tcs sample test

7/28/2019 TCS Sample Test

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TCS Sample Test1

The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead theay in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries ans also write code at the same rate.Suppose 12

such programmers take 12 minutes to write 12 lines of code in total. How long will it take 72 programmers to write 72 lines of code in total?

[1] 6

[2] 72

[3] 18

[4] 12

2

A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 4 faces of the outer surface of the cube are painted, totally how manyaces of the smaller cubes remain unpainted?

[1] 800

[2] 500

[3] 900

[4] 488

3

10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects are made to stand in a line and each person declares thathe person next to him on his right is guilty. The rightmost person is not questioned. Which of the following possibilities are true?

A. All suspects are lying or the leftmost suspect is innocent.

B. All suspects are lying and the leftmost suspect is innocent .

[1] A only

[2] Both A and B

[3] Neither A nor B

[4] B only

4

Alok is attending a workshop "How to do more with less" and today's theme is Working with fewer digits . The speakers discuss how a lot of miraculous mathematics can beachieved if mankind (as well as womankind) had only worked with fewer digits. The problem posed at the end of the workshop is How many 5 digit numbers can be formedsing the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4? Can you help Alok find the answer?

[1] 3125

[2] 625

[3] 375

[4] 500

5

The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to1000. How many 3s are used in numbering these buildings?

[1] 256

[2] 54

[3] 192

[4] 300

6

Alok and Bhanu play the following min-max game. Given the expression N = 9 + X + Y - Z where X, Y and Z are variables representing single digits (0 to 9), Alok would

like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Yor Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play toheir optimal strategies, the value of N at the end of the game would be

[1] 9

[2] 18

[3] 20

[4] 27

7

A sheet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40, statement n says: 'Exactly n of the statements on this sheet are false.' Whichstatements are true and which are false?

[1] All the statements are false.

[2] The 39th statement is true and the rest are false

[3] The odd numbered statements are true and the even numbered statements are false.

[4] The even numbered statements are true and the odd numbered statements are false.

8


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A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probabilityhat Q is closer to the center of the circle than the periphery?

[1] 0.75

[2] 0.5

[3] 0.25

[4] 1

9

On planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny plantoids called echina start growing on the rocks. echina grows in theorm of a circle and the relationship between the diameter of this circle and the age of echina is given by the formula

d = 4 * (t - 8) for t 8here d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 8mm. How many yearsack did the solar blast occur?

[1] 8

[2] 16

[3] 12

[4] 24

10

After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1letter is inserted in an improper envelope?

[1] 12/(12^12)

[2] 0

[3] 11/12

[4] 1/12

11


such programmers take 12 minutes to write 12 lines of code in total. How many programmers required to write 72 lines of code in total in 72 minutes?

[1] 18

[2] 12

[3] 72

[4] 6

12

A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says "At least n of the statements on this sheet are true." Whichstatements are true and which are false?

[1] The odd numbered statements are true and the even numbered are false

[2] The even numbered statements are true and the odd numbered are false.

[3] The first 13 statements are true and the rest are false.

[4] The first 26 statements are false and the rest are true.

13

There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a boxat random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is

[1] 14/19

[2] 37/38

[3] 1/2

[4] 3/4

14

Alok and Bhanu play the following min-max game. Given the expression N = 12 + X*(Y - Z) where X, Y and Z are variables representing single digits (0 to 9), Alok wouldlike to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Yor Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play toheir optimal strategies, the value of N at the end of the game would be

[1] 12

[2] -69

[3] 93

[4] 30

15

Planet fourfi resides in 4-dimensional space and thus the currency used by its residents are 3-dimensional objects. The rupee notes are cubical in shape while their coins arespherical. However the coin minting machinery lays out some stipulations on the size of the coins.


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The diameter of the coins should be at least 64mm and not exceed 512mm. Given a coin, the diameter of the next larger coin is at least 50% greater. The diameter of the coin must always be an integer.You are asked to design a set of coins of different diameters with these requirements and your goal is to design as many coins as possible. How many coins can you design?

[1] 8

[2] 9

[3] 5

[4] 6

16

Anoop managed to draw 7 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middlecircle touches two circles on either side. Find the ratio of the radius of the circles to the side of the square.

