SECTION-I 1....Countdown Cat Mock Test Paper-2 1 SECTION-I 1. Three horses A,B & C are the only horses competing in Western India Turf Club race in August 2007. …

Countdown Cat Mock Test Paper-2

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SECTION-I

1. Three horses A,B & C are the only horses competing in Western India Turf Club race in

August 2007. Viiji Malaya, an expert on racing horses claims that A is twice as likely to

win as C. Circus Poonawalah puts all his money on horse C, which belongs to his stud

farm, then with probability does Circus Poonawalah loses his money (he loses his money

when C loses this race)?

a. 4

7 b.

6

7 c.

5

7 d. Can‟t be determined e. None of these

2. Worried by the launch of the Indian Cricket League, BCCI announced an interesting

compensation scheme for its players, during England tour. Where the team was to play

three One Day International matches. For the total number of runs „x‟ scored by a player

in the three match tournament, the compensation is calculated as the minimum value of

the three numbers 1 3

2 2. 1 and - 72 4

x x x (in Rupees lakh). Due to falling revenue

from advertisement, Sachin Tendulkar is desperate to earn maximum possible

compensation during the tournament. What is the maximum compensation that Sachin

can earn (in Rupees Lakh)?

a. 2

23 b. 2 c.

17

5 d.

62

11 e. 7

3. Russian Scientist Borovosky defined first term of his series 1

25,b and thn term as

1 12 5 15n n

b n b where n is a natural number, then what will be the 200th term of

Borovosky‟s series?

a. 1995 597 b.

2005 c. 2015 597 d.

1995 597 e. 2015 597

4. Find the number of subsets X of {1,2,……….,10} such that X contain at least two elements

and such that no two elements of X differ by 1.

a. 132 b. 133 c. 134 d. 135 e. 136

5. Mukesh Khambani had taken a loan from his ICIC bank account for launch of his

ambitious project Reliance Flesh. One he received a statement from puzzle savvy ICIC

bank claiming the balance to be Rs. 40 2 57 40 2 57 ,x crore in his

account, then the value of x=(in Rs. crore)?

a.-9 b. -10 c. -11 d.-9.5 e. -10.5

6. How many factors does N=3 2 42 3 5 have that ends with zero?


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a. 60 b. 24 c. 36 d. 48 e. 60

7. CAT committee decided to give weightage to the speed with which a student attempts a

question paper. IIM Shilong suggested the formulae for calculating „speed quotient‟ for

every student as ,f x where f x is a real valued function for x to be the number of

questions attempted by the student in CAT, and f .x f y x f y If you attempted

100 questions in CAT then what was your „speed quotient‟?

a. 100 b. 1000 c. 10000 d. 100000 e. None of these

8. A standard deck of 50 cards consists of four different suits, each with 13 cards. How many

5-card hands are there such that all four suits are present? Present your answer in prime

factorization form.

a. 4 42 3 13 b.

3 42 3 13 c. 3 42 3 13 d.

42 3 13 e. 43 13

9. The area of a right angled triangle in the 1st quadrant is given by 1

2xy square units. When

x and y are the points satisfying the equation 2 3 30.x y what can be the maximum

area of the triangle?

a. 12 b. 30 c. 18 d. 24 e. 15

10. If loge

y a b x where a,b are some constants, then

a. 1

y a is proportional to

bx

b. logey is proportional to x

c. bx is proportional to

ye

d. y a is proportional to bx

e. bx is proportional to .ae

11. Crypticrating. Com is a website which provides ratings to movies on the basis of first

week‟s collection in selected cinema houses. Die Hard II was given a rating P(x)=

2

3

12 12P x ,

3 3

x x

x x

then find maximum possible rating for the movie, where x is first

week‟s collection in Rupees crore…….


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a.2

b.4

c.6

d.8

e. None of these

12. In the international-Number-of-planets Deciding committee‟s meeting, a young scientist

claimed that Indian mythological books had already calculated the number of planets in

the solar system. He demonstrated that a particular shloka mentioned the total number of

planets in the solar system to be equal to the maximum power of 98 that will divide 99!-

98! Perfectly. Then according to this shloka, how many planets are there in the solar

system?

a. 8 b. 9 c. 7 d. 10 e. 16

13. For an n-digit number N, SN=Sum of its digits and PN=Product of its digits. How many

natural numbers with less than four digits exist such that PN=2SN?

a. 9 b. 6 c. 12 d.18 e. 15

14. In the figure below, triangle ABC is rightangled at B. From a point S on AC, SP and SQ are

drawn perpendicular to AB and BC respectively. If AB=8cm and BC=15 cm, then the area

(in sq. cm) of rectangle PSQB is at most

a.20 b.28 c. 26 d. 30 e. 24

15. ABC is a Right Triangle. D and E are the mid points of side BC and AC respectively. The

circle is the incircle to the triangle AED. If AB=6 cm & BC=8 cm, then what is the radius of

the circle.

a. 2 3 cm b.3 3 cm c. 3

cm2

d.2 5

3 5. None


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16. Yashwant and Raj have got a certain number of red and yellow roses on Valentines day.

The ratio of red roses and yellow roses with them is 7:1 and 9:1 respectively. If in all they

have 90 roses, how many red roses could Raj have?

a. 9 or 60 b.10 or 50 c. 36 or 72 d. 9 or 45 e. Data sufficient

17. If a regular polygon has 18 more diagonals than sides, then interior angle of the polygon

is how many times each exterior angle?

a. 2.5 b. 3.5 c. 5 d. 4 e. None of these

18. If every pair from among the equation 2 20, 0x px qr x qx rp and

2 0x rx pq has common root, then the product of three common roots is…..

a. 2p qr b. 2pqr c. pqr d.

2 2 2p q r e. 3 3 3p q r

19. Mr. Sharma starts from his house to office 30 minutes later than his usual time so he

increases his speedy by 25% over his usual speed but still reaches 15 minutes late.

