people voted in each of the five rounds. The nominees for the most popular
sportsman award were P, Q, R, S, T and U. The following table provides information about the number of
votes received by each of these six nominees in the given rounds. One person can vote for only one nominee
in the given rounds.

I II III IV V
P 34 39 43 29 34
Q 26 39 31 35 29
R 52 32 43 36 41
S 21 34 28 29 28
T 43 43 36 35 44
U 24 13 19 36 24

Additional Information Given:

1. Persons, who voted for P in any round, voted for either S or T in the following round.
2. Only those persons, who voted for Q or U in any round, voted for P in the following round.
3. Persons, who voted for T in any round, voted for either R or U in the following round.
4. Persons who voted for S in round I, voted for S in each of the next three rounds.

23. Magic number for a nominee is defined as the number of nominees who have got lesser number of
votes than him/her in exactly two rounds. Find the aggregate sum of the magic numbers for all the
nominees.
(1) 0 (2) 1 (3) 2 (4) 3 (5) 4

24. Out of the number of persons who voted for P in any round, the number of persons who voted for S is
at least
(1) 10 (2) 12 (3) 9 (4) 8 (5) 11

25. The number of persons who voted for the same nominee across all the five rounds is at most
(1) 36 (2) 31 (3) 35 (4) 39 (5) 32

26. If out of the persons who voted for Q in round IV, maximum number of persons voted for R in round
V, then out of the persons who voted for U in round IV, at most how many persons voted for
Q in round V?
(1) 7 (2) 13 (3) 9 (4) 8 (5) 11

8 002
DIRECTIONS for Questions 27 to 30: Answer the questions on the basis of the information given below.
Five guests namely A, B, C, D and E are staying in a hotel. Each of theses five mentioned guests ordered one
item each for breakfast, lunch and dinner. The items ordered by the guests are distinct.
The following table provides information about the items ordered for breakfast, lunch and dinner by these
mentioned guests.

Item 1 Item 2 Item 3 Item 4 Item 5

Breakfast Biscuit Eggs Milk Salad Toast
Lunch Burger Continental Dosa Fruits Rice
Dinner Chicken Chinese Pizza Rotis Upma

Additional Information Given:

1. The only items that are classified as “Non – Vegetarian” are eggs, continental, chicken and burger.
Further, each of A, B and C did not order “Non – Vegetarian” items
2. B is a patient and ordered milk in the breakfast.
3. The items ordered by C have at least two items whose names start with the same alphabet. This holds
true for D as well as E.
4. E ordered exactly two “Non – Vegetarian” items but did not order chicken.
5. Out of the mentioned guests, there is only one guest who is from south India and he/she ordered both
dosa and upma.
6. The guest who ordered toast also ordered fruits.

27. Which of the mentioned guests is from south India?

(1) A (2) B (3) C (4) D (5) E

28. Which of the following item is also ordered by the guest who ordered fruits?
(1) Rice (2) Biscuit (3) Rotis (4) Pizza (5) None of these

29. Which of the following is not the guest who did not order Salad?
(1) E (2) D (3) B (4) A (5) C

30. Which of the following items is not ordered by the guest who ordered Rotis?
(1) Salad (2) Rice (3) Burger
(4) Both (1) and (2) (5) Both (2) and (3)

002 9
 SECTION – II

Sub-section II-A: Number of Questions = 10

Note: Questions 31 to 40 carry 2 marks each.

DIRECTIONS for Questions 31 to 34: The passage given below is followed by a set of questions. Choose
the best answer to each question.

PASSAGE

Wittgenstein’s Philosophical Investigations says that: “For a large class of cases - though not for all - in which
we employ the word “meaning” it can be defined thus: the meaning of a word is its use in the language.”

It is quite clear that here Wittgenstein is not offering the general theory that “meaning is use,” as he is sometimes
interpreted as doing. The main rival views that Wittgenstein warns against are that the meaning of a word is
some object that it names - in which case the meaning of a word could be destroyed, stolen or locked away,
which is nonsense - and that the meaning of a word is some psychological feeling - in which case each user of
a word could mean something different by it, having a different feeling, and communication would be difficult
if not impossible.

Knowing the meaning of a word can involve knowing many things: to what objects the word refers (if any),
whether it is slang or not, what part of speech it is, whether it carries overtones, and if so what kind they are,
and so on. To know all this, or to know enough to get by, is to know the use. And generally knowing the use
means knowing the meaning. Philosophical questions about consciousness, for example, then, should be
responded to by looking at the various uses we make of the word “consciousness.” Scientific investigations
into the brain are not directly relevant to this inquiry (although they might be indirectly relevant if scientific
discoveries led us to change our use of such words). The meaning of any word is a matter of what we do with
our language, not something hidden inside anyone’s mind or brain. This is not an attack on neuroscience. It
is merely distinguishing philosophy (which is properly concerned with linguistic or conceptual analysis) from
science (which is concerned with discovering facts).

One exception to the meaning-is-use rule of thumb is given in Philosophical Investigations Sect.561, where
Wittgenstein says that “the word “is” is used with two different meanings (as the copula and as the sign of
equality)” but that its meaning is not its use. That is to say, “is” has not one complex use (including both
“Water is clear” and “Water is H2O”) and therefore one complex meaning, but two quite distinct uses and
meanings. It is an accident that the same word has these two uses. It is not an accident that we use the word
“car” to refer to both Fords and Hondas. But what is accidental and what is essential to a concept depends on
us, on how we use it.