[1] 1:(2+ 62)

[2] 1:(4+ 73)

[3] (2+ 72):1

[4] 1:(2+ 72)

17

The teacher is testing a student's proficiency in arithmetic and poses the following question. 1/3 of a number is 3 more than 1/6 of the same number. What is the number? Canou help the student find the answer?

[1] 18

[2] 21

[3] 12

[4] 6

18


such programmers take 12 minutes to write 12 lines of code in total. How many lines of code can be written by 72 programmers in 72 minutes?

[1] 12

[2] 72

[3] 432

[4] 6

19

On the planet Oz, there are 8 days in a week- Sunday to Saturday and another day called Oz day. There are 36 hours in a day and each hour has 90 min while each minute has60 sec. As on earth, the hour hand covers the dial twice every day. Find the approximate angle between the hands of a clock on Oz when the time is 12:40 am.

[1] 111

[2] 89

[3] 251

[4] 71

20

The pacelength P is the distance between the rear of two consecutive footprints. For men, the formula, n/P = 144 gives an approximate relationship between n and P where, n= number of steps per minute and P = pacelength in meters. Bernard knows his pacelength is 164cm. The formula applies to Bernard's walking. Calculate Bernard's walkingspeed in kmph.

[1] 8.78

[2] 236.16

[3] 23.24

[4] 14.16

21

Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. Thegoal is to bring the gold coin to the top by repeatedly moving the topmost coin to another position in the stack. Alice starts and the players take turns. A turn consists of

oving the coin on the top to a position i below the top coin (0 i 20). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-movecannot be repeated; for example once a player makes a 2-move, on subsequent turns neither player can make a 2-move. If the gold coin happens to be on top when it's alayer's turn then the player wins the game. Initially, the gold coinis the third coin from the top. Then

[1] In order to win, Alice's first move can be a 0-move or a 1-move.

[2] In order to win, Alice's first move should be a 1-move.

[3] Alice has no winning strategy.

[4] In order to win, Alice's first move should be a 0-move.

22

36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36},


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{a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is

[1] 18

[2] 13

[3] 12

[4] 11

23

Ferrari S.p.A. is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsored drivers andanufactured race cars before moving into production of street-legal vehicles in 1947 as Ferrari S.p.A.. Throughout its history, the company has been noted for its continued

articipation in racing, especially in Formula One, where it has enjoyed great success. Rohit once bought a Ferrari. It could go 2 times as fast as Mohit's old Mercedes. If thespeed of Mohit's Mercedes is 32 km/hr and the distance travelled by the Ferrari is 952 km, find the total time taken in hours for Rohit to drive that distance.

[1] 14.88

[2] 15.88

[3] 476

[4] 29.75

24

Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is

[1] 1

[2] 4

[3] 3

[4] 0

25

A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

[1] 32

[2] 64

[3] 48

[4] 96

26

Two bowls are taken, one contains water and another contains tea. One spoon of water is added to second bowl and mixed well, and a spoon of mixture is taken from secondowl and added to the first bowl. Which statement will hold good for the above?

[1] Second liquid in first bowl is less than the first mixture in second bowl

[2] Second liquid in first bowl is more than the first mixture in second bowl

[3] Second liquid in first bowl is equal to the first mixture in second bowl

[4] none of these

27

A die is rolled and a coin is tossed. Find the probability that the die shows an odd number and the coin shows a head.

[1]

[2] 1/2

[3] 3/4

[4] 2/3

28

Rearrange and categorize the word 'RAPETEKA'?

[1] vehicle

[2] bird

[3] person

[4] city

29

A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise has covered1/5 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so aso tie the race?

[1] 40

[2] 5

[3] 8


5/12

[4] 37.80

30

There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160 .. in tank B. (Athe end of first hour, B has 10 litres, second hour it has 20, and so on). If 1/32 of B's volume is filled after 3 hours, what is the total duration required to fill it completely?

[1] 7 hours

[2] 10 hours

[3] 9 hours

[4] 8 hours

31

A sheet of paper has statements numbered from 1 to 30. For all values of n from 1 to 30, statement n says "At most n of the statements on this sheet are false". Whichstatements are true and which are false?

[1] All statements are true.

[2] The odd numbered statements are true and the even numbered are false.

[3] All statements are false.

[4] The even numbered statements are true and the odd numbered are false.