Another day he starts 15 minutes later than his usual time and increase his speed by 50%

comparatively to the provides day‟s speed and reaches 20 minutes before the office time.

what is the distance between his office and his house?

a. 10 km b. 15 km c. 5 km d. 20 km e. 25 km

20. Ram Lal professes to sell 2 kg of Kajoo at a loss of 20%, New to avoid the loss, he uses

two weighing stones, each of which is marked 1 kg, but weights less. By doing so he gains

2

6 %3

on selling every 2 kg of kajoo. If it is given that one of the stones weighs only 750

gm, then how much does the second stone weigh?

a. 900 gm b. 850 gm c. 750 gm d.600 gm e. None of these

SECTION-II


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Directions for questions 21 to 23: These questions are based on the following data.

J, K, L, M and N are five boys in a class. They are ranked in order of heights-from the

tallest to the shortest –and in order of cleverness-from the cleaverest to the dullest. K is

taller than N, but not as clear as J and L, whereas M is the cleverest of all but shorter than

J. While L is shorter than M but taller than K, who is not as clever as J. No two persons

got the same ranks in any of the characteristic.

21. If N is not the last in at least one of the two lists, which of the following is dullest of all the

five?

a. K b. L c. M d. J e. Cannot be determined

22. If L is third in order of cleverness, who is the dullest of all?

a. M b. N c. L d. K e. Can‟t be determined

23. Who among the following is cleverer as well as taller than K?

a. L b. N c. L and N d. J, L & M e. Can‟t be determined

Directions for question 24 & 25: These questions are based on the following data.

In a certain experiment, a genetically mutated bacterial cell is placed in an empty box.

The cell starts multiplying every day in such a way that on nth day from the start, all the

cells present on that day produce (n-1) cells each. The cells stop multiplying after a

certain number of days and due to a reverse reaction, from then on, everyday the cells

starts combining in sets of three to form larger cells, and any „incomplete set‟ of cells left

at the end of the day perish.

24. If the first day on which any cell perishes is the 59th day after the cells stopped

multiplying, then what is the minimum number of days for which the cells could have

multiplied?

a. 169 days b. 122 days c. 168 days d. 120 days d. 110 days

25. If the first day on which any cells perishes is the 59th day from the start of the experiment

then the cells stopped multiplying on the

a. 41st day from start b. 39th day from start c. 32nd day from start

d. 40th day from start e. 42nd day from start

Directions for questions 26 to 30: on the basis of following information:

Recently RGPV, Bhubaneswar organized a international conference on Number System.

Entire class of final semester of Mathematics from MLB College also participated in that.

These students were divided into groups and assigned several project work to be

completed during conference. One of the groups came up with a novel idea for the project

but fearing leaking of the idea to other groups decided to note their arithmetical

operations in a coded system called PGS (Private Group System).

In the PGS, every digit of the ordinary decimal system was assigned a different value as

shown along y-axis is scattered point diagram given below:


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In addition various decimal arithmetic operators were also changed as given below

Decimal

Operator

+ - x (/) =

PGS

Operator (/) x - + =

Other operators remain same as in ordinary decimal system. To take an example 21 in

ordinary decimal system is 4+1 in PGS: the answer is 2 in ordinary decimal system or 4 in

PGS.

26. The answer in PGS of the PGS expression 18 8 4 6 49 9 4 1 540 is

a. 270 b. 280 c. 420 d. 480 e. 860

27. Which expression in PGS is the equivalent of PGS expression:

9 11 6 9 5 11 16 99 7 3

a. 19+99 b. 17+77 c. 15+55 d. 13/33 e. 1333

28. If in PGS, 3

68 and 2-x 9 6,2

xy

y

then PGS expression

4?

9

x

y

(in PGS)

a. 16 b. 18 c. 24 d. 33 e. 66

29. How many of the following statements (where numbers are expressed in PGS) are true?

I. 100 is a perfect square II. 67 is a prime number

III. 418 is a perfect cube IV. 24 is a composite number

a. 1 b. 2 c. 3 d. 4 e. 0

30. How many of the following statements (where numbers are expressed in PGS) are NOT

true?

a. 462.6+146.4 is an integer

b. 174 is divisible by 3

c. 6923 on dividing by 8 gives a remainder of 1


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d. 973127=402

a. 0 b. 1 c.2 d. 3 e. 4

SECTION-III

Directions for questions 31 to 32: Answer the question on the basis of the information

given below. Xiachen Base of Indian Army has the following structure of a 33 square

grid.

A-Entry B-Front Wall

B-Parking D-Helipad

E-Supply Depot F-Base Kitchen

G- Office H-Arms and Ammunitions Depot

I-Prayer Hall

Following figure shows number of units deployed at different places at the Xiachen Base at

the beginning of the Morgil War with reference to the structure given above.

During the Morgil War, more units were sent to Xiachen Base and were positioned at

different places as per the following algorithm:

1. Choose any 22 table on the map and increase the number of units in each small

square (any one location) by one.

2. Only one set of 4 units can be increased at a time.

When the Morgil War ended, it was found that the final number of units deployed at

different places at the Xiachen Base was as follows:

Redevelopment of units means an addition of 4 units as per the algorithm given above.

31. How many times were the units redeployed during the Morgil War?

a. 4 b. 4 c. 6 d. 7 e. 8

A

B C

D

E F

G

H I

5

3 2

4 2 3

6

1 4

7

8 5

6 8 7

6

2 5


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32. Which of the two locations cannot have been redeplayed simultaneously?

a. Entry & Supply depot b. Front hall & Base Kitchen c. Office & supply depot

d. Prayer Hall & Base Kitchen e. Parking & front Hall

Directions for Questions 33 to 36: Each question to followed by two statement (A) and

(B). Mark your answer as

a. If the question can be answered by using either of the two statements alone.

b. If the question can be answered by using statements A alone.

c. If the question can be answered only by using both the statements together.

d. If the question cannot be answered even after combining the two statements.