This is not completely arbitrary, however. Depending on one’s environment, one’s physical needs and desires,
one’s emotions, one’s sensory capacities, and so on, different concepts will be more natural or useful to one.
This is why “forms of life” are so important to Wittgenstein. What matters to you depends on how you live
(and vice versa), and this shapes your experience. So if a lion could speak, Wittgenstein says, we would not
be able to understand it. We might realize that “roar” meant zebra, or that “roar, roar” meant lame zebra, but
we would not understand lion ethics, politics, aesthetic taste, religion, humor and such like, if lions have these
things. We could not honestly say “I know what you mean” to a lion. Understanding another involves empathy,
which requires the kind of similarity that we just do not have with lions, and that many people do not have
with other human beings.

10 002
When a person says something what he or she means depends not only on what is said but also on the context
in which it is said. Importance, point, meaning are given by the surroundings. Words, gestures, expressions
come alive, as it were, only within a language game, a culture, a form of life. If a picture, say, means something
then it means so to somebody. Its meaning is not an objective property of the picture in the way that its size
and shape are. The same goes of any mental picture. Hence Wittgenstein’s remark that “If God had looked
into our minds he would not have been able to see there whom we were speaking of.” Any internal image
would need interpretation. If I interpret my thought as one of Hitler and God sees it as Charlie Chaplin, who
is right? Which of the two famous contemporaries of Wittgenstein’s I mean shows itself in the way I behave,
the things I do and say. It is in this that the use, the meaning, of my thought or mental picture lies. “The arrow
points only in the application that a living being makes of it.”

31. What is the central theme of the passage?

(1) The meaning of a word is its use in the language.
(2) Meaning of a word is usually context dependent.
(3) How you live shapes your application.
(4) Empathy can help one understand word meanings accurately.
(5) Generally, knowing the use of a word means knowing its meaning.

32. Which of the following inferences is not true as per the passage?
a. ‘What is accidental and what is essential’ is not completely arbitrary because what is natural to a
lion may not be natural to a human being.
b. Wittgenstein offers at times the general theory that “meaning is use”.
c. God is unable to understand the thoughts going on in a human being’s mind owing to the objective
nature of human thoughts.
(1) a and b (2) Only a (3) Only b (4) b and c (5) a, b and c

33. Wittgenstein would be most likely to agree with which of the following statements?
(1) Scientific investigations are irrelevant when it comes to inquiry into the meanings of words.
(2) The contextual nature of word meanings makes communication easy.
(3) If one could standardize word meanings then ways of living would also get standardized.
(4) One should be content if one is able to ‘get by’ in one’s interactions.
(5) None of the above.

34. The last statement of the passage implies that

(1) The arrow represents what is considered as false.
(2) Application mitigates the validity of interpretation.
(3) Living beings cannot do without application.
(4) Application is the cause of interpretation.
(5) Interpretation cannot be validated without seeing the application.

002 11
DIRECTIONS for Questions 35 to 37: The sentences given in each question, when properly sequenced,
form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences
among the given choices to construct a coherent paragraph.

35. A. The word failure, it seems, is not good for building self-esteem in school children.
B. Liz Beattie, a 37-year old veteran primary-level instructor, proposed that the word failure should be
banned from classrooms and replaced with the more appealing phrase deferred success so as not to
discourage students from continuing efforts to achieve.
C. Although the motion ultimately experienced its own “deferred success,” it was not without supporters
among the 35,000-member teacher’s association.
D. One Wesley Paxton, a member of the PAT Council, expressed his enthusiastic agreement, saying:
“It’s time we made the word ‘fail’ redundant and replaced it with ‘please do a bit more’.”
E. In the summer of 2005, a British school teacher proposed a rather controversial motion to her
union, the Professional Association of Teachers (PAT).

(1) ADBCE (2) BACDE (3) EBCDA (4) CEDAB (5) ABCDE

36. A. In art, essentialism is the idea that certain concepts may be expressed organically in certain media.
B. Each medium has its own particular strengths and weaknesses, contingent on its mode of
communication.
C. This idea may be further refined and it may be said that the haiku is a poor vehicle for describing a
lover’s affection as opposed to the more organically correct sonnet.
D. Essentialism is attractive to artists because it not only delineates the role of art and media but also
prescribes a method for evaluating art.
E. A chase scene may be appropriate for motion pictures, but poorly realised in poetry because the
essential components of the poetic medium are ill suited to convey the information of a chase
scene.

(1) DCEBA (2) BDACE (3) DABEC (4) ABEDC (5) ABECD

37. A. Enter the virtual assistants who are entrepreneurial partners - highly skilled in their profession and
able to have an impact on the productivity of those they work with.
B. But most of the small businesses started today will reach an impasse very quickly - they will be
spending so much time on administrative tasks that they can no longer concentrate on growing their
business.
C. On the contrary, some believe that increasing numbers of small businesses will afford administrative
support experts with entrepreneurial spirit opportunities that have never before been possible.
D. Traditionally, the need for assistance has left the small business owner with several bleak options-
hire an expensive “temp” for a band-aid-style solution, take on a great deal of expense and
responsibility with a “permanent” employee, or-perhaps worst of all-turn away the work.
E. Corporate downsizing and the move towards small, home-based businesses could appear to be bad
news for the over 3 million people whose expertise lies in the administrative support arena.