32

A hunter leaves his cabin early in the morning and walks one mile due south. Here he sees a bear and starts chasing it for one mile due east before he is able to shoot the bear.After shooting the bear, he drags it one mile due north back to his cabin where he started that morning. What color is the bear?

[1] Brown

[2] Black

[3] Grey

[4] White

33

One day Rapunzel meets Dwarf and Byte in the Forest of forgetfulness. She knows that Dwarf lies on Mondays, Tuesdays and Wednesdays, and tells the truth on the otherdays of the week. Byte, on the other hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the week. Now they make the following statementso RapunzelDwarf: Yesterday was one of those days when I lie. Byte: Yesterday was one of those days when I lie too. What day is it?

[1] Thursday

[2] Tuesday

[3] Sunday

[4] Monday

34

10 people meet and shake hands. The maximum number of handshakes possible if there is to be no "cycle" of handshakes is (A cycle of handshakes is a sequence of k peoplea1, a2, ......, ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, ......, {ak-1, ak}, {ak, a1} shake hands).

[1] 6

[2] 7

[3] 8

[4] 9

35

For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paulicks A with the same probability as A's chances of winning. Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger teamas a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?

[1] 5/9

[2] 4/9

[3] 1/9

[4] 2/3

1

e IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to leadway in products and services in India. At Ti rnop, all programmers are equal in every respect. They receive identical salaries ans also write code at the same

e.Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How long will it take 72 programmers to write 72 lines of code in total?


6/12

)6)72)18)12

planation:

of people time work

12 12

x 72

rk = No of people * time

( P1 * T1 ) / W1 = ( P2 * T2 ) / W2

* 12 ) / 12 = ( 72 * x ) / 72

12.

2

ollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 4 faces of the outer surface of the cube are painted, totally howny faces of the smaller cubes remain unpainted?

)800)500)900)488

planation: The outside of the large cube = 5cm

e inside space = 3cm

al number of small cubes = (5*5*5) - (3*3*3) = 125 - 27 = 98

al number of faces = 98 * 6 = 588

w surface area of 4 faces = 4 * 5*5 = 100 cm^2

subtract 100 cubes as they have surface area 1cm^2 each

unpainted faces of cubes = 588 - 100 = 488

3

suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects are made to stand in a line and each personclares that the person next to him on his right is guilty. The rightmost person is not questioned. Which of the following possibilities are true?All suspects are lying or the leftmost suspect is innocent.All suspects are lying and the leftmost suspect is innocent .

)A only)Both A and B)Neither A nor B)B only

planation: considering

suspects are lying........S1

leftmost suspect is innocent......S2

h S1 and S2 cannot be true so it is S1 OR S2.

4

k is attending a workshop "How to do more with less" and today's theme is Working with fewer digits . The speakers discuss how a lot of miraculous mathematics canachieved if mankind (as well as womankind) had only worked with fewer digits. The problem posed at the end of the workshop is How many 5 digit numbers can bemed using the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4? Can you help Alok find the answer?

)3125)625)375)500

planation: Since each desired number is divisible by 4, So we must have 12,24,42,44,52 at the last two digits.

place can be filled by any of the remaining 5 numbers.

there are 5 ways of filling the 1st digits place.

milar 2nd digits and 3rd each digit place can be filled in 5 ways.

erefore Required number of numbers = 5*5*5*5=625.

5

e citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 8) buildingsmbered 1 to 1000. How many 3s are used in numbering these buildings?

)256)54)192)300

planation: Number of THREES between 1-100 ... 16

mber of THREES between 101-200...16

mber of THREES between 201-300....17

mbers of THREES between 301-400... 16+63

milarly number of THREES from 401 - 1000 ... 16* 4

erefore Total numbers of THREES = 192


7/12

6

k and Bhanu play the following min-max game. Given the expression N = 9 + X + Y - Z where X, Y and Z are variables representing single digits (0 to 9), Alok would to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X,r Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both playheir optimal strategies, the value of N at the end of the game would be

)9)18)20)27

planation: Considering equation: N = 9+X+Y-Z.

imum value of N: 9+ X+Y-Z = 18[considering X = Y = Z = 9]

ximum value of N: 9+X+Y-Z = 27 [considering Y = X=9, Z=0]

Alok and Bhanu tries to max and min the number N value and its value lies between 18 and 27.

Answer is 20.