33. There are two Arithmetic Progressions whose common difference differ by unit. What are

they?

A. Sum of the three consecutive terms in each is 15.

B. P and P1 be the product of three consecutive terms of the two APs such that P/P1=7/8.

34. Mr. Mohan goes from Bhilial to Raipur by rented car. The car meter has two parts, unit

part and decimal part. Unit part can be of two digits. Ten equivalent parts of decimal

make one unit. If meter reading is 1.9 it becomes 2.0 for next change of the meter. The

meter starts with I unit and decimal part which corresponds to charge of Rs. 6.00. How

much does Mr. Mohan Pay for the rented car?

A. The decimal part of meter changes after car travels for 500 mts and with every change

of decimal part there is increase of 50 paise over previous value.

B. The average speed of the car for entire journey is 60 kmph and the duration of travel

was 1.5 min.

35. A stationary submarine is 500 ft below the ship on the surface. The angle of elevation of

ship when seen from submarine is 450. At what angle should a torpedo to fired from

submarine so as to hit the ship which is travelling at speed of 40 first?

A. Speed of torpedo is 50ft/s

B. Ship is moving away from the submarine.

36. A tower is observed from two stations A and B where B is East of A. The tower is 100 m

due North of A and due North West of B. Find the height of the tower.

A. The distance between stations A and B is 100 m.

B. The angles of elevations of the tower from A and B are complementary.

Directions for questions 37 to 40: The following grid shows the score of an all play all

football tournament.


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Each win fetches a team 3 points and a draw 1 Point. In case of two teams ending up with

same points the team with greater goal difference (GD), which is the difference between

goals scored and goals against, will have higher ranking. In case that turns out to be

equal too, the team, which scored more goals, gets higher ranking. If all of them turns

out to be equal the team with more number of wins gets the higher ranking.

37. Which team won the tournament?

a. Arsenal b. Chelsea c. Man United d. Fulham d. Birmingham

38. Which team was placed last?

a. Southampton b. Leeds c. Man City d. Liverpool d. Fulham

39. Which team has scored the maximum number of goals?

a. Arsenal b. Man united c. Chelsea d. Liverpool d. Brimingham

40. The goal difference was highest for?

a. Arsenal b. Southampton c. Chelsea d. Liverpool d. Brimingham

SECTION-IV


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Directions for Questions 41to 43: Sentences given in each question, when properly

sequenced, from a coherent paragraph. The first and last sentences are 1 and 6, and the

four in between are labelled A, B,C and D. Choose the most logical order of these four

sentences from the five options to construct a coherent paragraph between sentences 1

and 6.

41. I. The term art is most widely used to describe a particular type of creative production

generated by human beings.

A. An artist makes a work of art, mostly with the intention to create an experience for

others.

B. It can be considered an expressive means of seeing things the artist‟s way.

C. There is no general agreed-upon definition of art, since it is a subjective value.

D. The denomination art implies some degree of aesthetic value, regardless of any

practical value of the art in question.

6. But something can be said about the terms on which this value is based. The impetus

art is often called creativity.

a. ABCD b. DBCA c. DABC d. BCAD e. CDBA

42. I. Computer programmer Thomas Anderson leads a secret life as a hacker under the alias

“Neo”.

A. Neo accepts

B. Swallowing a red pill, he be abrupty wakes up naked in a liquid-filled chamber, his body

connected by wires to a vast mechanical tower covered with identical pods.

C. Cryptic messages appearing on his computer monitor and an encounter with several

sinister agents lend him to a group led by the mysterious Morpheus, a man who offers

him the chance to learn the truth about the Matrix.

D. He wishes to learn the answer to the question.” What is the Matrix?”

a. DCBA b. ABCD c. BCDA d. DCAB e. DBCA

43. I. An early example of the doctrine of spiritual evolution is found in Samkhya, a teaching

that goes back more than two and a half thousand years.

A. As a result of the original root-prakriti undergoes a series of progressive

transformations or unfolding, in the form of successive essences called tattvas.

B. Pure spirit comes into proximity with prakriti disturbing its equilibrium.

C. The most subtle tattvas emerged first, then progressively grosser ones, each in a

particular order, and finally the elements and the organs of sense.

D. Unlike classic Hindusism, the traditional Samkhya philosophy is atheistic and dualistic.

6. The goal of evolution however, is paradoxically, the release of prurusha and the return

to the unmanifest condition. Hence everything is tending towards a goal of spiritual

quiescence.

a. DACA b. DCAB c. DBAC d. CBDA e. CDBA

Directions for questions 44 & 45: 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 sentence from the five choices to construct a coherent paragraph.


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44. A. They do not have a „real‟ body in the „outside‟ reality.

B. It is also possible that a simulated entity could be moved out of the simulation entirely

by means of mind transfer into a synthetic body.

C. Rather, each is a fully simulated entity, possessing appropriate level of consciousness

that is implemented using the simulation‟s own logic (i.e. using its own physics)

D. In a virtual-people simulation, every inhabitant is a native of the simulated world.

E. As such, they could be downladed from one simulation to another, or even archived

and resurrected at a later data.

a. DACEB b. DCAEB c. ACEDB d. BACDE e. BDACE

45. A. digital philosophy purports to solve certain hard problem in the philosophy of mind and

the philosophy of physics, since, following Leibniz, the mind can be given a computational

treatment.

B. Digital philosophy is a modern re-interpretation of Gottfried Leibniz‟s monist

metaphysics, one that replaces Leibniz‟s monads with aspects of the theory of cellular

automata.

C. The digital approach also dispenses with the non-deterministic essentialism of the

Copenhagen interpretation of quantum theory.

D. This approach to metaphysics has been multism since it posits the existence of multiple

universes.