(1) DCABE (2) ECBDA (3) DBACE (4) EDCBA (5) CDEBA

12 002
DIRECTIONS for Questions 38 to 40: In each question, the word at the top is used in five different ways,
numbered (1) to (5). Choose the option in which the usage of the word is incorrect or inappropriate.

38. Beam
(1) The work at the site came to a temporary halt when a worker was struck by a falling beam
(2) His only response to the news of his brother’s return was to beam in joy
(3) I was dazzled by a beam of sunlight that entered the dark room through a crack in the wall.
(4) In the end it was decided to beam the last episode on both the channels.
(5) IBA 2007 is a major international forum to discuss recent research and future prospects in Ion
Beam Analysis.

39. Face
(1) We were surprised when Paul did an about face on the plan we had agreed upon
(2) She persevered in the face of apparently insurmountable odds.
(3) Jim’s proposal was accepted even though it flew off the face of all conventional wisdom.
(4) Her friends were surprised at the way a timid speaker like Jenny could face down an experienced
debater like Mike.
(5) We had the opportunity to sit down face-to-face with Max Spevack, chairman of the Fedora project,
at the Red Hat Summit.

40. Act
(1) After the performance, everyone agreed that the new acrobat in the circus was a classy act.
(2) We had to cancel the inauguration when the air conditioning chose to act up again.
(3) The defence counsel asked the accused to act out the events of the fateful Saturday evening for his
benefit.
(4) The ambassador censured the attack on the border as an uncalled for act of belligerence.
(5) The genesis of an Act of Parliament is often a formal written proposal known as a White Paper,
which if accepted will be prepared in the form of a proposed law known as a Bill.

002 13
 Sub-section II-B: Number of Questions = 20

Note: Questions 41 to 60 carry 4 marks each.

DIRECTIONS for Questions 41 to 47: Each of the two passages given below is followed by a set of questions.
Choose the best answer to each question.

PASSAGE – 1

The question of silence is inseparable from a certain atopia. It is no-where to be heard, as there is no such
thing as a place without sound of any kind. Everyone knows that outer space, to be sure, is silent, but this
silence is only technical, and is a kind of limit-possibility, is an absolute in the way that death is an absolute.
It is always on the other side of the loud and noisy, bustling with activity so unlike death. Our science fiction
films always give us the roar of the rockets, the booming explosions, and the affective omniscience of film
music—the silence of space is made loud and noisy, bustling with activity so unlike death. The occasional
films which omit sound when outside the spacecraft still have to contend with the candy wrappers and plastic
lids and the coughing of the theatre space, so the silence of space can only be alluded to, barely auditioned.
Perhaps the closest we get to the silence of space is the tinny voice of the headset, and the rhythm of breathing
amplified in the astronaut’s helmet, the claustrophobia of atmospheric recirculation, such that silence is brought
so close that it frames our perceptions and the action. Silence then takes on the explosiveness of an immanent
possibility. Like death.

It is no accident that we bring up cosmic space in our first consideration of the thematic of silence. For we can
say, silence is the sound of space, quiet is always the sound of a place. For the closest approximation to
silence is quiet, but to think of quiet is always to suggest a quiet: the quiet of the library, of a forest clearing,
of anywhere at three in the morning. Silence, however, is a corollary of absolute space, of pure, uninterrupted
extension, the space of Descartes and Newton, amongst others, or space uninflected, the happy medium for
grids of all kinds. Noise localizes, for sounds have sources. They emanate from centers, or multiple centers, as
in the accumulation of the traffic hum which is the acoustic signature of urban spaces. Silence is as well the
transposition onto the acoustic plane of the blankness of paper, whether white or yellowy. Western art music
shares this white silence with writing and painting. Rauschenberg had presented, in the early fifties, a series of
monochrome paintings entitled the White Paintings. Here, too, the apparent emptiness reveals an active vitality
and presence of light, color, and movement. Rauschenberg’s radical move towards white paintings certainly
drove Cage to present his own “white” work, the silent piece. The imperative of silence for music, one can
imagine, originates from the margins of the notation system, the white in-between of notes and staff lines, as
well as the silence that is reading and writing, i.e. the silence of speechlessness, St. Augustine’s instinctive
horror at the silence of the figure at the lectern, the silence of unvocalized interiority, the silence necessary as
the medium of thought.

The superabundant display of vitality, which takes the form of knocking, hammering, and tumbling things
about, has proved a daily torment for some people. There are people, it is true—nay, a great many people—
who smile at such things, because they are not sensitive to noise; but they are just the very people who are not
sensitive to argument, or thought, or poetry, or art, in a word, to any kind of intellectual influence. On the
other hand, noise is a torment to intellectual people. In the biographies of almost all the great writers, or
wherever their personal utterances are recorded, complaints have been found regarding it.

Silence is an effect, specifically, a technological and architectural effect, a type of quiet that perhaps can trace
its lineage to the invention of masonry walls, i.e. walls composed of solid planes and thus impermeable to the
sounds that might creep in through a mesh of leaves or the gaps in bundled saplings. Silence as a fantasy or an
act of imagination will thus be linked to a certain stage of civilization. For we can imagine the difference

14 002
between death in the jungle and death in the polis. In the former situation, one imagines that the cessation of
movement on the part of the deceased may lead to a heightened sensitivity to the surrounding activity of the
place - the animal sounds, the wind in the foliage; in other words, all that may have been tuned out when
giving attention to another would uncannily return to the foreground. By contrast, city death implies the
silence of the tomb, prepared somewhat by the echoey sonorousness of the temple. Thus silence can be linked
to a certain stony sense of enclosure and interiority.