7

heet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40, statement n says: 'Exactly n of the statements on this sheet are false.' Whichtements are true and which are false?

)All the statements are false.)The 39th statement is true and the rest are false)The odd numbered statements are true and the even numbered statements are false. )The even numbered statements are true and the odd numbered statements are false.

planation: 3rd and 4th option does not satisfies the given condition and all the statement cannot be false.

option The 39th statement is true and the rest are false is answer

8

ircular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probabilityt Q is closer to the center of the circle than the periphery?

)0.75)0.5)0.25)1

planation: Let the sample space area be pi* r^2 => pi , considering r = 1m

d Event space area = pi/4, considering r= 1/2 m

the probability = (pi/4)/pi = 0.25

9planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny plantoids called echina start growing on the rocks. echina grows inform of a circle and the relationship between the diameter of this circle and the age of echina is given by the formula4 * (t - 8) for t 8

ere d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 8mm. Howny years back did the solar blast occur?

)8)16)12)24

planation: d = 4 * sqrt(t-8)

16 as r= 8

en thus 16 = 4 * sqrt(t-8)

sqrt (t-8)

= 16

24

10

er the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability thatactly 1 letter is inserted in an improper envelope?

)12/(12^12))0)11/12)1/12

planation: It cannot be exactly 1 as we need a minimum of two letters to be in improper envelope.

11

e IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to leadway in products and services in India. At Ti rnop, all programmers are equal in every respect. They receive identical salaries ans also write code at the same

e.Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How many programmers required to write 72 lines of code in total in 72 minutes?

)18)12)72)6


8/12

planation:

of people time work

12 12

72 72


( P1 * T1 ) / W1 = ( P2 * T2 ) / W2

* 12)/12 = ( X * 72 )/ 72

12

12

heet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says "At least n of the statements on this sheet are true." Whichtements are true and which are false?

)The odd numbered statements are true and the even numbered are false)The even numbered statements are true and the odd numbered are false.)The first 13 statements are true and the rest are false.)The first 26 statements are false and the rest are true.

13

ere are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you chooseox at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is

)14/19)37/38

)1/2)3/4

planation: Considering 10 red in 1st box and 10 green in 2nd box

bability of picking red = 1/2 * 1 + 1/2 * 0 = 1/2

w consider the other case, 9 red balls are transferred to green ball box.

w total balls in 2nd box will be 19.

al probability = probability to select 1st box + probability to select 2nd box

/2)*(1C1/1C1)+(1/2)*(9C1/19C1)

1/2)*(1+9/19)

1/2)*(28/19)

4/19

14

k and Bhanu play the following min-max game. Given the expression N = 12 + X*(Y - Z) where X, Y and Z are variables representing single digits (0 to 9), Alok would to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X,r Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both playheir optimal strategies, the value of N at the end of the game would be

)12)-69)93)30

planation: As Alok tries to maximize the number it can not be negative value,

option B is false.

imum value: 12+ X(Y-Z) = 12 [considering Y = Z = 9]

ximum value: 12+X(Y-Z) = 93 [considering Y = X=9, Z=0]

Alok and Bhanu tries to max and min the number N value must lies between 12 and 93.

15

net fourfi resides in 4-dimensional space and thus the currency used by its residents are 3-dimensional objects. The rupee notes are cubical in shape while their coins

spherical. However the coin minting machinery lays out some stipulations on the size of the coins.he diameter of the coins should be at least 64mm and not exceed 512mm.iven a coin, the diameter of the next larger coin is at least 50% greater.he diameter of the coin must always be an integer.u are asked to design a set of coins of different diameters with these requirements and your goal is to design as many coins as possible. How many coins can yousign?

)8)9)5)6

planation: 1st coin is of 64mm diameter

d coin is of 64+32 = 96mm

coin is of 96 + 48 = 144mm

coin is of 144+ 72 = 216mm

coin is of 216+108 = 324mm

coin is of 324+ 162= 486

coin no wards diameter > 512mm So, ans is 6

16

oop managed to draw 7 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each


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ddle circle touches two circles on either side. Find the ratio of the radius of the circles to the side of the square.

