COMMON
ADMISSION TEST(CAT)
Entrance Examination
Question
Paper -2006

Instructions:

1.  This test has three
sections that examine various abilities. Each section has 25 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 each group of questions. Read these
direactions carefully
and answer the questions by
darkening the appropriate circles on the Answer sheet. There is only one
correct
answer of each
question.
3.
Each section carries 100 marks. All questions
carry four marks each. Each wrong answer will attract a

penalty of one mark.
4.  Do your rough work only on
the Test Booklet and NOT on the Answer Sheet.
5.  Follow the instructions of the
invigilator. Candidates found violating the instructions will be
disqualified.

Section -
I

Section - I has 25
questions.

1    Q.
K,L,M,N,O,P,Q,R,S,U and W are the only ten members in a department. There
is a proposal to from within the members of the department, subject to the
following conditions:
1. A team must include exactly one among P,R and
S.
2. A team must include either M or Q, but not both.
3. If a team
includes K, then it must also include the other two.
4. If a team
includes one among S,U and W, then it must also include the other
two.
5. L and N cannot be members of the same team.
6. L and U
cannot be members of the same team.
The size of a team is defined as
the number of members in the team.

5    (5)
Who can be a member of a team of size 5
?

A.
K
B.
L
C.
M
D.
P

2    Q. Mathematicans are assigned a number
called Erdos number (named after the famous mathematician, Paul
Erdos).Only Paul Erdos himself has an Erdos number of Zero. Any
mathematician who has written a research paper with Erdos has an Erdos
number of 1. For other mathematicians, the calculation of his/her Erdos
number is illustrated below :
Suppose that a mathematician X has
co-authored papers with several other mathematicians. From among them,
mathematician Y has the smallest Erdos number. Let the Erdos number of Y
be y. Then X has an Erdos number of y + 1.
Hence any mathematician with
no co-authotship chain connected to Erdos has an Erdos number of
infinity.
In a seven day long mini-conference organized in memory of
Paul Erdos, a close group of eight mathematicians, call them A,B,C,D,E,F,G
and H, discussed some research problems. At the beginning of the
conference,A was the only participant who had an infinite Erdos number.
Nobody had an Erdos number less than that of F.

On the third day of the conference F co-authored a paper jointly
with A and C. This reduced the average Erdos number of the group of
eight mathematicians to 3. The Erdos number of B,D,E,G and  H
remained uncharged with the writing of this paper. Further, no other
co-authorship among any three members would have reduced the average
Erdos number of the group of eight to as low as 3.

At the end of the third days, five members of this group had
identical Erdos numbers distinct from each other.

On the fifth day, E co-authored a paper with F which reduced the
group's average Erdos number by 0.5. The Erdos numbers of the remaining
six were unchanged with the writing of this paper.

No other paper was written during the conference.

5    (2) How many participants had
the same Erdos number at the beginning of the conference
?

A.
2
B.
3
C.
4
D.
5

3    Q. Two traders, Chetan and Michael, were
involved in the buying and selling of MCS shares over five trading days.
At the beginning of the first day, the MCS share was priced at Rs 100,
while at the end of the fifth day it was priced at Rs 110. At the end of
each day, the MCS share price either went up by Rs 10, or else, it came
down by Rs 10. Both Chetan and Michael took buying and selling decision at
the end of each trading day. The beginning price of MCS share on a given
day was the same as the ending price of the previous day. Chetan and
Michael started with the same number of shares and amount of cash, and had
enough of both. Below are some addition facts about how Chetan and Michael
traded over the five trading days.

Each day if the price went up, Chetan sold 10 shares of MCS at the
closing price. On the other hand, each day if the price went down, he
bought 10 share at the closing price.

If on any day, the closing price was above Rs 110, then Michael sold
10 shares of MCS, while if it was below Rs 90, he bought 10 shares, all
at the closing price.

