mec placement
Company Name: TCS
Type: Fresher Job Interview
Type: Fresher Job Interview
1. Given a collection of points P in the plane , a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (.i.e no three points in P lie on a line) is
(a) 3
(b) 5
(c) 2
Ans. Will be same as no of points in the plane, IE 5
(a) 3
(b) 5
(c) 2
Ans. Will be same as no of points in the plane, IE 5
2. How many four digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4?
Can you help Alok find the answer?
(a) 100
(b) 125
(c) 75
(d) 85
Ans. 5^n-1= 5^4-1=125, n= no of digits
Can you help Alok find the answer?
(a) 100
(b) 125
(c) 75
(d) 85
Ans. 5^n-1= 5^4-1=125, n= no of digits
3. On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4* (t-9) for t ≥ 9
Where 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 12mm. How many years back did the solar blast occur?
(a) 17
(b) 21.25
(c) 12
(d) 12.06
Ans. c
Where 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 12mm. How many years back did the solar blast occur?
(a) 17
(b) 21.25
(c) 12
(d) 12.06
Ans. c
4. 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 and manufactured race cars before moving into production of street-legal vehicles in 1947 as Feraari S.P.A. Throughout its history, the company has been noted for its continued participation in racing, especially in Formula One where it has employed great success. Rohit once bought a Ferrari . It could go 4 times as fast as Mohan's old Mercedes. If the speed of Mohan's Mercedes is 46 km/hr and the distance traveled by the Ferrari is 953 km, find the total time taken for Rohit to drive that distance.
(a) 20.72
(b) 5.18
(c) 238.25
(d) 6.18
Ans. b
(a) 20.72
(b) 5.18
(c) 238.25
(d) 6.18
Ans. b
5. A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says 'At least n of the statements on this sheet are false.' Which statements are true and which are false?
(a) The even numbered statements are true and the odd numbered are false.
(b) The odd numbered statements are true and the even numbered are false.
(c) The first 35 statements are true and the last 35 are false.
(d) The first 35 statements are false and the last 35 are false.
Ans. c
Note: For this type of Questions, follow this:
At least- Ist half are true, Last half are false
Exactly- Last second one is true or (N-1)th Statement is true
Almost- All are true.
(a) The even numbered statements are true and the odd numbered are false.
(b) The odd numbered statements are true and the even numbered are false.
(c) The first 35 statements are true and the last 35 are false.
(d) The first 35 statements are false and the last 35 are false.
Ans. c
Note: For this type of Questions, follow this:
At least- Ist half are true, Last half are false
Exactly- Last second one is true or (N-1)th Statement is true
Almost- All are true.
6. There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B. (At the end of first hour, B has 10 liters, second hour it has 20, and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?
(a) 26 hrs
(b) 25 hrs
(c) 5 hrs
(d) 27 hrs
Ans. a
(a) 26 hrs
(b) 25 hrs
(c) 5 hrs
(d) 27 hrs
Ans. a
7. There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80, 160... in tank B. (At the end of first hour, B has 10 liters , second hour it has 20, and so on). If tank B is 1/16 filled after 4 hours, what is the total duration required to fill it completely?
(a) 8hrs
(b) 25 hrs
(c) 5 hrs
(d) 27 hrs
Ans. a
(a) 8hrs
(b) 25 hrs
(c) 5 hrs
(d) 27 hrs
Ans. a
8. Unnecessary data. A lady has fine gloves and hats in her closet- 18 blue- 32 red , 10 white , 25 yellow, 55 purple, 30 orange. The lights are out and it is totally dark inspite of the darkness. She can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color of blue, red, yellow?
(a) 59
(b) 8
(c) 50
(d) 42
Ans. a(32+25+2)
Note: For this type of questions:
Bigger+Middle+1 (Suppose 18, 32, 25 =32+25+1), If you do not find answer in options, choose the one closer tho the answer you got.
(a) 59
(b) 8
(c) 50
(d) 42
Ans. a(32+25+2)
Note: For this type of questions:
Bigger+Middle+1 (Suppose 18, 32, 25 =32+25+1), If you do not find answer in options, choose the one closer tho the answer you got.
9. 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 the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries and 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?
(a) 6
(b) 18
(c) 72
(d) 12
Ans. d
Note: N1T1/W1=N2T2, W=No. of Lines, N=No. of PRGMRS, T=Time
(a) 6
(b) 18
(c) 72
(d) 12
Ans. d
Note: N1T1/W1=N2T2, W=No. of Lines, N=No. of PRGMRS, T=Time
10. The citizens of planet nigiet are 6 fingered and have thus developed their decimal system in base 6. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
(a) 256
(b) 54
(c) 192
(d) 108
Ans. d
Note: First find no. 3s in 1000 (Decimal only), Definately you will get 300, Now convert 300 into 300 base 6 by this 3*6^2+0*6^1+0*6^0
(a) 256
(b) 54
(c) 192
(d) 108
Ans. d
Note: First find no. 3s in 1000 (Decimal only), Definately you will get 300, Now convert 300 into 300 base 6 by this 3*6^2+0*6^1+0*6^0
11. 12 people {a1, a2, …, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a11, a12}, {a12, 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
(a) 12
(b) 4
(c) 18
(d) 11
Ans. B (N/3)
(a) 12
(b) 4
(c) 18
(d) 11
Ans. B (N/3)
12. Alice and Bob play the following coins-on-a-stack game. 100 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The 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 consists of moving the coin on the top to a position i below the top coin (0 = i = 100). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot 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 a player’s turn then the player wins the game.
A. Alice has no winning strategy.
B. Initially, the gold coins the third coin from the top. Then
C. In order to win, Alice’s first move should be a 0-move.
D. In order to win, Alice’s first move should be a 1-move.
Ans. D
Alice starts and the players take turns. A turn consists of moving the coin on the top to a position i below the top coin (0 = i = 100). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot 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 a player’s turn then the player wins the game.
A. Alice has no winning strategy.
B. Initially, the gold coins the third coin from the top. Then
C. In order to win, Alice’s first move should be a 0-move.
D. In order to win, Alice’s first move should be a 1-move.
Ans. D
13. 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.’ Which statements are true and which are false?
