@TCS-mock Test
30 Questions
| Attempts: 115
This exam is based on the new TCS exam pattern. If you get above 60 % in this exam means you are in good touch with all the topics.
30 questions 80 minutes
Questions marked (#) are high priority questions.
You are having 2 chances. . . .
All the best. . .
Questions and Answers
- 1.
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.
- A.
1:(2+ 6√2)
- B.
1:(4+ 7√3)
- C.
(2+ 7√2):1
- D.
1:(2+ 7√2)
Correct Answer
A. 1:(2+ 6√2)Explanation
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 circles will contribute 10r and last circle will contribute r + sqrt(2) * r . Length of diagonal = 12r + 2sqrt (2) r = sqrt (2) * s where s -> side of square. So, ratio of r:s = 1/( 2 + 6 * sqrt(2)) = 1: [ 2+ 6 sqrt(2)]Rate this question:
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- 2.
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 are spherical. However the coin minting machinery lays out some stipulations on the size of the coins.Ӣ The diameter of the coins should be at least 64mm and not exceed 512mm.Ӣ Given a coin, the diameter of the next larger coin is at least 50% greater.Ӣ 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?
- A.
8
- B.
9
- C.
5
- D.
6
Correct Answer
D. 6Explanation
1st coin is of 64mm diameter 2nd coin is of 64+32 = 96mm 3rd coin is of 96 + 48 = 144mm 4th coin is of 144+ 72 = 216mm 5th coin is of 216+108 = 324mm 6th coin is of 324+ 162= 486 7th coin no wards diameter > 512mm So, ans is 6Rate this question:
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- 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 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 to tie the race?
- A.
40
- B.
5
- C.
8
- D.
37.8
Correct Answer
D. 37.8Explanation
After tortoise covers 1/5th distance hare starts the race When hare covers 1/8th of distance tortoise meets hare So distance covered by tortoise = 1-(1/5 + 1/8) = 27/40 Time taken by both is same time = dist/speed So (dist/ speed) of tortoise = (dist / speed) of hare let speed of tortoise be t and of hare be h 27/40t = 1/8h h = (40/(8*27) )* t = 5/27 * t Now for the next part hare has to cover 7/8 th distance when tortoise covers 1/8 th distance so we get 1/8t = 7/8h h = 7t so the factor by which h's speed increases = 7t/ (5/27 * t) which we get as 37.8Rate this question:
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- 4.
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 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.
12
- B.
30
- C.
93
- D.
69
Correct Answer
B. 30Explanation
As Alok tries to maximize the number it can not be negative value, So option B is false. Minimum value: 12+ X(Y-Z) = 12 [considering Y = Z = 9] Maximum value: 12+X(Y-Z) = 93 [considering Y = X=9, Z=0] As Alok and Bhanu tries to max and min the number N value must lies between 12 and 93.Rate this question:
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- 5.
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.
The odd numbered statements are true and the even numbered are false
- B.
The first 13 statements are true and the rest are false.
- C.
The even numbered statements are true and the odd numbered are false
- D.
The first 26 statements are false and the rest are true.
Correct Answer
B. The first 13 statements are true and the rest are false. -
- 6.
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 many programmers required to write 72 lines of code in total in 72 minutes?
- A.
18
- B.
12
- C.
72
- D.
6
Correct Answer
B. 12Explanation
No of people time work 12 12 12 X 72 72 Work = No of people * time i.e. ( P1 * T1 ) / W1 = ( P2 * T2 ) / W2 (12 * 12)/12 = ( X * 72 )/ 72 X = 12Rate this question:
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- 7.
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.
12/(12^12)
- B.
11/12
- C.
0
- D.
1/12
Correct Answer
C. 0Explanation
It cannot be exactly 1 as we need a minimum of two letters to be in improper envelope.Rate this question:
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- 8.
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
- A.
14/19
- B.
37/38
- C.
1/2
- D.
3/4
Correct Answer
A. 14/19Explanation
Considering 10 red in 1st box and 10 green in 2nd box probability of picking red = 1/2 * 1 + 1/2 * 0 = 1/2 Now consider the other case, 9 red balls are transferred to green ball box. Now total balls in 2nd box will be 19. Total probability = probability to select 1st box + probability to select 2nd box = (1/2)*(1C1/1C1)+(1/2)*(9C1/19C1) = (1/2)*(1+9/19) = (1/2)*(28/19) = 14/19Rate this question:
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- 9.
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
- B.
0.75
- C.
0.5
- D.
0.25
Correct Answer
D. 0.25Explanation
Let the sample space area be pi* r^2 => pi , considering r = 1m and Event space area = pi/4, considering r= 1/2 m So, the probability = (pi/4)/pi = 0.25Rate this question:
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- 10.