41. What does the author imply by stating that ‘silence of space is a kind of limit possibility’?
(1) The concept of silence of space is very restricted in nature.
(2) The occurrence of space silence is less in everyday life because of the constant sound of other
different things such as the roaring of rockets.
(3) The silence of space occurs outside the earth and it also attracts for itself an active search for other
types of noises which can substitute for this assumed silence.
(4) The space is presented as a busy place always bustling with some type of activity or the other.
(5) Human beings compensate for the silence of space by creating various types of sounds and noises
such as the moving of rockets, huge explosions etc.

42. What does the author imply by comparing silence with the space of Descartes and Newton?
(1) The author tries to state the relationship between cosmic space and the concept of silence.
(2) The author tries to focus on the localization of noise and the sources from where they emerge.
(3) The author tries to state the relevance of Descartes and Newton’s theories with respect to space.
(4) The author tries to emphasize on the closeness between silence and quiet.
(5) The author makes an indirect reference to the unaltered original space that was referred to by
Descartes and Newton.

43. The above passage does not imply that:

(1) Vitality cannot be expressed through science.
(2) The concept of silence is a condition of inherent possibility and represents a rigid form of closeness.
(3) Silence is many times approximated with quiet.
(4) Silence is a type of technological and architectural effect.
(5) Silence is important for music.

44. Which of the following statements can be inferred from the passage?
(1) St Augustine was filled with remorse at the silence of the figure of the lectern.
(2) Silence can be as explosive as quiet.
(3) Silence can be seen as a corollary of absolute space, unlike quiet.
(4) Intellectual people are insensitive to noise.
(5) It is preferable to die in a city rather than in a jungle as one can die peacefully.

PASSAGE – 2

There are grounds for thinking that, when compared to researchers in similar fields, management researchers
are particularly susceptible to conflicts of interest and affiliation bias. In all areas of scientific study it is
recognized that affiliations, particularly those related to funding, have the potential to influence the way that
research issues are defined and findings presented. In fields such as medical research, it is a condition of
publication that researchers must state any potential conflicts of interest so that their affiliations can be taken
into account when reviewing the findings of a given study. However, it is rare for affiliations to be declared in
the reviewing or publication of management research, despite the widespread practice of researchers engaging
in management consultancy in areas related to their academic study. In addition, it is unusual for the adoption
of joint research and consultancy roles to be seen as anything other than an advantage to the community,

002 15
leading to greater congruence between practitioner and researcher concerns. Another contextual factor that
affects management researchers differently from other social scientists stems from their engagements with
powerful individuals and organizations. One of the main purposes of ethical regulation in social research is to
protect vulnerable research participants from exploitation and potential harm, which might result from their
involvement in the research process. The burden of responsibility for ensuring informed consent to research
participation rests with the researcher even though the extent to which participants can ever be fully informed
of the demands and uses of research is questionable. The principle of informed consent can be traced to the
formation of the Nuremburg Code, which has informed subsequent ethics codes and human rights treatises
throughout the world. The Nuremberg Code represented an attempt to formulate a universal natural law
standard for human experimentation. Its importance stemmed from the appalling nature of the atrocities that
stimulated its formation, and the desire of Nuremberg Trial judges to go beyond charging and convicting
individual doctors in paving the way for a reconstituted moral vision. At the heart of the code is the principle
of informed consent, which forms the basis for ensuring the protection of vulnerable people. However, this
strong pronouncement on the rights of research subjects was almost immediately undermined by later codes,
which isolated the Nazi experiments, treating them as a barbaric aberration that could not occur elsewhere in
the Western world. The Nuremberg Code was therefore superseded by the Declaration of Helsinki, which
sought to balance the interests of the subject against the need for scientific research. Despite these modifications,
the protection of human subjects through informed consent remains a fundamental principle in most ethics
codes in the social as well as biological sciences.

In psychological research, power relations tend to favour the researcher who is often a professional psychologist
carrying out research on their own patients. In education, research participants are often children who are at a
power disadvantage relative to those who are carrying out the studies. The question for management researchers
is whether the principle of informed consent is an appropriate mechanism for dealing with the ethical
implications of relationships with research participants in this field of study. There are undoubtedly some
instances when it is, such as when university students are asked to participate in research. However, unlike
many other social researchers, the relationships between management researchers and their participants are
often characterized by a power imbalance that favours the research subject rather than the researcher.

45. What is the author attempting to illustrate through this passage?

(1) Relationship between medical, psychological and management research.
(2) How the present limitations in the field of research are a disadvantage to the management researcher.
(3) The effects of set codes in the fields of research.
(4) Ways to approach management research.
(5) The unique effects of certain factors on management researchers.

46. According to the author, which of the following statements would be true?
(1) The objective of research supersedes the need for protection of human subjects.
(2) The appropriate use of the principle of informed consent depends on the individual field of study.
(3) The Declaration of Helsinki was formulated to restore the power to the researcher.
(4) Affiliations are declared in the publication of management research issues.
(5) Power relations cease to produce an effect on research projects.

47. According to the passage, which of the following is a marked achievement of the Nuremberg code?
(1) The formation of the Declaration of Helsinki.
(2) The formation of an ideal law for human experimentation.
(3) The formation of an ethical grounding in research.
(4) The formation of a law.
(5) The formation of a balance between the interests of the subject with the need for scientific research.