5    (7) If
Michael endd up with Rs. 100 less cash than Chetan at the end of day 5,
what was the difference in the number of shares possessed by Michael and
Chetan(at the end of day 5)
?

A. Michael had
10 less shares than
Chetan
B. Michael had
10 more shares than
Chetan
C. Chetan had
10 more shares than
Michael
D. Both had
the same number of shares

4    Q. Answer
Questions 1 to 5 on the basis of the information given below:

A
significant amount of traffic flows from point S to point T in the one-way
street network shown below. Points A,B,C and D are junctions in the
network, and the arrows mark the direction of traffic flow. The fuel cost
in rupees for travelling along a street is indicated by the number
adjacent to the arrow representing the street.

Motorists
travelling from point S to point T would obviously take the route for
which the total cost of travelling is the minimum. If two or more routes
have the same least travel cost, then motorists are indifferent between
them. Hence, the traffic gets evenly distributed among all the least cost
routes.
The government can control the flow of traffic only by levying
appropriate toll at each junction. For example, if a motorist takes the
route S-A-T (using junction A alone), then the total cost of travel would
be Rs 14(i.e., Rs 9 +Rs 5) plus the toll charged at junction
A.

5    (5) The government wants to devise a
toll policy such that the total cost to the commuters per trip is
minimized. The policy should also ensure that not more than 70% of the
total traffic passes through junction B. The cost incurred by the commuter
travelling from point S to T under this policy will be :

A. Rs
7
B. Rs
9
C. Rs 10

D. Rs
13

5    Q. In a Class X Board examination, ten
papers are distributed over five Groups -PCB, Mahematics, Social Science,
Vernacular and English. Each of the ten papers is evaluated out of 100.
The final score of a student is calculated in the following manner. First,
the Group Scores are obtained by averaging marks in the papers within the
Group. The final score is the simple average of the Group Scores. The data
for the top ten students are presented below. (Dipan's score in English
Paper II has been intentionally removed in the table.)

Note
: B or G against the name of a student respectively indicates whether
the student is a boy or a girl.

5    (5) Had
Joseph, Agni, Pritam and Tirna each obtained Group Score of 100 in the
Social Science Group, then their standing in decreasing order of final
score would be :

A.
Pritam,Joseph,Tirna,Agni

B.
Joseph,Tirna,Pritam,Agni

C.
Pritam,Agni,Joseph,Tirna

D. Joseph,Tirna,Pritam,Agni

Section -
II

Section - II has 25
questions.

6    Q.
An equilateral triangle BPC is drawn inside a square ABCD. What is the
value of the angle APD in degrees ?

A. 75
B. 90
C. 150
D.
120

7    Q. The passage given below is followed
by a set of five questions. Choose the most appropriate answer to each
question. Fifteen years after communism was officially pronounced dead,
its spectre seems once again to be haunting Europe. Last month, the
Council of Europe's parliamentary assembly voted to condemn the "crimes of
totalitarian communist regimes," linking them with Nazism and complaining
that communist parties are still "legal and active in some countries."
Now, Goran Lindblad, the conservation Swedish MP behind the resolution,
wants to go further. Demands that European Ministers launch a
continent-wide anti-communist campaign-including school textbook
revisions, official memorial days, and museums-only narrowly missed the
necessary two-thirds majority. Mr.Lindblad pledged to bring the wider
plans back to the council of Europe in the coming months.