E. In a digital universe, existence and thought would be equivalent to computation, thus

computation is the single substance of a monist metaphysics while subjectively arises

from computational university.

a. BAECD b. BCDAE c. BEACD d. BACED e. ABCED

Directions for questions 46 & 47: Define the italicized words below with the help of the

appropriate word in the context.

46. At the bell, the pugilists moved to the centre of the ring and touched gloves. Pugilists

are……..

a. Complacents b. Charitables c. Prizefighters d. Benefactors e. Validictor

47. The firm is still in business. Its “ Going-out-of Business” last year was just a hype. Hype

means…………

a. Placidity b. Exaggeration c. Complacency

d. Deceptive Marketing communication e. None of these

Directions for questions 48 to 50: Read the passage given below and answer the

questions that follow:


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What happens if you take two mirrors and arrange them so that they are facing each

other in empty space? You first reaction might be “ nothing at all” In fact, both mirrors

are mutually attracted to each other by the simple presence of the vacuum. This startling

Phenomenon was first predicted in 1948 by the Dutch theoretical physicist Hendrik

Casimir while was working at Philips Research Laboratories in Eindhoven on-of things-

colloidal solutions. The phenomenon is now dubbed the Casimir effect, while the force

between the mirrors is known as the Casimir force.

For many year Casimir effect was little more than a theoretical curiosity. But interest in

the phenomenon has blossomed in recent years. Experimental physicists have realized

that the Casimir effects the working of micromachined devices, while advances in

instrumentation have enabled the force to be measured with ever-greater accuracy.

The new enthusiasm has also been fired by fundamental physics. Many theorists have

predicted the existence of “large” extra dimensions in 10- and 11-dimenstional unified

filed Theories of the fundamental forces. These dimensions, they say, could modify

classical Newtonian gravitation at sub-milimetre distances. Measuring the Casimir effect

could therefore help physicists to test the validity of such radical ideas.

Although the Casimir force seems completely counter intuitive, it is actually well

understood. In the old days of classical mechanics, the idea of a vacuum was simple. The

vacuum was what remained if you emptied a container of all its particles and lowered the

temperature down to absolute zero. The arrival of quantum mechanics, however,

completely changed our notion of a vacuum. All fields in particular electromagnetic fields-

have fluctuations. In other words at any given moment their actual value varies around a

constant, mean value. Even a perfect vacuum at absolute zero has fluctuating fields

known as “Vacuum fluctuations”, the mean energy of which corresponds to half the

energy of a photon.

However, vacuum fluctuations are not some abstraction of a physicist‟s mind. They have

observable consequence than can be directly visualized in experiments on a microscopic

scale. For example, an atom in an excited state will not remain there infinitely long, but

will return to its ground state by spontaneously emitting a photon. This phenomenon is

consequence of vacuum fluctuations. Imagine trying to hold a pencil upright on the end of

your finger. It will stay there if your hand is perfectly vacuum fluctuations. Imagine trying

to hold a pencil upright on the end of your finger. It will stay there if your hand is

perfectly stable and nothing perturbs the equilibrium. But the slightest perturbation will

make the pencil fall into a more stable equilibrium position. Similarly, vacuum fluctuations

cause an excited atom to fall into its ground state.

The Casimir force is the most famous mechanical effect of vacuum fluctuations. Consider

the gap between two plane mirrors as a cavity. All electromagnetic fields have a

characteristic “ spectrum” containing many different frequencies. In a free vacuum, all of

the frequencies are of equal importance. But inside a cavity, where the field is reflected

back and forth between the mirrors, the situation is different. The field is amplified if

integer multiples of half wavelength can fit exactly inside the cavity. This wavelength

corresponds to a “cavity resonance”. At other wavelengths in contrast, the field is

suppressed. Vacuum fluctuations are suppressed or enhanced depending on whether their

frequency corresponds to a cavity resonance or not.


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An important physical quantity when discussing the Casimir force is the “field radiation

pressure” Every field –even the vacuum field-carries energy. As all electromagnetic fields

can propagate in space they also exert pressure on surfaces, just as a flowing river

pushes on a floodgate. This radiation pressure increases with the energy-and hence the

frequency –of the electromagnetic field. At a cavity-resonance frequency, the radiation

inside the cavity is stronger than outside and the mirrors are therefore pushed apart.

Out of resonance, in contrast, the radiation pressure inside the cavity is smaller than

outside and the mirrors are drawn towards each other.

It turns out that, on balance, the attractive components have a slightly strong the man

the repulsive ones. For two perfect, plane parallel, mirrors the Casimir force is therefore

attractive and the mirrors are pulled together. The force, F, is proportional to the cross-

sectional area A of the mirrors, increases 16 fold every time the distance, d between the

mirrors is halved F-A/d. Apart from these geometrical quantities the force depends only

on fundamental values- Planck‟s constant and the speed of light.

While the Casimir force is too small to be observed for mirrors that are several metres

apart, it can measured if the mirrors and within microns of each other. For example, two

mirrors with an area of 1cm2 separated by a distance of 1 m have an attractive Casimir

force of about 10-7 N roughly the weight of a water droplet that is half a millimeter is

diameter. Although this force might appear small, at distance below a micrometer the

Casimir force becomes the strongest force between two neutral objects. Indeed at

separations of 10 nm-about a hundred times the typical size of an atom the Casimir effect

produces the equivalent of 1 atmosphere of pressure.

Although we do not deal directly with such distances in our everyday lives, they are

important is nanoscale structure and microelectomechanical system (MEMS). These are “

intelligent” micron-sized devices in which mechanical elements and moving parts, such as

tiny sensors and actuators, are carved into a silicon substrate. Electronic components are

then wired on to the device to process information that it senses or to drive the

movement of its mechanical parts. MEMS have many possible applications in science and

engineering, and are already used as car-air-bag pressure sensors.