A. The even numbered statements are true and the odd numbered statements are false.
B. The last second statement is true and the rest are false.
C. The odd numbered statements are true and the even numbered statements are false.
D. All the statements are false.
A. The even numbered statements are true and the odd numbered statements are false.
B. The last second statement is true and the rest are false.
C. The odd numbered statements are true and the even numbered statements are false.
D. All the statements are false.
14. 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 people a1, a2, ……, ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, ……, {ak-1, ak}, {ak, a1} shake hands).
(a)7
(b) 6
(c) 9
(d) 8
Ans. c **(N-1)**
(a)7
(b) 6
(c) 9
(d) 8
Ans. c **(N-1)**
15. 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 1 letter is inserted in an improper envelope?
(a) 0
(b) 12/212
(c) 11/12
(d) 1/12
Ans. a
(a) 0
(b) 12/212
(c) 11/12
(d) 1/12
Ans. a
16. 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 that the 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.
B. leftmost suspect is innocent.
C. leftmost suspect is guilty
(a) A only
(b) A or C
(c) A or B
(d) B only
Ans. c
A. All suspects are lying.
B. leftmost suspect is innocent.
C. leftmost suspect is guilty
(a) A only
(b) A or C
(c) A or B
(d) B only
Ans. c
17. 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
(a) 4
(b) 3
(c) 0
(d) 1
Ans. a 3 lines are given so answer is 4 one incenter and 3 excenters. If it is 3 line segments then answer would be 1
(a) 4
(b) 3
(c) 0
(d) 1
Ans. a 3 lines are given so answer is 4 one incenter and 3 excenters. If it is 3 line segments then answer would be 1
18. Alok and Bhanu play the following min-max game. Given the expression N = 15 + 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, Y or 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 to their optimal strategies, the value of N at the end of the game would be
Ans. 15+18 =33
Note: For this type of questions:
x+y-z=11
x-y-z=2
x*(y+z)=18
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, Y or 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 to their optimal strategies, the value of N at the end of the game would be
Ans. 15+18 =33
Note: For this type of questions:
x+y-z=11
x-y-z=2
x*(y+z)=18
19. 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 covered 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 increase its speed so as the win the race? (for this values are changed)
(a) 8
(b) 5
(c) 37
(d) 80
Ans. c
(a) 8
(b) 5
(c) 37
(d) 80
Ans. c
20. A sheet of paper has statements numbered from 1 to 45. For all values of n from 1 to 45, statement n says “At most n of the statements on this sheet are false”. Which statements are true and which are false?
A. The odd numbered statements are true and the even numbered are false.
B. The even numbered statements are true and the odd numbered are false.
C. All statements are true.
Ans. c
A. The odd numbered statements are true and the even numbered are false.
B. The even numbered statements are true and the odd numbered are false.
C. All statements are true.
Ans. c
21. 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 1face of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?
(a) 900
(b) 488
(c) 563
(d) 800
Ans. c
Note: ** 588-(25* No. of painted faces)
(a) 900
(b) 488
(c) 563
(d) 800
Ans. c
Note: ** 588-(25* No. of painted faces)
22. 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 the way 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 many lines of code can be written by 72 programmers in 72 minutes?
(a) 72
(b) 432
(c) 12
(d) 144
Ans. b
(a) 72
(b) 432
(c) 12
(d) 144
Ans. b
23. 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? Can you help the student find the answer?
(a) 12
(b) 18
(c) 6
(d) 21
Ans. b
Note: Alok and Bhanu play the following min-max game. Given the expression N = X – Y – Z
(a) 12
(b) 18
(c) 6
(d) 21
Ans. b
Note: Alok and Bhanu play the following min-max game. Given the expression N = X – Y – Z
24. 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, Y or 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 to their optimal strategies, the value of N at the end of the game would be
(a) 2
(b) 4
(c) 9
(d) -18
Ans. a
(a) 2
(b) 4
(c) 9
(d) -18
Ans. a
25. Horse started to chase dog as it relieved stable two hrs ago. And horse started to ran with average speed 22km/hr, horse crossed 10 mts road and two small pounds with depth 3m, and it crossed two small street with 200 mts length. After traveling 6 hrs, 2hrs after sunset it got dog. compute the speed of dog?
Ans. As we have speed and travel time of horse, we can get distance traveled by it.
Note: Hence d = 22*6 = 132km,
Exactly this 132km was traveled by dog in 8 hours (as it started two hours earlier).
Hence speed of dog = 132/8 = 16.5km/hr
Ans. 16.5km/hr.
Ans. As we have speed and travel time of horse, we can get distance traveled by it.
Note: Hence d = 22*6 = 132km,
Exactly this 132km was traveled by dog in 8 hours (as it started two hours earlier).
Hence speed of dog = 132/8 = 16.5km/hr
Ans. 16.5km/hr.
26. A and B play a game between them. The dice consist of colors on their faces (instead of number). When the dice are thrown, A wins if both show the same color, otherwise B wins. One die has 3 red faces and 3 blue faces. How many red and blue faces should the other die have if the both players have if the both players have the same chances of winning?
(a) 5 red and 1 blue faces.
(b) 1 red and 5 blue faces.
(c) 3 red and 3 blue faces.
Ans. c
(a) 5 red and 1 blue faces.
(b) 1 red and 5 blue faces.
(c) 3 red and 3 blue faces.
Ans. c
27. In planet OZ planet there are 8 days, Sunday to Saturday and 8th day is Oz day. There is 36 hours in a day. What is angle between 12.40?