He has
chosen a good year for his ideological offensive : this is the 50th
anniversary of Nikita Khrushchev's denunciation of Josef Stalin and the
subsequent Hungarian uprising, which will doubtless be the cue for further
excoriation of the communist record. Paradoxically, given that there is no
communist government left in Europe outside Moldova, the attacks have if
anything, become more extreme as time has gone on. A clue as to why that
might be can be found in the rambling report by Mr.Lindblad that led to be
Council of Europe declaration. Blaming class struggle and public
ownership, he explained "different elements of communist ideology such as
equality or social justic still seduce many" and "a sort of nostalgia for
communism is still alive." Perphaps the real problem for Mr.Lindblad and
his right wing allies in Eastern Europe is that communism is not dead
enough-nd they will only be content when they have driven a stake through
its heart. The fashionable attempt to equate communism and Nazism is in
reality a moral and historical nonsense. Despite the cruelties of the
Stain terror, there was no Soviet Terblinka or Sorbibor, no extermination
camps built to murder millions. Nor did the Soviet Union launch the most
devastating war in history at a cost of more than 50 million lives-in fact
it played the decisive role in the defeat of the German war machine.
Mr.Lindblad and the Council of Europe adopt as fact th ewildest estimates
of those "killed by communist regimes"(mostly in famines) from the
fiercely contested Black Book of communism, which also underplays the
number of deaths attributable to Hitler. But, in any case, none of this
explains why anyone might be nostalgic in former communist states, now
enjoying the delights of capitalist restoration. The dominant account
gives no sense of how communist regimes renewed themselves after 1956 or
why Western leaders feared they might overtake the capitalist world well
into the 1960s. For all its brutalities and failures, communism in the
Soviet Union, Eastern Europe and elsewhere delivered rapid
industrialization, mass education, job security, and huge advances in
social and gender equality. Its existence helped to drive up welfare
standards in the west, and provided a powerful counterweight to Western
global domination.

5    (5)
Which of the following cannot be inferred as a compelling reason for the
silence of the Council of Europe on colonial atrocities
?

A. The Council
of Europe being dominated by erstwhile
coloialists.
B.
Generating support for condemning communist
idology.
C.
Unwillingness to antagonize allies by raking up an embarrassing
issue
D. Greater value
seemingly placed on European lives

8    Q. 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.

10    (5) Age has
a curvilinear relationship with the exploitation of opportunity.
Initially, age will increase the likelihood that a person will exploit an
enterpreneurial opportunity because people gather much of the knowledge
necessary to exploit opportunities oner the course of thier lives, and
because age provides credibility in transmitting that information to
others. However, as people become older, their willingness to bear risks
declines, thier opportunity costs rise, and they become less receptive to
new information.

A. As a result,people transmit more information rather than experiment
with new ideas as they reach an advanced
age.
B. As a
result,people are reluctant to experiment with new ideas as they reach an
advanced age.
C. As a
result,only people with lower opportunity costs exploit opportunity when
they reach an advanced
age.
D. As a
result,people become reluctant to expliot entrepreneurial opportunities
when they reach an advanced age.

9    Q. Each
question has a set of four Sequentialy ordered statements.Each statement
can be classified as one of the following: Facts,Which deal with
pieces of information that one has heard,seen or read and which are open
to discovery or verification(the answer option indicates such a statement
with an 'F') Inferences,Which are conclusions drawn about the
Unknown,on the basis of the known(the answer option indicates such a
statement with an 'I') Judgements,Which are option that imply
approval or disapproval of persons,objects,situations and occurrences in
the past,the present or the future(the answer option indicates such a
statement with a 'J') Select the answer option that best describes the
set of four statements

2    (2) (1)
Inequitable distribution of all kinds of resources is certainly one of the
strongest and most sinister sources of conflict.

(2) Even without
war, we know that conflicts continue to trouble us - they only change in
character.

(3) Extensive disarmament is the only insurance for our
future, imagine the amount of resources that can be released and
redeployed.

(4) The economies of the industrialized western world
derive 20% of their income from the sale of all kinds of
arms.

A.
IJJI
B.
JIJF
C.
IIJF
D.
JIIF

10    Q.

8    (8)
(1) According to all statistical indications, the Sarva Shiksha Abhiyan
has managed to keep pace with its ambitious goals.

(2) The Mid-Day
Meal scheme has been a significant incentive for the poor to send their
little ones to school, thus establishing the vital link between healty
bodies and healthy minds.