As MEMS device are fabricated on the micron and submicron scale, the Casimir force can

cause the tiny elements in a device to strick together-as reported recently by Michael

Roukes and co-workers at the California Institute of Technology. But the Casimir force can

be used to control the mechanical motion of a MEMS device. The researches suspended a

polysilicon plate from a torsional rod-a twisting horizontal bar just a few microns in

diameter. This made the plate rotate. They also studied the dynamical behaviour of the

MEMS device by making the plate oscillate. The Casimir force reduced the rate of

oscillation and led to nonlinear phenomena, such as hysteresis and bistability in the

frequency response of the oscillator. According to the team, the system‟s behaviour

agreed well with theoretical calculations.

48. For two perfect, plane parallel mirrors, the Casimir force is not


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a. attractive b. repulsive

c. amenable to measurement d. considered to be a strong force

e. greater than Newtonian force

49. Which of the following is true according to passage?

a. Casimir force is to small to be observed for the mirrors that are several nanometers a

part.

b. Casimir force becomes the strongest force between two neutral objects at distance

below a micrometer.

c. At separations of 100nm, the Casimir effect produces the equivalent of one atmosphere

of pressure.

d. Both (b) and (c)

e. Both (a) and (c)

50. The Casimir effect is important is applications like

a. nanoscale structure

b. MEMS.

c. car air-bag pressure sensors.

d. all the above

e. None of the above

Directions for questions 51: Each question has a pair CAPITALIZED words

followed by pairs of words. Choose the pair words that express a

relationship similar to that expressed in the capitalized pair.

51. MAWKISH: MAUDLIN

a. smug: sunggly b. wry: sardonic c. Perceptive: deep

d. erudite: educated e. turpid: tarnish

Directions for questions 52 & 53: Each statement below is followed by three

assumptions I, II, and III. From the choices given, select the assumptions which is/are

implicit in the statement.

52. The grocery store found its sales rising sharply after it advertised on FM radio.

I. Advertising on FM ratio raises sales.

II. FM ratio is a good medium of advertising.

III. Advertising on FM radio may be an excellent way for the grocery store to increase

sales.

a. I is implicit b. II is implicit c. II is implicit

d. II & III are implicit d. None of these

53. Many people receive their salaries in the form of cheques instead of coins and notes, and

most affluent people meet their expenses by paying cheques.

I. A cheque is a mode of payment

II. Coins and notes are cumbersome.


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III. Only wealthy people pay by cheques.

a. Only I is implicit b. Only II is implicit c. I and II are implicit.

d. Only III is implicit e. I and III are implicit

Directions for questions 54 & 55: Each statement below has a part missing. There are

choices given as continuation of the statement. Choose the one which best fits as

continuation of the given sentence.

54. If Intermittent Explosive Disorder still sounds like a new name for a very old problem.

a. diagnosing IED may at least prevent sufferers from being diagnosed with something

they have not got

b. to diagonose IED may at least prevent sufferers from diagnosing with something they

have not got

c. diagnosing IED may at least prevent sufferers diagnosing with something they have not

got

d. to diagnose IED may at least prevent sufferers from being diagnosed something they

have not got

e. None of the choices fits.

55. India‟s progress in reducing malnutriation over the last decade.

a. had been much worse than the record of other countries with comparative socio-

economic indicators

b. has been much worse than the record of other countries with comparable socio-

economic indicators

c. has been more worse than other countries with comparable socio-economic indicators

d. has been much more worse than the record of other countries with comparative socio-

economic indicators

e. has been much worst than the record of other countries with comparable socio-

economic indicators.

Directions for questions 56 to 58: Select the option that fills the blanks most suitably.

56. When huge media________________ sue thousands of individual users, they fuel the

________ that copyright law is just a tool for the powerful, not a means to improve

society by encouraging creativity and innovation.

a. barons, fire b. magnates, anticipation c. conglomerates, argument

d. Paparazzi, expectation

57. The bill sailed through the cabinet and breezed through the parliamentary sub-

committees, but now it‟s _____________ in partisan politics and special-interest

bargaining and is not likely to come out_____________.

a. entangled, unaltered b. snarled, unscathed c. delayed, forthwith


16

58. The tsunami that devastated large ____________ of Asia last December also sparked

hope that it would force opponents in civil wars to _____________ armed struggle in

favour of cooperation and rebuilding.

a. tracts, abjure b. sea-coasts, abnegate c. continent, shun

d. swathes, flummoxed e. None of these

Directions for questions 59 to 60: Read the passage given below and answer the

questions that follow.

To have a second language at your disposal, even if you only know it enough to read it

with pleasure, is a sensible advantage. Our educationists are too often never too far

enough in any one to derive any use or enjoyment from their study. The boy learns

enough Latin to desist it; enough Greek to pass an examination; enough French to get

from Calais to Paris; enough German to exhibit a diploma; enough Italian or Spanish to

tell which, but not enough to any secure the enormous boon of access to a second

literature.

Choose well, choose wisely, and choose one. Concentrate upon that one. Do not be

content until you find yourself reading it with real enjoyment. The process of reading for

pleasure in another language rests the mental muscles; it enlivens of ideas. The mere

form of speech excites the activity of separate brain cells, relieving in the most effective

manner the fatigue of those in hackneyed use. One may imagine that a man who below

the trumpet for his living would be glad to play the violin for his amusement. So it is with

reading in another language than your own.

59. What is the use of learning a second language?

a. to pass an examination b. To desist it c. To exhibit a diploma.

d. It is sensible advantage e. To get help while being in another country.

60. How is fatigue relieved by studying another language?

a. It initiates the reader b. It relieves in the most effective manner.

c. It tires the mind of the reader d. It dulls the mind. e. None of the above.