(a) 80
(b) 81
(c) 87
(d) 89
Ans. 89
(a) 80
(b) 81
(c) 87
(d) 89
Ans. 89
Exam/Interview Date : 19-Dec-2010
Rajalakshmi Engineering College, Chennai
1) 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 and manufactured race cars before moving into production of street-legal vehicles in 1947 as Feraari S.P.A. Throughout its history, the company has been noted for its continued participation in racing, especially in Formula One where it has employed great success. Rohit once bought a Ferrari. It could go 4 times as fast as Mohan's old Mercedes. If the speed of Mohan's Mercedes is 46 km/hr and the distance traveled by the Ferrari is 953 km, find the total time taken for Rohit to drive that distance.
a) 20.72 b) 5.18 c) 238.25 d) 6.18
Ans: b
2) A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says 'At least n of the statements on this sheet are false.' Which statements are true and which are false?
a) The even numbered statements are true and the odd numbered are false.
b) The odd numbered statements are true and the even numbered are false.
c) The first 35 statements are true and the last 35 are false.
d) The first 35 statements are false and the last 35 are false.
Ans: c
3 questions of same type stating at most, exactly
3) 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. (At the end of first hour, B has 10 litres, second hour it has 20, and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?
a) 26 hrs b) 25 hrs c) 5 hrs d) 27 hrs
Ans: a
4) 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 that the person next to him on his right is guilty. The rightmost person is not questioned. Which of the following possibilities are true?
4) 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 that the 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
B. leftmost suspect is innocent
C. leftmost suspect is guilty
a) A only b) A or C c) A or B d) B only
Ans: c
5) Alok and Bhanu play the following min-max game. Given the expression
5) Alok and Bhanu play the following min-max game. Given the expression
N = 15 + 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, Y or 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 to their optimal strategies, the value of N at the end of the game would be
Ans: 15+18 =33
3 questions of the same type with different equations for N
6) 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 1face of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?
a) 900 b) 488 c) 563 d) 800
Ans: c
7) In planet OZ planet there are 8 days, sunday to saturday and 8th day is Oz day. There is 36 hours in a day. What is angle between 12.40?
8) Horse started to chase dog as it relieved stable two hrs ago. And horse started to ran with average speed 22km/hr, horse crossed 10 mts road and two small pounds with depth 3m, and it crossed two small street with 200 mts length. After traveling 6 hrs, 2hrs after sunset it got dog. compute the speed of dog?
7) In planet OZ planet there are 8 days, sunday to saturday and 8th day is Oz day. There is 36 hours in a day. What is angle between 12.40?
8) Horse started to chase dog as it relieved stable two hrs ago. And horse started to ran with average speed 22km/hr, horse crossed 10 mts road and two small pounds with depth 3m, and it crossed two small street with 200 mts length. After traveling 6 hrs, 2hrs after sunset it got dog. compute the speed of dog?
Ans: As we have speed and travel time of horse, we can get distance travelled by it.
Hence d = 22*6 = 132km,
Hence d = 22*6 = 132km,
Exactly this 132km was travelled by dog in 8 hours (as it started two hours earlier).
Hence speed of dog = 132/8 = 16.5km/hrAns: 16.5km/hr.
Values are also changed in some types
9) 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 the way 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?
Hence speed of dog = 132/8 = 16.5km/hrAns: 16.5km/hr.
Values are also changed in some types
9) 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 the way 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?
a) 6 b) 18 c) 72 d) 12
10) Middle – earth is a fictional land inhabited by Hobbits, Elves, dwarves and men. The Hobbits and the Elves are peaceful creatures who prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage in physical games. The game is as follows . A tournol is one where out of the two teams that play a match, the one that loses get eliminated. The matches are played in different rounds where in every round, half of the teams get eliminated from the tournament. If there are 8 rounds played in a knock-out tournol how many matches were played?
a) 257 b) 256 c) 72 d) 255
11) 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 1 letter is inserted in an improper envelope?
a) 0 b) 12/212 c) 11/12 d) 1/12
Ans: a
12) The citizens of planet nigiet are 6 fingered and have thus developed their decimal system in base 6. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
12) The citizens of planet nigiet are 6 fingered and have thus developed their decimal system in base 6. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
a) 256 b) 54 c) 192 d) 108
Ans: d
13) A and B play a game between them. The dice consist of colors on their faces(instead of number). When the dice are thrown, A wins if both show the same color, otherwise B wins. One die has 3 red faces and 3 blue faces. How many red and blue faces should the other die have if the both players have if the both players have the same chances of winning?
a) 5 red and 1 blue faces.
b) 1 red and 5 blue faces.
c) 3 red and 3 blue faces.
Ans: c
14) 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, Paul picks 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 team has 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?
a) 5/9
b) 1/9
c) 2/3
d) 1/3 (For this question they changed the values)
15) A manufacturer undertakes to supply 2000 pieces of a particular component at Rs.25 per piece. According to his estimates, even if 5% fail to pass the quality tests, then he will make a profit of 25%. However, as it turned out, 50% of the components were rejected. What is the loss to the manufacturer?
14) 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, Paul picks 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 team has 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?
a) 5/9
b) 1/9
c) 2/3
d) 1/3 (For this question they changed the values)
15) A manufacturer undertakes to supply 2000 pieces of a particular component at Rs.25 per piece. According to his estimates, even if 5% fail to pass the quality tests, then he will make a profit of 25%. However, as it turned out, 50% of the components were rejected. What is the loss to the manufacturer?
(a) Rs.12000 (b) Rs.13000 (c) Rs.14000 (d) Rs.15000
16) 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
a) 1 b) 0 c) 4 d) 2
a) 1 b) 0 c) 4 d) 2
17) Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 7 points in the plane in general position(.i.e no three points in P lie on a line) is
a) 3 b) 7 c) 2 d) 1
Ans: 7
a) 3 b) 7 c) 2 d) 1
Ans: 7
18) 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 people a1, a2, ……, ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, ……, {ak-1, ak}, {ak, a1} shake hands).
a) 7 b) 6 c) 9 d) 8
Ans: c
Velammal Engineering College, Chennai
1. 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 the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries and 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?