(3) Only about 13 million children in the
age group of 6 to 14 years are out of school.

(4) The goal of
universalisation of elementray education has to be a pre-requisite for the
evolution and development of our
country.

A.
IIJF
B.
JIIJ
C.
IJFJ
D.
IJFI

11    Q.

1    (1)
In the context of science, according to the passage, the interaction of
dogmatic beliefs and critical attitude can be best described as
:

A. A duel
between two warriors in which one has
die.
B. The effect of
a chisel on a marble stone while making a
sculpture.
C. The
feeddtock(natural gas) in fertilizer industry being transformed into
fertilizers.
D. A
predator killing its prey.

Section -
III

Section - III has 25
questions.

12    Q.
A group of 630 children is arranged in rows for a group photograph
session.Each row contains three fewer children than the row in front of
it.What number of rows is not possible?

A. 3
B. 6
C. 5
D.
4

13    Q. The Sum of the four Consecutive two
-digit odd number , when divided by 10 ,become a perfect square . which of
the following can possibly be one of these four number?

A. 21
B.
25
C. 41
D. 67

14    Q. When you reverse
the digits of the number 13,the number increases by 18. How many other two
digit numbers increase by 18 when their digits are reversed ?

A.
5
B. 6
C. 7
D. 10

15    Q. The number
of solutions of the equation 2x + y= 40, where both x and y are positive
integers and x ≤ y is :

A. 7
B. 13
C. 14
D.
18

16    Q. What values of x satisfy
x2/3 + x1/3 -2 ≤ 0 ?

A. -8 ≤ x ≤ 1
B. -1 ≤
x ≤ 8
C. 1 < x < 8
D. 1 ≤ x ≤
8

17    Q. Which among 21/2,
31/3, 41/4, 61/6 and 121/12 is
the largest ?

A. 21/2
B. 31/3
C.
41/4
D. 61/6

18    Q.
There are 6 task and 6 persons. Task 1 cannot be assigned either to person
1 or to person 2; task 2 must be assigned to either person 3 or to person
4. Every person is to be assigned one task. In how many ways can the
assignment be done ?

A. 144
B. 180
C. 192
D.
360

19    Q. A survey was conducted of 100
people to find out whether they had read recent issues of golmal, a
monthly magazine. The summarized information regarding readership in 3
months is given below:
Only September :18; September but not August
:23; September and July :8; September :28; July :48; July and August :10;
None of the three months :24
What is the number of surveyed people who
have read excatly two consecutive issues(out of the three)?

A.
7
B. 9
C. 12
D. 14

20    Q. the sum
of four consecutive two-digit odd numbers when divided by 10 ,becomes a
perfect square.which of the following can possible be one of these four
numbers?

A. 5
B. 6
C. 7
D.
8

21    Q. Arun, Barun and Kiranmala start from
the same place and travel in the same direction at speeds of 30, 40 and 60
km/hr, respectively. Barun starts two hours after Arun. If Barun and
Kiranmala overtake Arun at the same instant, how many hours after Arun did
Kiranmala start ?

A. 3
B. 3.5
C. 4
D.
4.5

22    Q. The length, breadth and hieght of
a room are in the ratio 3:2:1. If the breadth and height are havled while
the lenght is doubled, then the total area of the four walls of the room
will:

A. remain the same
B. decrease by 30%
C. decrease by
15%
D. decrease by 18.75%

23    Q.

Consider a sequence where the nth term, tn =
n/(n + 2), n= 1,2 , ....... . The value of
t3*t4*t5*.........*t53
equals :

A. 2/495
B. 2/477
C. 12/55
D.
1/1485

24    Q. Consider the set S =
{1,2,3,.....,1000}. How many arithmatic progressions can be formed from
the elements of S that start with 1 and end with 1000 and have at least 3
elements ?

A. 3
B. 4
C. 6
D. 7