16 002
Directions for questions 48 to 50: Each of the following questions has a paragraph from which the last
sentence has been deleted. From the given options, choose the one that completes the paragraph in the most
appropriate way.

48. Existentialism is the view of life which focuses on “a man” and in so doing denies that any man is to be
measured or equated against any class called “man” in any sense of experience. Since “man” traditionally
is classified in terms of his mind, body and will against the framework of an external world, the existential
position denies, utterly, the certainty of any external world, as object, and denies, utterly, the assertion
that any rule – physical, emotive, or intellectual - is valid in relation to the single individual.
__________________ .
(1) The exponent of existentialism considers the traditional world to be one of illusion.
(2) Man is not an accidental expression of colliding atoms which continuously move in a random
fashion.
(3) It is quite interesting to analyze organized religion with this background.
(4) It is the consciousness of a man that he is existing in terms of his own flowing of experience, a flow
which is governed by natural laws.
(5) Therefore, the existentialist is free to choose because there are no objective standards to inhibit or
constrain his choice.

49. What is nonlinear science all about? The core ideas are not hard to describe. Nonlinear dynamics arise
from repeated iteration or feedback. A system, whether physical or mathematical, starts in some initial
state. That initial state provides the input to a feedback mechanism which determines the new state of
the system. The new state then provides the input through which the feedback mechanism determines
the system’s next state and so on. Each successive state is causally dependent on its predecessor.
__________________ .
(1) Mathematics aside, nonlinearity has a crucial contribution to make towards general friction regardless
of technological developments.
(2) Sometimes the fundamentals of nonlinear science evade understanding.
(3) The dynamics of non-linear science are being deeply pondered by scientists.
(4) The attempt to apply the ideas of nonlinear science are resisted by the widespread predominance of
linear modes of thought.
(5) But what happens to the system over the course of many iterations can be more complex and less
predictable than one might suppose.

50. Anyone who’s ever played with an Erector Set knows intuitively that as long as the structural members
remain well-connected, a framework may become twisted and distorted if you throw it to the floor, but
it will never just collapse into pieces under any scenario involving self-related and self-proportional
forces. Even if a giant came along and stomped on one of the Towers, the continuous vertical strength
of the specially fabricated multi-story core columns, with their welded connections and dense cross-
bracing, would cause the building to split out over a multi-floor region. _____________________
(1) The vertical spacing of the office floors did not correlate to periodic points of weakness in the
column assemblies.
(2) This would be very much like the effect of a thunderstorm on a boat.
(3) This would be very similar to the effect of an earthquake on a bridge.
(4) This would be very much like the forces operating on a truss.
(5) This would be very much like pushing down on a bundle of archery bows.

002 17
DIRECTIONS for Questions 51 and 52: In each of the following questions a paragraph is given followed by
five summaries. Choose the best summary.

51. Studying the phenomenon of childhood brings on also issues relating to children burial rites in all types
of communities. Children burials and children graves are inherent parts of archaeological discoveries
made at Moravian settlement agglomerations. In the recent years, extensive archaeological rescue
research – especially in Central Moravia – has considerably extended the amount of knowledge on the
Neolithic burial rite. Most new findings come from the Linear Pottery Culture period, while the period
of the Culture with Stroke-Ornamented Pottery shows constant stagnation, and the Moravian Painted
Ware Pottery Culture has yielded only random individual finds.
(1) Extensive archaeological rescue research – especially in Central Moravia – has considerably extended
the amount of knowledge on Neolithic burial rites.
(2) Archaeological discoveries made at Moravian settlement agglomerations, especially in Central
Moravia – have considerably extended the amount of knowledge on children burial rites, though
the number of findings from each culture period varies.
(3) Archaeological discoveries made at Moravian settlement agglomerations, have considerably increased
the number of findings from each culture period because of the renewed interest in children burial
rites.
(4) Children burials and children graves are inherent parts of archaeological discoveries made at Moravian
settlement agglomerations, which exhibit different findings from recent culture periods.
(5) Archaeological discoveries made at Moravian settlement agglomerations exhibit different number
of findings from different culture periods.

52. The priestly caste of Jews - called Cohanim in Hebrew - have recently been conducting DNA tests to
see whether or not they are actually linked to Aaron, the brother of Moses, as written in the Jewish
Bible. This arose when a tribe in South Africa, known as the Lemba, wanted to find out more about their
heritage. Claiming they were Jews because they followed dietary laws similar to those of Kashruth,
scientists in England decided that they could perform DNA tests of Jews who claimed to be Cohanim
and the Lemba to see if there were any similarities in the readings. Because neither Aaron’s nor Moses’
grave are to be found, as written in the last chapter of Deuteronomy, the scientists had to figure out how
they were going to go about proving this.
(1) Because neither Aaron’s nor Moses’ grave are to be found, Scientists in England decided that they
could perform DNA tests of Jews who claimed to be Cohanim and the Lemba to see if there were
any similarities in the readings.
(2) Scientists were reluctant to figure out how they were going to perform DNA tests of Jews who
claimed to be Cohanim and the Lemba because neither Aaron’s nor Moses’ grave are to be found.
(3) Scientists had to figure out how they were going to perform DNA tests of Jews who claimed to be
Cohanim and the Lemba as their claims appeared to be apocryphal.
(4) Scientists in England decided that they could perform DNA tests of Jews who claimed to be Cohanim
and the Lemba to see if there were any similarities in the readings.
(5) Scientists in England decided to perform DNA tests of Jews who claimed to be Cohanim and the
Lemba to validate their claims of lineage, but they were to figure out the mode as they faced
constraints.