( I got this ques 3 times with values changed)
( I got this ques 3 times with values changed)
2. Alok and Bhanu play the following min-max game. Given the expression N = 24 + 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, Y or 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 to their optimal strategies, the value of N at the end of the game would be(i got this ques 2 times with equations changed)
Ans: 35
Ans: 35
3. 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." Which statements are true and which are false?
a) All statements are false
b) The odd numbered statements are true the even numbered are false
c) All statements are true
d) The even numbered statements are true and the odd numbered are false
(like this i got another ques with stmts numbered from 1 to 10)
a) All statements are false
b) The odd numbered statements are true the even numbered are false
c) All statements are true
d) The even numbered statements are true and the odd numbered are false
(like this i got another ques with stmts numbered from 1 to 10)
4. The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 100 (in base 8) buildings numbered 1 to 100. How many 3s are used in numbering these buildings and give the answer in base 10 system? (my friends got same ques with give the ans in base 7, base 6, base 5etc)
5. A result of global warming is that the ice of some glaciers is melting. Twelve years after the ice disappears tiny plants, called lichens, start to grow on the rocks. Each lichens grows approximately in the shape of a circle. The relationship between the diameter of this circle and the age of the lichen can be approximated with the formula
d = 13 * (t-11) for t > 11 where d represents the diameter of the lichen in millimeters, and t represents the number of years after the ice disappeared. Using the above formula, calculate the diameter of the lichen, 36 years after the ice has disappeared.
a) 468 mm b) 457 mm c) 325 mm d) 11 mm
a) 468 mm b) 457 mm c) 325 mm d) 11 mm
6. 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 probability that Q is closer to the center of the circle than the periphery?
a) 1/4 b) 1/2 c)3/4 d) 1/3
a) 1/4 b) 1/2 c)3/4 d) 1/3
7. After the typist writes 25 letters and addresses 25 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?
a) 11/12 b) 0 c) 1/12 d) 1/6
a) 11/12 b) 0 c) 1/12 d) 1/6
8. 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 be achieved 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 formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4? Can you help Alok find the answer?
a) 375 b) 625 c) 500 d) 3125
a) 375 b) 625 c) 500 d) 3125
7. 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
a) 1 b) 0 c) 4 d) 2
a) 1 b) 0 c) 4 d) 2
(For this question they changed the value of third side but the ans for this type of question is always one)
8. 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 111cm. The formula applies to Bernard’s walking. Calculate Bernard’s walking speed kmph.
9. Alice and Bob play the following coins-on-a-stack game. 50 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The 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 consists of moving 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-move cannot 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 a player's turn then the player wins the game. Initially, the gold coinis the third coin from the top. Then
a) In order to win, Alice’s first move should be a 0-move.
b) In order to win, Alice’s first move should be a 1-move.
c) Alice has no winning strategy.
d) In order to win, Alice’s first move can be a 0-move or a 1-move
a) In order to win, Alice’s first move should be a 0-move.
b) In order to win, Alice’s first move should be a 1-move.
c) Alice has no winning strategy.
d) In order to win, Alice’s first move can be a 0-move or a 1-move
10. 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, Paul picks 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 team has 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?
a) 5/9
b) 1/9
c) 2/3
d) 1/3 (For this question they changed the values)
11. 33 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 33 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {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?
(ans is 11)
(ans is 11)
12. One 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 hours has 90 min while each minute has 60 sec. As on earth, hour hand covers the dial twice every day. Find the approximate angle between the hands of clock on Oz when time is 15.40 am?
13. Planet fourfi resides in 4 – dimensional space and thus the currency used by its residents are 3 – dimensional objects. The rupees notes are cubical in shape while their coins are spherical. However the coin minting machinery lays out some stipulations on the size of the coins.
The diameter of the coins should be at least 16mm and not exceed 64mm·
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?
The diameter of the coins should be at least 16mm and not exceed 64mm·
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?
14. A hare and tortoise 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 tortoise has covered 1/5 its distance and that 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 as to tie the race?
a) 8
b) 37.80
c) 40
d) 5 (For this question they changed the value 1/5 to 1/3 and 1/8 to 1/7)
a) 8
b) 37.80
c) 40
d) 5 (For this question they changed the value 1/5 to 1/3 and 1/8 to 1/7)
15. 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 middle circle touches two circles on either side. Find the ratio of the radius of the circles to the side of the square.
2)Öa) 1:(2 + 7
3)Öb) 1:(4 + 7
2):1Öc) (2 + 7
2) ( For me they changed 7 circles to 9 circles)Öd) 1:(2 + 6
2)Öa) 1:(2 + 7
3)Öb) 1:(4 + 7
2):1Öc) (2 + 7
2) ( For me they changed 7 circles to 9 circles)Öd) 1:(2 + 6
16. 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 and manufactured race cars before moving into production of street-legal vehicles in1947 as Ferrari S.p.A. Throughout its history the company has been noted for its continued 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 old Mercedes. If the speed 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.
17.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 box at random and a ball at random from the chosen box, the probability of getting a red is maximized. This maximum probability is
a) 37/38 b) 1 / 2 c) 14/19 d) 3 / 4 (values are changed for me. I think it is 23 red and 30 green)
a) 37/38 b) 1 / 2 c) 14/19 d) 3 / 4 (values are changed for me. I think it is 23 red and 30 green)
18. 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 that the 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
B) the leftmost suspect is guilty
C) rightmost suspect is guilty
a)A only
b)A and B
c)B only
d)A and C
A) All suspects are lying
B) the leftmost suspect is guilty
C) rightmost suspect is guilty
a)A only
b)A and B
c)B only
d)A and C
19. 1/3rd of the number is 3 more than 1/6th of the number, then find the number?
a) 24 b) 12 c) 18 d) 20
20. 21 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 people a1, a2, … , aK such that the pairs (a1, a2), (a2, a3),… , (a (k-1), a k) , (ak, a1) shake hands.
a) 17 b) 18 c) 19 d) 20
a) 24 b) 12 c) 18 d) 20
20. 21 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 people a1, a2, … , aK such that the pairs (a1, a2), (a2, a3),… , (a (k-1), a k) , (ak, a1) shake hands.
a) 17 b) 18 c) 19 d) 20
21. 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. (At the end of first hour, B has 10 liters, second hour it has 20, and so on) If tank B is 1/16 filled after 17 hours, what is the total durations required to fill it completely?
a) 4 hours b) 21 hours c) 22 hours d) 24 hours
a) 4 hours b) 21 hours c) 22 hours d) 24 hours
22. Middle-earth is a fictional land inhabited by hobbits, Elves, dwarves and men. The Hobbits and the Elves are peaceful creatures who prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage in physical games. The game is as follows. A tournoi is one, where out of two teams that play a match, the one that loses get eliminated. The matches are played in different rounds where in every round; half of the teams get eliminated from the tournament. If there are 6 rounds played in a knock-out tournoi how many matches were played?