)1:(2+ 62))1:(4+ 73))(2+ 72):1)1:(2+ 72)

planation: The extreme circles will have radius perpendicular to sides of square so the part of diagonal till the centre of circle will be sqrt(2) * r and remaining portion is r , 5 more

cles will contribute 10r and last circle will contribute r + sqrt(2) * r .

ngth of diagonal = 12r + 2sqrt (2) r = sqrt (2) * s where s -> side of square.

ratio of r:s = 1/( 2 + 6 * sqrt(2)) = 1: [ 2+ 6 sqrt(2)]

17

e teacher is testing a student's proficiency in arithmetic and poses the following question. 1/3 of a number is 3 more than 1/6 of the same number. What is thember? Can you help the student f ind the answer?

)18)21)12)6

planation: Let the number be X

3)X = 3+ (1/6)X

6) X = 3

18

18e IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to leadway in products and services in India. At Ti rnop, all programmers are equal in every respect. They receive identical salaries ans also write code at the same

e.Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How many lines of code can be written by 72 programmers in 72 minutes?

)12)72)432)6

planation:

of people time work

12 12

72 x


* 12) /12 = ( 72 * 72 ) / x

( P1 * T1 ) / W1 = ( P2 * T2 ) / W272 * 72 / 12 = 432.

19

the planet Oz, there are 8 days in a week- Sunday to Saturday and another day called Oz day. There are 36 hours in a day and each hour has 90 min while eachnute has 60 sec. As on earth, the hour hand covers the dial twice every day. Find the approximate angle between the hands of a clock on Oz when the time is 12:40.

)111)89)251)71

planation: Angle traced by hour hand in 12.40 hrs = (360/18) * ( 112/9) = 2240/9.

gle traced by minute hand in 40 min = (360/90) * 40 = 160.

gle between hour hand and minute hand = (2240/9) - 160 = 88.88.

proximately 89 degrees.

20

e pacelength P is the distance between the rear of two consecutive footprints. For men, the formula, n/P = 144 gives an approximate relationship between n and Pere, n = number of steps per minute and P = pacelength in meters. Bernard knows his pacelength is 164cm. The formula applies to Bernard's walking. Calculaternard's walking speed in kmph.

)8.78)236.16)23.24)14.16

planation: n/P = 144 gives an approximate relationship between n and P where, n = number of steps per minute and P = pacelength in meters. Bernard knows his pacelength is

4cm.

mber of steps in one minute = 144*1.64

tance travelled in 1 minute = 144*1.64*1.64 mtrs

tance travelled in one hr = 144*1.64*1.64*60/1000 km = 23.24 km

21

ce and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins.


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e goal is to bring the gold coin to the top by repeatedly moving the topmost coin to another position in the stack. Alice starts and the players take turns. A turn consistsmoving the coin on the top to a position i below the top coin (0 i 20). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-movennot be repeated; for example once a player makes a 2-move, on subsequent turns neither player can make a 2-move. If the gold coin happens to be on top when it'slayer's turn then the player wins the game. Initially, the gold coinis the third coin from the top. Then

)In order to win, Alice's first move can be a 0-move or a 1-move.)In order to win, Alice's first move should be a 1-move.)Alice has no winning strategy.)In order to win, Alice's first move should be a 0-move.

planation: Number of coins on top of the Gold coin remains same with the Alice's first move i.e 0-move or 1-move.

nce Options [1],[2] and [3] cannot be true.answer [3]

22

people {a1, a2, ..., a36} meet and shake hands in a ci rcular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35,6}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is

)18)13)12)11

planation: Take a2 in the set now a1 and a3 have shaken hands with him.

has not so we take a5 in the set thus a4 and a6 have shaken hands with the set

a7 has not so we take a8...

s we leave a gap of two people and select the third person in the set.

answer is 36/3 = 12

23

rrari S.p.A. is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsored drivers andnufactured race cars before moving into production of street-legal vehicles in 1947 as Ferrari S.p.A.. Throughout its history, the company has been noted for its

ntinued participation in racing, especially in Formula One, where it has enjoyed great success. Rohit once bought a Ferrari. It could go 2 times as fast as Mohit's oldrcedes. If the speed of Mohit's Mercedes is 32 km/hr and the distance travelled by the Ferrari is 952 km, f ind the total time taken in hours for Rohit to drive thattance.