18 002
DIRECTIONS for Questions 53 to 56: In each question there are five sentences or parts of sentences that
form a paragraph. Identify the sentence(s) or part(s) that is/are correct in terms of grammar and usage. Then
choose the most appropriate option.

53. A. It is an irony given that Brasilia was built at breakneck speed.

B. The dream of moving the capital from Rio on the Atlantic coast to the
C. centre of the country, had existed for above a century but Kubitschek pursued it with urgency.
D. Commercial and residential zones were seeming meticulously demarcated.
E. Cars zipped alongside wide highways past buildings that projected simplicity and modernity with
fine lines and waves.

(1) A & B (2) B & C (3) A, B, D & E (4) A, B & E (5) A, B & C

54. A. Young describes the sight of a room full of

B. major celebrities as “overpowering seductive”.
C. I think they look silly parked alongside one another, like the Ferraris at the super car show I stumbled
upon on a recent trip to Florida.
D. The owners of these status symbols thought they would be looking even cooler clustered together
with others of their kind.
E. Big mistake! Once your eyes had adjusted to the glare from the bonnets, you saw them for what
they were - a paltry collection of consumer durables.

(1) A, B & C (2) A, B & E (3) A, C, D & E (4) C & E (5) A, C & E

55 A. Obviously, they have to be extended and silly, but still characters that you
B. could definitely meet rather than over-the-top caricature.
C. They also have to be fun to do;
D. You have to enjoy playing the character. If people look alike they’re
E. enjoying themselves, that comes across on screen and that’s how you find your fan base.

(1) A & D (2) A & B (3) B, D & E (4) A, C & E (5) A, B & C

56. A. If staying outside the park boundaries precludes dawn and dusk animal sighting, daytime drives
and walks make up for that.
B. This rolling wilderness, studded with the great angular-branched baobab trees, and intersected by
the Ruaha river,
C. is known for its magnificent elephant population as well as for other mammals and, in particular, its
bird life.
D. A driving safari can cover the ground and will deliver you to concentrations of animals - anxious
zebras, shifty buffaloes, distinguished elephants – but
E. walking safaris take you closer, physically and mentally both, to the soil.

(1) A & B (2) B, C & D (3) C & E (4) C, D & E (5) E only

002 19
Directions for questions 57 to 60: Each of the following questions has a paragraph with one italicized word
that does not make sense. Choose the most appropriate replacement for that word from the options given
below the paragraph.

57. Haldiman was an experienced military commander. However, he still needed timely intelligence on
enemy troop movements if he were to have any hope of stopping a large force. Couriers attempting to
get from Lake Champlain to Clinton’s Headquarters in New York were continually intercepted .Clinton
seemed to consider Haldimand’s need for information as secondary to the main war effort. There were
hints of frustration in some of Haldimand’s letters at this seemingly factacious behavior on the part of
Clinton.
(1) devastating (2) caustic (3) recalcitrant (4) pernicious (5) acerbic

58. The principle of fairness grounds a moral obligation not to bamboole as part of a fair scheme of cooperation,
also called ‘the duty of fair play.’ The principle is standardly summarized as follows. If some people are
contributing to the production of a public good, one should not simply enjoy the benefits without doing
one’s share in the production of that good.
(1) exhaust (2) constrain (3) intrude (4) manipulate (5) free ride

59. Conflict has continued between Ireland and England for centuries. In spite of this, the two languages
spoken by the English and Irish existed side by side, with many of the English living in Ireland learning
the native language. However in Ireland, a change was to come. In an attempt to enforce complete
annixation, the English passed laws to suppress the native Irish language.
(1) subjugation (2) downthrow (3) regimen (4) abstinence (5) forbearance

60. In a short time the family realized that the dog had many positive attributes. It had large bat-like ears
that were sensitive and had strong attention. In fact the family realized that apart from a cuntimecious
taste that it had shown towards books, eating the first edition copy of a famous Memoir, the dog had
been purpose- built.
(1) intense (2) extraneous (3) perverse (4) incendiary (5) beguilement

20 002
 SECTION – III

Sub-section III-A: Number of Questions = 10

Note: Questions 61 to 70 carry 2 marks each.

61.
x−y
Given that   % of
x+y
(x2 − y2 ) +  xx +− yy  % of ( x − y )2 = 40, where x ≠ ± y and x ≠ 0.

x+y  2 
Find the value of   % of  .
 x   x2 − y2 
 
(1) 2 × 10–5 (2) 10–6 (3) 2 × 10–6 (4) 10–5 (5) None of these

62. Let A be a two-digit number and B be another two-digit number formed by reversing the digits of A.
If A + B + (Product of digits of the number A) = 145, then what is the sum of the digits of A?
(1) 12 (2) 10 (3) 13 (4) 9 (5) 11

63. Suresh and Ramesh are playing a game with a fair die marked 1, 2, 3, 4, 5 and 6 on its six faces. On his
turn, a player rolls the die and notes the number s obtained. They roll the die turn by turn. The player,
who gets 6 first wins the game. If Suresh gets the first turn to roll the die, then the probability of Ramesh
winning the game is
1 5 6 5 1
(1) (2) (3) (4) (5)
6 6 11 11 11