If it is mathches then formula is 2^n-1
If it is players then it is 2^n
If it is players then it is 2^n
23. Given a collection of points P in the plane , a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 9 points in the plane in general position (.i.e no three points in P lie on a line) is
a) 7 b) 9 c) 8 d) 10
a) 7 b) 9 c) 8 d) 10
24. A lady has fine gloves and hats of different colours of hats in her closet-18 blue,32 red and 25 yellow.the lights are out and it is totally dark.In spite of thr ddarkness,she can make out of the difference which is hat and a glove.she takes an item out of the closet only if he sure that it is glove .how many gloves must she take out make sure that she has a pair of each color.
a)6 b)8 c)60 d)59 (For me they changed the values of blue,red and yellow colours)
a)6 b)8 c)60 d)59 (For me they changed the values of blue,red and yellow colours)
25. (There was a long story, I'll cut short it). There are 5 materials to make a perfume: Lilac, Balsalmic, Lemon, Woody and Mimosaic. To make a perfume that is in demand the following conditions are to be followed: Lilac and Balsalmic go together. Woody and Mimosaic go together, Woody and Balsalmic never go together. Lemon can be added with any material. (Actually they had also mentioned how much amount of one can be added with how much quantity of the other; but that's not needed for the question.) All of the following combinations are possible to make a perfume except:
(Like this model. But they changed the story by adding lemon, sweet etc and we have to find the option that gives ans for the impossible combination that is given in questions. Its a easy and logical type question)
26. One question like that there are 40 barreals are there and one is poisoned. If a drop is consumed he will die in 14 hrs then how many least mice are required to find the poisoned barreal?
26. One question like that there are 40 barreals are there and one is poisoned. If a drop is consumed he will die in 14 hrs then how many least mice are required to find the poisoned barreal?
P V P Siddhartha Institute, Vijayawada
1) (1/3) of a number is 6 more than the (1/6) of the same number?
a) 6 b) 18 c) 36 d) 24
2) There are two water tanks A and B, A is much smaller than B. While water fills at the rate of 1 liter every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B. 1/8 th of the tank B is filled in 22 hours. What is the time to fill the tank fully?
a) 26 B) 25 c) 5 d) 27
a) 6 b) 18 c) 36 d) 24
2) There are two water tanks A and B, A is much smaller than B. While water fills at the rate of 1 liter every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B. 1/8 th of the tank B is filled in 22 hours. What is the time to fill the tank fully?
a) 26 B) 25 c) 5 d) 27
3) 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 coverd 1/4 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 increse its speed so as to tie the race?
Ans: 35.00
Ans: 35.00
4) 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". Which statements are true and which are false?
This type of question repeated for me three time just replacing atmost with exactly, atleast.
This type of question repeated for me three time just replacing atmost with exactly, atleast.
7) On the planet Oz, there are 8 days in a week Sunday to Saturday and another day call Oz day. There are 36 hours in a day and each hour has 90 mins while each minute 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 10.40 am.
Ans: Aroung 59 degrees
Ans: Aroung 59 degrees
8) 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 buildings numbered 1 to 1000. How many 4's are used in numbering these buildings?Express your answer in base10?
Ans: 192
Ans: 192
9) A girl has to make pizza with different toppings. There are 8 different toppings. In how many ways can she make pizzas with 2 different toppings?
a) 16 b) 56 c) 112 d) 28
a) 16 b) 56 c) 112 d) 28
10) A car manufacturer produces only red and blue models which come out of the final testing area at random. What are the odds that five consecutive cars of same color will come through the test area at any one time?
a)1 in 16 b)1 in 125 c)1 in 32 d)1 in 25
a)1 in 16 b)1 in 125 c)1 in 32 d)1 in 25
11) A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color?
a) 50 b) 8 c) 60 d) 42
a) 50 b) 8 c) 60 d) 42
This type was repeated two times
14) Middle- earth is a fictional land inhabited by hobbits, elves, dwarves and men. The hobbits and elves are peaceful creatures that prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage in physical games. The game is as follows. A tournament is one where out of the two teams that play a match, the one that loses get eliminated. The matches are played in different rounds, where in every round; half of the teams get eliminated from the tournament. If there are 8 rounds played in knock out tournament, how many matches were played?
a) 257 b) 256 c) 72 d) 255
a) 257 b) 256 c) 72 d) 255
Ans)255
15)20 men handshake with each other without repetition. What is the total number of handshakes made?
a)190 b)210 c)150 d)250
16) Alok and Bhanu play the following min-max game. given the expression
N= 12+X*(Y-Z)
15)20 men handshake with each other without repetition. What is the total number of handshakes made?
a)190 b)210 c)150 d)250
16) Alok and Bhanu play the following min-max game. given the expression
N= 12+X*(Y-Z)
Where X, Y, Z are variables repersenting 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,Y,Z). Alok then chooses next value and Bhanu the variable to substitute the value finally Alok proposes the value for the remaining variable Assumig both play to their optimal strategies the value of N at the end or the game would be?
This type also repeated for three time with change of exp
Ans: Better go through the options given NEVER place 0 or 9 in the Expression
20) On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4*√ (t-9) for t ≥ 9 where 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 7mm. How many years back did the solar blast occur?
a) 17 b)21.25 c)12.25 d)14.05
21) 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 and manufactured 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 participation in racing, especially in Formula One where it has employed great success .Rohit once bought a Ferrari. It could go 4 times as fast as Mohan's old Mercedes. If the speed of Mohan's Mercedes is 35 km/hr and the distance traveled by the Ferrari is 490 km, find the total time taken for Rohit to drive that distance.
a) 20.72 b) 5.18 c) 238.25 d) 6.18
Ans) simple one you can slove it
22) How many 9 digit numbers are possible by using the digits 1,2,3,4,5 which are divisible by 4 if the repetition is allowed?
a) 5^7 b) 5^6 c) 5^9 d) 5^8
Ans: 5^8
23) Given a collection of points P in the plane , a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 11 points in the plane in general position (.i.e no three points in P lie on a line) is
a) 3 b) 11 c) 2 d) 8
24) In a family there are some boys and girls. All boys told that they are having equal no of brothers and sisters and girls told that they are having twice the no. of brothers than sisters. How many boys and girls present in a family?