17

SECTION-I

1. b 2. c 3. e 4. b 5. b 6. c 7. a 8. b 9. c 10. c

11. b 12. b 13. e 14. d 15. e 16. d 17. b 18. c 19. a 20. c

SECTION-II

21. a 22. e 23. a 24. d 25. d 26. d 27. a 28. b 29. c 30. b

SECTION-III

31. c 32. c 33. e 34. d 35. e 36.d 37. b 38. a 39. b 40. c

SECTION-IV

41. c 42. d 43. c 44. a 45. d 46.c 47. b 48. b 49. c 50. b

51. b 52. b 53. a 54. a 55. b 56.c 57. b 58. d 59.d 60.b

Explanation sol:


18

1. Probability that C wins=x

Probability that B wins =2x

Probability that A wins=4x

Since they are only horses competing.

4x+2x+x=1

x=1

7

C lose with probability 1 6

17 7

Hence, (b) is the correct answer.

2. The three numbers 1

2 2, 12

x x and 3

74

x

can be viewed as the coordinates of points

lying on the lines

1 -3

2 2 I , 1 2 and y= 7 32 4

y x y x x respectively.

Draw all three lines on the same set of axes and find the points of intersection.

Subtract equation (2) from equation (1) to get 3 3

0 1 12 2

x x

Substitute 2

3x

into equation (1) are get

22 2

3y

2

3y

Thus, the point of intersection of the lines y=2x+2 and 1 -2 2

1 is ,2 3 3

y x


19

Similarly, we find 20 62

,11 11

as the point of intersection of the lines y=2x+2 and

3 24 17

7, and ,4 5 5

y

as the points of intersection of the lines 1 -3

1, and y= 7,2 4

y x x

The minimum value of the three numbers 1 -3

2 2, 1, and 72 4

x x x is shown in the

diagram as the smallest of the coordinates of points on the three lines for a given value of

x. The maximum of these y-coordinates is 17

.5

3. 1 12 5 15nn bb n

1 5 15 12n nb b n

3 2

3

4

4

4 2

4

5

n

201 201

200

1 5 3 4 5

1 5 15 12

Put n=2, then b 5 3 8 5

5 5 3 9

5 15 9

=5 3 2

Put n=3, then b 5 3 12 5

5 5 6 21

5 3 3

Thus, we can say that

b 5 1 3 1

5 3 199 5 597.

Hence, e is the correct

n n

n n

b b n

b b n

b

b

n n

b

answer.

4. For k objects to be chosen out of 10 given objects, we get k-1 gaps in between k objects,

where 2.k

Hence task becomes equivalent to choosing k objects from 10-(k-1)=10-K+1 objects,

where k=2,3,4 or 5.= 9 8 7 9

2 3 4 5 36 36 35 6 113.C C C C

5. note 40 2 57. on squary both sides we get

2 2 2

2 2

2

2 57 57 40 2

2 57 2 57 2 50

100 10 , hence x=-10

x

x x

x x

6. 3 2 4N=2 2 5

Since zero consists of 2 and 5 so


20

Ways of choosing 2=3 1 2 32 ,2 and 2

Ways of choosing 3=3 0 1 23 ,3 ,3

Ways of choosing 5=4 1 2 3 45 ,5 ,5 and 5

Total number of factors ending in zero=3 3 4 36 .

So option (c) is correct.

7. Given f x f y x f y

Taking x=0, y=0

0 0 0 0

0 0 ........... 1

Let f 0

From 1 ,

Putting k=100, we get f 100 100

Hence, a is the correct answer.

f f f

f f f

K

f k k

8. There are 134 ways to do this with a 4-card hand, since for each suit we select one card.

Any of the remaining 48 cards can be added for a fifth card. However, this counts twice

the number of ways to select two cards from the suit of the fifth card, so the answer is

4 1 4113 48 2 3 13

2

9. x,y have maximum value when 2x+3y 30 …………….(1)

2x+3y 30

1

Area= maximum if x=y.2

xy

From equation (1)x=y=6 satisfy the equation.

So, the maximum area=1 1

6 6 18 sq.units 2 2

xy

10. Given y=a+b logex.

elogy a

by a

x x eb

by a y

b b y a bba

ex e x e x

e

is proportional to ey.

11. Let 2

2

12 12

3 3

x xy

x x


21

2 2

2

2

3 3 12 12

or y-1 3 12 3 12 0

for real x, 3y-12 4 1 3 12 0

or 3 y-4 3 12 4 4 0

or 3 y-4 8 0

or y-4 8 0

8 4.

so maximum value of y is 4.

y x x x x

x y x y

y y

y y

y

y

y

12. 99!-98!=(99-1)98!=9898!

Now 98= 2 17 2

Power of 7 dividing 98!=2

98 9814 2.

7 7

So

2 16 82

98! 98! 98! 98!so

7 2 7 298 7 2n n n n

8 8 9

98! 98! 98 98 98!

78 98 98 98

So, the maximum power of 98 will be 9 that will divide 99!-98!

13. For n=1, there is no number for which PN=2SN.

For n=2, let the two-digit number be 10a+b.

Then if PN=2SN, ab=2 (a+b)2

22

ba b

b

The only two-digit numbers satisfying the above equation are 36,44 and 63.

For n=3, let the three digit number be

100a+10b+c

Then, If PN=2SN, abc=2 (a+b+c)

Since abc is even, atleast one of a,b and c has to be even.

Let us assume „a‟ as even. Then a=2, 4, 6 or 8.

For a=2, bc=2+b+c2

1

bc

b

The only possible values of b and c are (2,4) and (4,2)

For a=4, 2bc=4+b+c4

2 1

bc

b

The only possible values of b and c are (1,5), (2,2) and (5,1)

For a=6, 3bc=6+b+c6

3 1

bc

b


22

No values of b and c satisfy the above equation.

For a=8, 4bc=8+b+c8

4 1

bc

b

The only possible values of b and c are (1,3) and (3,1)

The three-digit numbers for which PN=2SN are

3 numbers using 2,2,4



i.e. total 15 three digit numbers

Thus, for n<4, PN=2SN is true for 18 members.