64. The nth term of two different series are Rn = R1 × Sn–1 and Sn = S1 × Rn–1. If R1 = x, S1 = y (where
x, y > 0 ), then which of the following is equal to Rn + Sn (if n > 3)?
(1) 2x2y2 (2) 2xy(Rn–2 + Sn–2) (3) xy(Rn–3 + Sn–3)
(4) xy(Rn–2 + Sn –2) (5) None of these

65. When a two–digit number N is divided by the sum of its digits, the result is Q. Find the minimum
possible value of Q.
(1) 10 (2) 2 (3) 5.5 (4) 1.9 (5) 7

66. In a quadrilateral ABCD, E is a point on AB. If ∠ADE = ∠DEC = ∠ECB = 30°, AD = 2 units and
BC = 4 units, then what is the area of the ∆DEC?
(1) 4 sq. units (2) 6 sq. units (3) 2 sq. units (4) 1 sq. units (5) 3 sq. units

67. What is the sum of the roots of all the quadratic equations that can be formed such that both the roots of
the quadratic equation are common with the roots of equation (x – a)(x – b)(x – c) = 0 ?
(1) 3(a + b + c) (2) 2(a + b + c) (3) (a + b + c) (4) 4(a + b + c) (5) 3a + 3b + 4c

002 21
68. There is a 5 digit natural number N1 = abcde whose digits a, b, c, d and e are in an arithmetic progression
and there is another 4 digit number N2 = ABCD whose digits A, B, C, D are in a geometric progression.
Which of the following statements is invalid ?
(1) Sum of digits of N2 is 15
(2) N1 has 12 possible values
(3) N1 + N2 has 24 possible values
(4) N1 is never divisible by 4
(5) None of these

DIRECTIONS for Questions 69 and 70: Answer the questions on the basis of the information given below.
A very large open tub is circular in shape and is filled with water. From a point X, two friends Jack and Straw
start swimming simultaneously at constant speeds in the opposite directions. The tub has a circumference of
100 metres. The water inside the tub flows in the clockwise direction at a uniform speed. Jack swims along the
water flow. The two friends meet for the first time, at a distance of 30 metres from the point X in the clockwise
direction. Straw reversed the direction in which he was swimming immediately after they met for the first
time. The time duration from the 1st meeting to the 2nd meeting is 10 seconds.

X
S tra w Jack

69. Find the distance between the point X and the point at which they meet for the second time.
(1) 60 metres in the clockwise direction.
(2) 90 metres in the clockwise direction.
(3) 45 metres in the anticlockwise direction.
(4) 0 metres.
(5) Cannot be determined.

70. If the ratio of the speeds of Jack and Straw is 2:5, then the speed at which water flows is
2 1 4
(1) 3 m/s (2) 1 m/s (3) m/s (4) m/s (5) m/s
3 3 3

22 002
 Sub-section III-B: Number of Questions = 20

Note: Questions 71 to 90 carry 4 marks each.

71. In an island, which had a total population of 55009, a war was fought between ‘Benos’ and ‘Malos’ the
only tribes residing in the island. During the war every ‘Benos’ fought with a different number of
‘malos’. One of them fought with exactly 140 ‘Malos’, a second one fought with exactly 141 ‘Malos’,
a third one fought with exactly 142 ‘Malos’, a fourth one with with exactly 143 ‘Malos’ and so on till
one of them fought with every ‘Malos’ residing in the island. Find the number of ‘Malos’ residing in the
island.
(1) 27435 (2) 33000 (3) 30000 (4) 27574 (5) 50000

DIRECTIONS for Questions 72 and 73: Answer the questions on the basis of the information given below.
In a class comprising of boys and girls, ‘k’ oranges were distributed such that everyone in the class gets at
least one orange and atmost three oranges. The aggregate number of boys and girls who got three oranges is
40. The aggregate number of boys who got at least two oranges and the number of girls who got at least
1 orange is 100. The aggregate number of boys and girls who got at least two oranges is 60 and the aggregate
number of boys who got atleast one orange and the number of girls who got exactly three oranges is 100.

72. Which of the following value of ‘k’ is consistent with the information given above?
(1) 225 (2) 230 (3) 255 (4) 270 (5) 265

73. Which of the following can be the number of girls who got exactly two oranges?
(1) 17 (2) 19 (3) 23
(4) Both (1) and (2) (5) Both (2) and (3)

74. When Saurav was born, his mother Lakshmi was 24 years old. When Saurav turned 50, his mother was
still alive. In these 50 years how many times was Lakshmi’s age divisible by Saurav’s age?
(Assume that the number that denotes the age of a person is always an integer.)
(1) 6 (2) 7 (3) 8 (4) 12 (5) 24

75. A is the set of first 40 natural numbers. B is a subset of A such that there exist atleast 2 pairs of elements
in B whose difference is 12. If n is the number of elements in B, then which of the following is correct?
(1) n ≥ 14 (2) n ≥ 24 (3) n ≥ 26 (4) n ≥ 28 (5) n ≥ 30

76. The sum of the number of factors of the number N and N2 is 34. How many such distinct numbers
N < 150 exist ?
(1) 6 (2) 5 (3) 4 (4) 3 (5) 2

002 23
77. Let f(x) be a function that satisfies f(x – 2) = – f (x + 2) for every real number x. From x = – 2 to x = 2,
the graph of f(x) is as shown below.