Ans: 4 boys and 3 girls
Ans) simple one you can slove it
22) How many 9 digit numbers are possible by using the digits 1,2,3,4,5 which are divisible by 4 if the repetition is allowed?
a) 5^7 b) 5^6 c) 5^9 d) 5^8
Ans: 5^8
23) Given a collection of points P in the plane , a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 11 points in the plane in general position (.i.e no three points in P lie on a line) is
a) 3 b) 11 c) 2 d) 8
24) In a family there are some boys and girls. All boys told that they are having equal no of brothers and sisters and girls told that they are having twice the no. of brothers than sisters. How many boys and girls present in a family?
Ans: 4 boys and 3 girls
25) Alok and Bhanu play the following coins in a circle game. 99 coins are arranged in a circle with each coin touching two other coin. Two of the coins are special and the rest are ordinary. Alok starts and the players take turns removing an ordinary coin of their choice from the circle and bringing the other coins closer until they again form a (smaller) circle. The goal is to bring the special coins adjacentto each other and the first player to do so wins the game. Initially the special coins are separated by two ordinary coins O1 and O2. Which of the following is true?
a) In order to win, Alok should remove O1 on his first turn.
b) In order to win, Alok should remove one of the coins different from O1 and O2 on his first turn.
c) In order to win, Alok should remove O2 on his first turn.
d) Alok has no winning strategy.
b) In order to win, Alok should remove one of the coins different from O1 and O2 on his first turn.
c) In order to win, Alok should remove O2 on his first turn.
d) Alok has no winning strategy.
G.Pulla Reddy Engg College, Hyderabad
(Written Test: 35 questions 80 mins)
1) Given a collection of points P in the plane , a 1-set is a point in P that can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (.i.e no three points in P lie on a line) is
a) 3 b) 5 c) 2
2) How many four digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4?
Can you help Alok find the answer?
a) 100 b) 125 c) 75 d) 85
3) On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula
d = 4* (t-9) for t ≥ 9
Where 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 12mm. How many years back did the solar blast occur?
a) 17 b) 21.25 c) 12 d) 12.06
Ans: c
4) 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 and manufactured race cars before moving into production of street-legal vehicles in 1947 as Feraari S.P.A. Throughout its history, the company has been noted for its continued participation in racing, especially in Formula One where it has employed great success .Rohit once bought a Ferrari . It could go 4 times as fast as Mohan's old Mercedes. If the speed of Mohan's Mercedes is 46 km/hr and the distance traveled by the Ferrari is 953 km, find the total time taken for Rohit to drive that distance.
a) 20.72 b) 5.18 c) 238.25 d) 6.18
Ans: b
5) A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says ' At least n of the statements on this sheet are false. ' Which statements are true and which are false?
a) The even numbered statements are true and the odd numbered are false.
b) The odd numbered statements are true and the even numbered are false.
c) The first 35 statements are true and the last 35 are false.
d) The first 35 statements are false and the last 35 are false.
Ans: c
6) 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. (At the end of first hour, B has 10 litres, second hour it has 20, and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?
a) 26 hrs b) 25 hrs c) 5 hrs d) 27 hrs
Ans: a
7)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. (At the end of first hour, B has 10 litres , second hour it has 20, and so on). If tank B is 1/16 filled after 4 hours, what is the total duration required to fill it completely?
a) 8hrs b) 25 hrs c) 5 hrs d) 27 hrs
Ans: a
8) Unnecessary data. A lady has fine gloves and hats in her closet- 18 blue- 32 red , 10 white , 25 yellow, 55 purple, 30 orange. The lights are out and it is totally dark inspite of the darkness. She can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each colour of blue, red, yellow?
a) 59 b) 8 c) 50 d) 42
Ans: a(32+25+2)
9) 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 the way 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?
a) 6 b) 18 c) 72 d) 12
Ans: d (w1/w2=m1*t1/m2*T2)
10) The citizens of planet nigiet are 6 fingered and have thus developed their decimal system in base 6. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
a) 256 b) 54 c) 192 d) 108
Ans: d
11) 12 people {a1, a2, …, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a11, a12}, {a12, 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
a) 12 b) 4 c) 18 d) 11
Ans: B
12 ) Alice and Bob play the following coins-on-a-stack game. 100 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The 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 consists of moving the coin on the top to a position i below the top coin (0 = i = 100). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot 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 a player’s turn then the player wins the game.
A. Alice has no winning strategy.
B. Initially, the gold coinis the third coin from the top. Then
C. In order to win, Alice’s first move should be a 0-move.
D. In order to win, Alice’s first move should be a 1-move.
Ans: D
13) 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.’ Which statements are true and which are false?
A. The even numbered statements are true and the odd numbered statements are false.
B. The last second statement is true and the rest are false.
C. The odd numbered statements are true and the even numbered statements are false.
D. All the statements are false.
14) 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 people a1, a2, ……, ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, ……, {ak-1, ak}, {ak, a1} shake hands).
a)7 b) 6 c) 9 d) 8
Ans: c
15) 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 1 letter is inserted in an improper envelope?
a) 0 b) 12/212 c) 11/12 d) 1/12
Ans: a
16) 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 that the 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
B. leftmost suspect is innocent .
C. leftmost suspect is guilty
a) A only b) A or C c) A or B d) B only
Ans: c
17) 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
a) 4 b) 3 c) 0 d) 1
Ans: a 3 lines are given so ans is 4 one incenter and 3 excenters. If it is 3 line segments then ans would be 1
18) Alok and Bhanu play the following min-max game. Given the expression
N = 15 + 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, Y or 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 to their optimal strategies, the value of N at the end of the game would be
Ans: 15+18 =33
19) 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 covered 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 increase its speed so as the win the race?(for this values are changed)
a) 8 b) 5 c) 37 d) 80
Ans: c
20) A sheet of paper has statements numbered from 1 to 45. For all values of n from 1 to 45, statement n says “At most n of the statements on this sheet are false”. Which statements are true and which are false?