Hence, (5) is the correct answer.

14. Let QC=x 18

QS= and BQ=15-x15

x

Area of 8x 8

PSQB= 15 1515 15

x x x

The product of two factors x and 15-x (two numbers, whose sum is a constant) is

maximum when x=15-x, i.e. when x =7.5

The maximum possible value of the area is 28

7.5 3015

15. Since AD & DE are medians so area of

2 2 2

2 22 2

1 1ADE= 6 8 6 , length of AD is 6 4 2 13

4 2

Also DE is the median to the ADC, so using Apollonius theorem we have

AD DCED EC 9 or ED=3 cm.

2

now in ADE using r s=A we have

2 13 5 3S= 4 13

2

cm

cm.

6Thus r= 8 2 13

4 13

16. Let yashwant have 7x red and x yellow roses

Total no. of roses with him=8x

Let Raj have 9y red and y yellow roses.

Total no. of roses with him=10y.

It is given that 8x+10y=90

Or 4x+5y=45

X should multiple of 5 satisfy this eq.

S may be 5 or 10 and corresponding value of y is 5 or 1.

If x is 5, y=5 Raj have 45 red roses.

If x is 10, y=1Raj have 9 red roses.


23

So Raj have 9 or 45 red roses.

17. Let the number of sides of polygon be n.

We know that ratio of sides and diagonals of polygon=2: (n-3)

225 36 0

18 3

n=9, n=-4 [n=9 is taken]

Interior angle I n 2Also, using formulae,

Exterior angle (E) 2

9 21 7Or

E 2 2

Or I=3.5 E

nn n

n n

or

18. The given equation are

2

2

2

0........................

0..........................

0..........................

let , be the roots of (i)

let , , be the roots of (ii)

let , be the roots of (iii)

So

x px qr i

x qx rp ii

x rx pq iii

2 2

,

=qr, =rp a=pq

,

pqr

so pqr

Option c answer

19. On the first day. Mr. Sharma increases his speed by 25% it means the ratio of the new

speed to that of the original speed =5:4.

The ratio of the new time taken to that of the original time taken=4:5

He compensates 15 minutes by doing so

Now he would be taking 60 minutes instead of 75 minutes.

Now according to the options, if we consider option (1) i.e. 10 km as the distance then the

increased speed becomes 10 km/hr.

Again A/q, Mr Sharma increases his speed by 50% again on another day

Mr. speed becomes 15 km/hr

Mr. Sharma would only take 10/15=2/3 hrs i.e. 40 min to reach his office

Option (a) answer

20. Let the CP of 2 kg kajoo=Rs 100,

the SP of 2 kg kajoo=(100-20%) of 100=Rs. 80

Again A/q. (by using the stones), the new SP is equal to Rs. 106.67

There is a gain of 33.33%

As we know (by product constancy)


24

There is a gain of 33.33%

The stones must be weighing 25% less

The combined weight of both the stones is 1500 gm instead of 2000 g

One of the stones weighs 750 g

The other of the stones weighs 750g

Hence, Option (c) answer

21. The arguments are:

Height cleverness

J>M>L>K>N M>J, L>K

Now as N Can‟t be lost in both the lists, K is dullest of all

22. It can either K or N.

23. (a)

24. The number of cells after the first day=(1+0)=1

After second day=1 (1+1)=2!

i.e. after nth day there will be n! cells.

Let the cells multiply for n days

There are n! cells when the cells start combining in seats of 3.

Since the first cell that perishes, does so on the 59th day the highest power of 3 than can

perfectly divide n! is 338

From the choices we get n=120 or 122.

Since n is the minimum number of days for which the cells multiplied, n=120.

25. Here let the cells initially multiply for d days hence they combine for (58-d) days before

the first cell perishes on day 59.

From choices we get d=40, we have the highest power which can divide 40!=18 giving 58

days before cells start perishing.

26. 18 8 4 6 49 9 4 1 540......in PGS

16 6 2 23 3 2 1 520.......in decimal

=8 16 520=260...........in decimal

=480......in PGS

27. The given PGS expression in decimal system

3 4 10 5 14 9

11 3 11 11 33 7

3 4 11 5 6 3 2 6

11 3 10 11 11 11 3 11

1319 99......in PGS

33

28. The given equations in decimal system

7x+8y=46

8x-3y=4


25

On solving x=2, y=4

PGS expression (4-x)/(9-y)

= 2 3y in decimal system

= 2 2 3 4 16 in decimal system

=18 in PGS

29. Expressed in decimal system.

(I) 100 is a perfect square (True)

(II) 49 is a prime number (False)

(III) 216 is a perfect cube (True)

(IV) 82 is a composite number (True)

Hence 3 statements are true.

30. Expressed in decimal system

(A) 248.4/124.2=2 is an integer (True)

(B) 192 is divisible by 7 (False)

(C) 4387 on dividing by 6 gives a remainder of 1 (True)

(D) 397-189=208 (True)

Hence 1 statement is not true.

31. C

32. Clearly office was never redeplayed.

Alternative method for questions 32 &32:

Since four units were added during each redeployment and a total of 24 units were added

during the war (initial 30 units to final 54 units), the number of times units were

redeployed=24

64

Solutions for 33 to 35:

33. Both the statements alone are not sufficient to get the answer Using both the statement

together, we have a-b,a,a+d & A-p, A,A+p. Where p=d+1.

S=3a=3A=15 therefore a=A=5.

Also P/P1=a (a2+d2)/A (A2-P2)=7/8. By solving this we will get two values of d as this will

form Quadratic equation. Thus we will be having two such series.