Which of the following shows the correct graph of f(x) from x = 96 to x = 104?

(1) (2)

(3) (4)

(5) None of these

78. Amol owns a factory that can produce a maximum of 1300 units in one day. The variable cost of
producing each unit is same. The fixed cost of running the factory for one day is Rs. 20000 and the total
cost of producing 1200 units in a day is Rs. 200000. The selling price is Rs. 190 per unit when 1000
units are produced in a day. For every subsequent increase of 100 units in the production, the selling
price per unit reduces by Rs. 5. The maximum possible profit that can be earned in one day is
(1) Rs. 20000 (2) Rs. 18000 (3) Rs. 18700 (4) Rs. 16000 (5) None of these

24 002
 x x
79. Find the number of positive integral solutions of the equation   =  
 28   37 
Here, [x] denotes the greatest integer less than or equal to x.
(1) 27 (2) 28 (3) 38 (4) 58 (5) 57

80. Raju travels from town A to town B, by road. The road map that he uses as a guide is as given below.

A B

Each of the straight line drawn in the map above is a road on which he cannot travel more than once. In
how many ways can Raju travel from town A to town B ?
(1) 32 ways (2) 81 ways (3) 145 ways (4) 243 ways (5) 729 ways

81. In the figure given below, ABCD is a rectangle. Under a rectangular co-ordinate system X-Y, coordinates
of the vertices A and C are (5, 0) and (0, –10) respectively and diagonal BD lies on the straight line L.
The position of the rectangle is now changed is a way such that the coordinates of vertices A and C are
(0, 10) and (5, 0) respectively and diagonal BD lies on the straight line M. Find the point of intersection
of lines L and M. BC = 10 m, AB = 5 m.

B 5m A

10 m

C D

 5   5
(1) (0, 0) (2)  − , 5  (3)  5,  (4) (5, 0) (5) (0, –5)
 2   2

82. In the figure given below, ABC, DEF and GHI are equilateral triangles having the same area. It is also
given that BD = DG = GC. Find the ratio of the area of the figure EJKL to the area of the figure AKHIB.

A E H

J L
K

B D G C F I

3 1 2 3 2
(1) (2) (3) (4) (5)
17 6 19 11 17

002 25
83. A rod of length ‘L’ cm is broken into two parts of lengths L1 cm and L2 cm, where L1 = 2a × 3b and
L2 = 3a × 2b. If the mid-point of the rod is at a distance of 90 cm from the ends, then find the value of
L1 × L2 (Here, a and b are positive integers).
(1) 7776 (2) 8176 (3) 8076 (4) 7716 (5) Data insufficient

84. Gopal is a shopkeeper who has put two articles viz. P and Q on sale. He has offered two discount
schemes viz. A and B under either of which a customer ends up paying the same amount of money.
Scheme A: With the purchase of article P, 50% discount is given on the article Q, if purchased.
Scheme B: With the purchase of article Q, 40% discount is given on the article P, if purchased.
Now, Gopal decided to give a discount of 40% instead of 50% on the article Q in scheme A. What
should be the discount offered on the article P in scheme B such that the customer will still pay the same
amount irrespective of the scheme he chooses ?
(1) 30% (2) 24% (3) 36% (4) 40% (5) 32%

85. The radius of the circle with center at O is 5 cm. The length of each of the chords PQ and RS is 8 cm.
Another circle with center at C is drawn such that it touches the circle and the chords PQ and RS. Given
that the line joining the centers of the two circles passes through M, find the radius of the circle C.

O C

R M S
Q

3
(1) 1 + 2 2 cm (2) 2 + 3 cm (3) 2 + 2 cm (4) 3 + cm (5) 2 3 cm
2

86. The terms of the sequence x1, x2, x3…..xn satisfies the relation xn – xn–1 + xn–2 = 0, where n > 2. If the
(x + x 2 )
sum of first 88 terms and the first 89 terms is 150 and 120 respectively, then find the value of 1 .
2
(1) 124 (2) – 124 (3) – 30 (4) 30 (5) 90

87. ABCD is a rectangle such that DC = 8 cm. E is a point on the side AB. The line DE is extended to a point
F outside the rectangle. If the ratio of the area of the ∆ADE, ∆BEF and the quadrilateral EBCD is 1:3:6,
then the ratio of the area of the ∆AEF to the area of the ∆AED is
(1) 6 : 5 (2) 5 : 6 (3) 15 : 2 (4) 7 : 2 (5) None of these

88. A, B and C are positive integers (A, C ≠ 1) that satisfy A × B = C and B × C = A. Which of the following

is equal to the expression (A logC BC × BlogCB + BlogACA × ClogAC ) ?

(1) AB + C (2) B(C + A) (3) C(A + B) (4) B(B + C) (5) AC + B

26 002
89. In the figure given below ABCD is an isosceles trapezium and PQSR is a square. If the length of the
segment BC, PQ and AD is 2, 3 and 6 units respectively, then find the area of the trapezium ABCD.

B C

P Q

A R S D

(1) 14 sq. units (2) 12 sq. units (3) 16 sq. units (4) 18 sq. units (5) 20 sq. units

90. P is the set of all the triplets of distinct natural numbers, which are in an arithmetic progression. If the
product of the numbers in each triplet is less than 100 then the number of elements in the set P is
(1) 20 (2) 10 (3) 14 (4) 8 (5) 18

002 27
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