A. The odd numbered statements are true and the even numbered are false.
B. The even numbered statements are true and the odd numbered are false.
C. All statements are true.
Ans: c
21) 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 1face of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?
a) 900 b) 488 c) 563 d) 800
Ans: c
22) 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 the way 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 many lines of code can be written by 72 programmers in 72 minutes?
a) 72 b) 432 c) 12 d) 144
Ans: b
23) 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?Can you help the student find the answer?
a) 12 b) 18 c) 6 d) 21
Ans: b
Alok and Bhanu play the following min-max game. Given the expression
N = X – Y – Z
24) 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, Y or 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 to their optimal strategies, the value of N at the end of the game would be
a) 2 b) 4 c) 9 d) -18
Ans: a
25) Horse started to chase dog as it relieved stable two hrs ago. And horse started to ran with average speed 22km/hr, horse crossed 10 mts road and two small pounds with depth 3m, and it crossed two small street with 200 mts length. After traveling 6 hrs, 2hrs after sunset it got dog. compute the speed of dog?
Ans: As we have speed and travel time of horse, we can get distance travelled by it.
Hence d = 22*6 = 132km,
Exactly this 132km was travelled by dog in 8 hours (as it started two hours earlier).
Hence speed of dog = 132/8 = 16.5km/hr
Ans: 16.5km/hr.
26) A and B play a game between them. The dice consist of colors on their faces(instead of number). When the dice are thrown, A wins if both show the same color, otherwise B wins. One die has 3 red faces and 3 blue faces. How many red and blue faces should the other die have if the both players have if the both players have the same chances of winning?
a) 5 red and 1 blue faces.
b) 1 red and 5 blue faces.
c) 3 red and 3 blue faces.
Ans: c
27) In planet OZ planet there are 8 days, sunday to saturday and 8th day is Oz day. There is 36 hours in a day. What is angle between 12.40?
a) 80 b) 81 c) 87 d) 89
Ans: 89
The questions are like..
Q.1. The ticket for a journey is in the range of 1 to 63 paise. You have 63 paise in your pocket and so on. and the question is You have to change the money into coins and all denominations are available at final. You have to buy the ticket and you should have at least one coin? (not same figures)
Ans. 64 (Just add 1 to highest i.e. 63+1)
Q.1. The ticket for a journey is in the range of 1 to 63 paise. You have 63 paise in your pocket and so on. and the question is You have to change the money into coins and all denominations are available at final. You have to buy the ticket and you should have at least one coin? (not same figures)
Ans. 64 (Just add 1 to highest i.e. 63+1)
Q.2. The sum of two numbers is given and product is also given find the square of difference of two numbers..
Ans. (a-b)2=a2+b2+2ab..
Ans. (a-b)2=a2+b2+2ab..
Q.3. The dog and here are running, dog crosses the roads, rivers and different. Here start running after 2 hours of dog running, dog runs 30kmph in 6 hours then what is the average speed of here?
(values are not same)
Ans. 30*6/4
(values are not same)
Ans. 30*6/4
Q.4. In a restaurant there are different nine flavours of pizzas.....
Q.5. A length of rod is turned into triangle. The sides of a triangle are 12,16,10. if this rod is turned into square then find the area of the square?
Ans. rod length=12+16+10=38
length of the side is a square=38/4;
area=(38/4)*(38/4)
Ans. rod length=12+16+10=38
length of the side is a square=38/4;
area=(38/4)*(38/4)
Q.6. There are some chocolates. A woman can eat 3chocolates and a man can eat 1 chocolate and a child can eat half chocolate. then 20 chocolates is divided in...
Ans. Go through the options( 5Woman, 3man, 4children).
Q.7. A water tank is filled in the way as 256,128,64,... th parts in every hour, then in how many hours the tank will filled?
Ans. 256,128,64,32,16,8,4,2,1 ( 9 hours) values are not same..
Ans. Go through the options( 5Woman, 3man, 4children).
Q.7. A water tank is filled in the way as 256,128,64,... th parts in every hour, then in how many hours the tank will filled?
Ans. 256,128,64,32,16,8,4,2,1 ( 9 hours) values are not same..
Q.8. The age of Ram and Sayam are in the ratio 5:6 and after 4 years their ratios are 7:8 then what is the present age of Sayam?
Ans. 12years (names and values may change)
Ans. 12years (names and values may change)
TCS Aptitude Test 1
| Question 1 |
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, Paul picks 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 team has 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?
| 5/9 | |
| 1/9 | |
| 2/3 | |
| 4/9 |
| Question 2 |
A and B play a game between them. The dice consist of colors on their faces(instead of number). When the dice are thrown, A wins if both show the same color, otherwise B wins. One die has 3 red faces and 3 blue faces. How many red and blue faces should the other die have if the both players have if the both players have the same chances of winning?
| 5 red and 1 blue faces | |
| 1 red and 5 blue faces | |
| 3 red and 3 blue faces | |
| wrong question |
| Question 3 |
The citizens of planet Nigiet are 6 fingered and have thus developed their decimal system in base 6. A certain street in Nigiet contains 1000 base buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
| 256 | |
| 54 | |
| 192 | |
| 108 | |
| Question 4 | |
A lady has fine gloves and hats in her closet- 18 blue- 32 red , 10 white , 25 yellow, 55 purple, 30 orange. The lights are out and it is totally dark inspite of the darkness. She can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each colour of blue, red, yellow?
| 59 | |
| 8 | |
| 50 | |
| 42 | |
| Question 5 | |
If A, B and C are the mechanisms used separately to reduce the wastage of fuel by 30%, 20% and 10%. What will be the fuel economy if they were used combined?