34. To find the amount to the paid for Car we need to find amount for a decimal part of the

meter. Using statement (A) alone we get that the decimal part changes after every 500

metres. But this is not sufficient, as we do not know the distance travelled. Using

statement (B) alone we can find the distance travelled only. Hence both statements alone

are not sufficient. But using both the statements, we can find out total changes in decimal

parts (changes in decimal part=total distance/(decimal part) which is useful to find total

amount above Rs. 6.00

35. This problem can be solved by using both the statements if one assumption that all the

objects move in same vertical plane is made. But such an assumption cannot be made in

DS Problems. Ans. (e)


26

36. If tower is represented by T. Then using statement (A) alone we have that triangle TAB is

isosceles right-angled triangle (as 0ABT= 45 . So BT=10 2 . But this is not sufficient to

get height of the tower. Statement (B) alone is not sufficient as we do not have any of

the distance. Using both the statements together, If 1T is the top of the tower then in

1 1

1

1

TT A,TT AT tan and in TT,B.

TT BT tan 90- . using both the equations we can get

TT , which is height of the tower. Ans d

Solutions for 37 to 40:

Team with

points

Goals for Goals Against Goal difference

Aresenal-15 (4

wins, 3 draws)

19 13 6

Man United-15

(5 wins)

24 15 9

Chelsea -18 (5

wins, 3 drawns)

20 11 9

Liverpool-11 (3

wins, 2 draws)

10 16 -6

Newcastle-10 (2 wins, 4 draws)

13 17 -4

Brimingham-16 (2 wins, 1 draw)

17 18 -1

Man City-9 (2 wins, 3 draws)

17 18 -1

Leeds-10 (2 wins, 4 draws)

17 18 -1

Southamption-8 (2 wins, 2

draws)

9 16 -7

Fulham-11 (3

wins, 2 draws)

16 17 -1

37. b

38. a

39. b

40. c

41. Topic of art‟s definition introduced by statement I has been appropriately picked up by

D,A aptly describes artistic process. B appropriately sums up an artist‟s perspective. C‟s

summing up the difficulty in defining art appropriately precedes statement 6 the summing

up of the conclusion of the passage. DAB is the key, DABC (c) the best sequence.

42. D‟s „He‟ refers to „Computer programmer Thomas Anderson‟ mentioned in statement I. C

answers D‟s question aptly, describing Neo‟s meeting the mysterious‟ Morpheus‟, which

„Neo‟ in A accepts. B further describing the „Swallowing of red pill‟ by Neo, precedes


27

statement 6 which sums up the passage. DC an B6 being mandatory, DCAB (d), is the

right sequence.

43. D describes „The traditional Samkhya philosophy‟, statement I having introduced the

ancient „Samkhya philosophy‟. B advances the argument telling how „ Pure spirit comes

into proximity with Prakriti”, A tells what results. C further advances the argument/thesis

and correctly precedes. Statement 6 which sums up the passage aptly logically. DBA is

the key, DBAC (c) the right sequence.

44. D being the general statement is the best opener, introducing the topic „virtual-people

simulation‟. A‟s they refers to the virtual-people of statement D, C advances the topic with

further description, same is done by E.B concludes the passage appropriately. DAC is the

key, DACEB (a) is the right sequence.

45. B introduces the topic „ Digital philosophy‟ so is the best opener. A describes the

functioning and processes of „Digital philosophy‟. C with its „ digital approach‟ etc. is at

the right place. E further advances the thesis/argument. D best concludes the passage

with its telling how. “This approach to metaphysics has been dubbed multism‟. BAC is the

key and BACED (d) the right sequence.

46. The word „puglist‟ means‟ a boxer, especially a professional prizefighter‟ Hence, the

answer is option (c)

47. In the given context, „hype‟ refers to „exaggeration‟. Hence the answer is option (b)

48. It is clear from the passage that the Casimir force is not repulsive when two perfect plane

parallel mirror come in contact. Other options 1,3,4 & 5 are no way related to it. So can

be ruled out.

49. According to the passage option (c) holds the true key when the Casimir force produce the

equivalent effect of 1 atmosphere of pressure at separation of 100 nm. Rest of the options

can be eliminated straightway.

50. As per the passage the Casimir effect is important in application especially in MEMS.

(Microelectromechanical system) other options are also applicable but it revolves around

option (b) only.

51. Both the words mean foolishly sentimental. Wry means sardonic. An erudite person is not

just educated; he is learned Hence, (b)

52. The grocery sales has increased after advertisement on FM radio. So the statement

directly relates from assumption II. which says the same.


28

53. In the given statement there is no description about advantages and disadvantages of

cheques of coins and notes, it only talks about the cheques as one of the mode of

payment. Hence assumption 1.

54. The gerund „ diagnosing‟ is right not the „to infinitive‟. The „sufferers‟ are „being diagnosed

with‟. Choice (a)

55. „Comparative‟ means relative and „comparable‟ means similar. The latter is right in the

context. The words for comparison can be „much worse‟ but not‟ more worse‟ (double

comparison) or „much more worse‟, Choice (b)

56. The first blank can be filled up using several options. It is the second blank that holds the

key.

Because huge media…………..sue small interest users, the connotation is that the law is for

the powerful. The above argument is fuelled. So option (c)

57. The bill had smooth sailing earlier. But is now caught up in petty politics, and is not likely

to come out unharmed. The only choice is between options (1) and (2). The second option

„unaltered‟ in (a) does not convey the negativity required. Answer (b)

58. Options (a), (b) and (c) are rendered incorrect by the use of the words „ abjure‟. „sea-

coasts‟ and „continent‟ Although (a) and (d) are close answers, the right answer should be

(d) as „abjure‟ conveys renunciation, as if on oath. Answer (d)

59. Except one language (Which helps in securing degree/diploma) 2nd language has a

sensible advantage over the 1st. Hence option (d)

60. The level of fatigue can best be relieved in the most effective manner if one goes by

reading another language. It provides relief to the brain. So option (b)


29

Documents

SECTION-I 1....Countdown Cat Mock Test Paper-2 1 SECTION-I 1. Three horses A,B & C are the only horses competing in Western India Turf Club race in August 2007. …