)14.88)15.88)476)29.75

planation: Time = (Distance/Speed) = (952/32)

erefore the total time = time = (952/32)/2 = 14.88

24

ven 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is

)1)4)3)0

planation: Only incenter point is equidistant from all sides

25

ox contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

)32)64)48)96

planation:

26

o bowls are taken, one contains water and another contains tea. One spoon of water is added to second bowl and mixed well, and a spoon of mixture is taken fromcond bowl and added to the first bowl. Which statement will hold good for the above?

)Second liquid in first bowl is less than the first mixture in second bowl)Second liquid in first bowl is more than the first mixture in second bowl)Second liquid in first bowl is equal to the first mixture in second bowl)none of these


11/12

27

ie is rolled and a coin is tossed. Find the probability that the die shows an odd number and the coin shows a head.

))1/2)3/4)2/3

planation: The sample space S of the experiment described in question 5 is as follows

{ (1,H),(2,H),(3,H),(4,H),(5,H),(6,H)T),(2,T),(3,T),(4,T),(5,T),(6,T)}

E be the event "the die shows an odd number and the coin shows a head". Event E may be described as follows

{(1,H),(3,H),(5,H)}

e probability P(E) is given by

E) = n(E) / n(S) = 3 / 12 = 1 / 4

28

arrange and categorize the word 'RAPETEKA'?

)vehicle)bird)person)city

planation:

akeet -bird

29

are and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise hasvered 1/5 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increasespeed so as to tie the race?

)40)5)8)37.80

planation: After tortoise covers 1/5th distance hare starts the race

en hare covers 1/8th of distance tortoise meets hare

distance covered by tortoise = 1-(1/5 + 1/8) = 27/40

me taken by both is same time = dist/speed

(dist/ speed) of tortoise = (dist / speed) of hare

speed of tortoise be t and of hare be h 27/40t = 1/8h

(40/(8*27) )* t = 5/27 * t

w for the next part hare has to cover 7/8 th distance when tortoise covers 1/8 th distance

we get 1/8t = 7/8h h = 7t

the factor by which h's speed increases = 7t/ (5/27 * t) which we get as 37.8

30

ere are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160 .. in tank B.the end of fi rst hour, B has 10 litres, second hour it has 20, and so on). If 1/32 of B's volume is filled after 3 hours, what is the total duration required to fill it

mpletely?

)7 hours)10 hours)9 hours)8 hours

planation: Bs volume after 4 hours 1/16

volume after 5 hours 1/8

volume after 6 hours

volume after 7 hours

tank will be filled in 8 hour

31

heet of paper has statements numbered from 1 to 30. For all values of n from 1 to 30, statement n says "At most n of the statements on this sheet are false". Whichtements are true and which are false?

)All statements are true.)The odd numbered statements are true and the even numbered are false.)All statements are false.)The even numbered statements are true and the odd numbered are false.

32

unter leaves his cabin early in the morning and walks one mile due south. Here he sees a bear and starts chasing it for one mile due east before he is able to shootbear. After shooting the bear, he drags it one mile due north back to his cabin where he started that morning. What color is the bear?


12/12

)Brown)Black)Grey)White

planation: Only white bears leaves in south and north pole

33

e day Rapunzel meets Dwarf and Byte in the Forest of forgetfulness. She knows that Dwarf lies on Mondays, Tuesdays and Wednesdays, and tells the truth on the

er days of the week. Byte, on the other hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the week. Now they make the followingtements to Rapunzel Dwarf: Yesterday was one of those days when I lie. Byte: Yesterday was one of those days when I lie too. What day is it?

)Thursday)Tuesday)Sunday)Monday

34

people meet and shake hands. The maximum number of handshakes possible if there is to be no "cycle" of handshakes is (A cycle of handshakes is a sequence of kople a1, a2, ......, ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, ......, {ak-1, ak}, {ak, a1} shake hands).

)6)7)8)9

planation: The maximum possible non cyclic handshakes are

,a2),(a2,a3),(a3,a4),(a4,a5),(a5,a6),(a6,a7),(a7,a8),(a8,a10),(a10,a9) i.e 9

35

r the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Pawith the same probability as A's chances of winning. Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team hasbability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?

)5/9)4/9)1/9)2/3

planation: Paul picks A with the same probability as Aschances of winning

probability of picking a winner = prob picking of ghana * ghana winning + prob picking of bolivia * bollivia winning

/3 * 2/3 + 1/3 * 1/3

/9

tcs sample test

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