| 30% | |
| 20% | |
| 10% | |
| insufficient data | |
| Question 6 | |
12 people {a1, a2, …, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a11, a12}, {a12, 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
| 12 | |
| 4 | |
| 18 | |
| 11 | |
| Question 7 | |
Horse started to chase dog as it relieved stable two hrs ago. And horse started to ran with average speed 22km/hr, horse crossed 10 mts road and two small pounds with depth 3m, and it crossed two small street with 200 mts length. After traveling 6 hrs, 2hrs after sunset it got dog. Compute the speed of dog?
| 20Km/hr | |
| 16.5Km/hr | |
| 22.5Km/hr | |
| 18Km/hr | |
| Question 8 | |
Alok and Bhanu play the following min-max game. Given the expression N = 15 + 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, Y or 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 to their optimal strategies, the value of N at the end of the game would be
| 33 | |
| 30 | |
| 28 | |
| 35 | |
| Question 9 | |
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 that the 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 B. leftmost suspect is innocent . C. leftmost suspect is guilty
| A only | |
| A or C | |
| A or B | |
| B only | |
| Question 10 | |
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 middle circle touches two circles on either side. Find the ratio of the radius of the circles to the side of the square.
| 1:(4+ 7v3) | |
| 1:(2+ 6v2) | |
| 1:(2+ 7v2) | |
| (2+ 7v2):1 | |
| Question 11 | |
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 1 letter is inserted in an improper envelope?
| 0 | |
| 12/212 | |
| 11/12 | |
| 1/12 | |
| Question 12 | |
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 box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is
| 3/4 | |
| 37/38 | |
| 1/2 | |
| 14/19 | |
| Question 13 | |
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
| 4 | |
| 3 | |
| 1 | |
| 0 | |
| Question 14 | |
A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement and says “At least n of the statements on this sheet are true.” Which statements are true and which are false?
| The odd numbered statements are true and the even numbered are false | |
| The first 26 statements are false and the rest are true. | |
| The even numbered statements are true and the odd numbered are false. | |
| The first 13 statements are true and the rest are false. | |
| Question 15 | |
Entry ticket to an exhibition ranges from 1p to 31p. You need to provide exact change at the counter. You have 31p coin. In how many parts will you divide 31p so that you will provide the exact change required and carry as less coins as possible?
| 21 | |
| 31 | |
| 6 | |
| 32 | |
| Question 16 | |
Which is the smallest no divides 2880 and gives a perfect square?
| 1 | |
| 2 | |
| 5 | |
| 6 |
A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says ‘ At least n of the statements on this sheet are false. ‘ Which statements are true and which are false?
| The even numbered statements are true and the odd numbered are false. | |
| The odd numbered statements are true and the even numbered are false. | |
| The first 35 statements are true and the last 35 are false. | |
| The first 35 statements are false and the last 35 are false. | |
| Question 18 | |
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. (At the 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?
| 9 hours | |
| 7 hours | |
| 8 hours | |
| 10 hours | |
| Question 19 | |
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 1face of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?
| 900 | |
| 488 | |
| 563 | |
| 800 | |
| Question 20 | |
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 be achieved if mankind (as well as woman kind) had only worked with fewer digits. The problem posed at the end of the workshop is how many 5 digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4? Can you help Alok find the answer?
| 375 | |
| 3125 | |
| 500 | |
| 625 | |
| Question 21 | |
A lady has fine gloves and hats in her closet- 18 blue- 32 red and 25 black. The lights are out and it is totally dark inspite of the darkness. She can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each colour?
| 60 | |
| 50 | |
| 8 | |
| 42 | |
| Question 22 | |
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. (At the end of first hour, B has 10 litres, second hour it has 20, and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?
| 26 | |
| 25 | |
| 5 | |
| 27 | |
| Question 23 | |
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? Can you help the student find the answer?
| 12 | |
| 18 | |
| 6 | |
| 21 | |
| Question 24 | |
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 the way 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?
| 6 | |
| 18 | |
| 72 | |
| 12 | |
| Question 25 | |
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 probability that Q is closer to the center of the circle than the periphery?
| 0.75 | |
| 1 | |
| 0.25 | |
| 0.5 | |
| Question 26 | |
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
| 4 | |
| 3 | |
| 0 | |
| 1 | |
| Question 27 | |
Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line; i.e. the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The maximum value of n1(P) over all configurations P of 10 points in the plane is
| 5 | |
| 3 | |
| 9 | |
| 10 | |
| Question 28 | |
Form 8 digit numbers from by using 1, 2,3,4,5 with repetition is allowed and must be divisible by 4?
| 31250 | |
| 97656 | |
| 78125 | |
| 97657 | |
| Question 29 | |
A sheet of paper has statements numbered from 1 to 45. For all values of n from 1 to 45, statement n says “At most n of the statements on this sheet are false”. Which statements 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. | |
| All statements are true. | |
| All statements are false. | |
| Question 30 | |
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 covered 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 increase its speed so as the win the race?
| 8 | |
| 5 | |
| 37 | |
| 80 | |
| Question 31 | |
The ratio of incomes of C and D is 3:4.the ratio of their expenditures is 4:5.Find the ratio of their savings if the savings of C is one fourths of his income?
| 2:4 | |
| 1:4 | |
| 3:4 | |
| 4:5 | |
| Question 32 | |
A can do a piece of work in 20 days, which B can do in 12 days. In 9 days B does ¾ of the work. How many days will A take to finish the remaining work?
| 5 | |
| 10 | |
| 15 | |
| 20 | |
| Question 33 | |
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 walking speed in kmph.
| 23.62 | |
| 8.78 | |
| 11.39 | |
| 236.16 | |
| Question 34 | |
In planet OZ planet there are 8 days, sunday to saturday and 8th day is OZ day. There is 36 hours in a day. What is angle between 12.40 ?
| 80 | |
| 81 | |
| 87 | |
| 89 | |
| Question 35 | |
In the class of 40 students, 30 speak Hindi and 20 speak English. What is the lowest possible number of students who speak both the languages?
| 5 | |
| 20 | |
| 15 | |
| 10 |
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