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.
All the statements are false.
- B.
The 39th statement is true and the rest are false
- C.
The odd numbered statements are true and the even numbered statements are false.
- D.
The even numbered statements are true and the odd numbered statements are false.
Correct Answer
B. The 39th statement is true and the rest are falseExplanation
3rd and 4th option does not satisfies the given condition and all the statement cannot be false. So, option The 39th statement is true and the rest are false is answerRate this question:
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- 11.
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 the form 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 = 8 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 8mm. How many years back did the solar blast occur?
- A.
24
- B.
16
- C.
12
- D.
8
Correct Answer
A. 24Explanation
d = 4 * sqrt(t-8) d = 16 as r= 8 given thus 16 = 4 * sqrt(t-8) 4 = sqrt (t-8) t-8 = 16 t = 24Rate this question:
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- 12.
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, 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.
9
- B.
18
- C.
20
- D.
27
Correct Answer
C. 20Explanation
Considering equation: N = 9+X+Y-Z. Minimum value of N: 9+ X+Y-Z = 18[considering X = Y = Z = 9] Maximum value of N: 9+X+Y-Z = 27 [considering Y = X=9, Z=0] As Alok and Bhanu tries to max and min the number N value and its value lies between 18 and 27. So, Answer is 20.Rate this question:
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- 13.
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 or the leftmost suspect is innocent.B. All suspects are lying and the leftmost suspect is innocent .
- A.
A only
- B.
Both A and B
- C.
Neither A nor B
- D.
B only
Correct Answer
A. A onlyExplanation
considering All suspects are lying........S1 the leftmost suspect is innocent......S2 Both S1 and S2 cannot be true so it is S1 OR S2.Rate this question:
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- 14.
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 many faces of the smaller cubes remain unpainted?
- A.
800
- B.
500
- C.
900
- D.
488
Correct Answer
D. 488Explanation
The outside of the large cube = 5cm The inside space = 3cm Total number of small cubes = (5*5*5) - (3*3*3) = 125 - 27 = 98 Total number of faces = 98 * 6 = 588 now surface area of 4 faces = 4 * 5*5 = 100 cm^2 so subtract 100 cubes as they have surface area 1cm^2 each so unpainted faces of cubes = 588 - 100 = 488Rate this question:
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- 15.
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.
18
- B.
21
- C.
12
- D.
6
Correct Answer
A. 18Explanation
Let the number be X (1/3)X = 3+ (1/6)X (1/6) X = 3 X = 18Rate this question:
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- 16.
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 to 1000. How many 3s are used in numbering these buildings?
- A.
256
- B.
54
- C.
192
- D.
300
Correct Answer
C. 192Explanation
Number of THREES between 1-100 ... 16 Number of THREES between 101-200...16 Number of THREES between 201-300....17 Numbers of THREES between 301-400... 16+63 Similarly number of THREES from 401 - 1000 ... 16* 4 Therefore Total numbers of THREES = 192Rate this question:
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- 17.
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.
3125
- B.
625
- C.
375
- D.
500
Correct Answer
B. 625Explanation
Since each desired number is divisible by 4, So we must have 12,24,32,44,52 at the last two digits. 1st place can be filled by any of the remaining 5 numbers. So, there are 5 ways of filling the 1st digits place. Similar 2nd digits and 3rd each digit place can be filled in 5 ways. Therefore Required number of numbers = 5*5*5*5=625Rate this question:
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- 18.
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.
12
- B.
72
- C.
432
- D.
8
Correct Answer
C. 432Explanation
No of people time work 12 12 12 72 72 x Work = No of people * time (12 * 12) /12 = ( 72 * 72 ) / x i.e. ( P1 * T1 ) / W1 = ( P2 * T2 ) / W2 X = 72 * 72 / 12 = 432.Rate this question:
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- 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 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 am.
- A.
111
- B.
89
- C.
251
- D.
71
Correct Answer
B. 89Explanation
Angle traced by hour hand in 12.40 hrs = (360/18) * ( 112/9) = 2240/9. Angle traced by minute hand in 40 min = (360/90) * 40 = 160. Angle between hour hand and minute hand = (2240/9) - 160 = 88.88. Approximately 89 degrees.Rate this question:
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- 20.
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.
4/9
- C.
1/9
- D.
2/3
Correct Answer
A. 5/9 -
- 21.
(#)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?
- A.
Brown
- B.
Grey
- C.
White
- D.
Black
Correct Answer
C. WhiteExplanation
Only white bears leaves in south and north poleRate this question:
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- 22.
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?
- A.
All are true
- B.
The odd numbered statements are true and the even numbered are false
- C.
All are false
- D.
The even numbered statements are true and the odd numbered are false
Correct Answer
C. All are false -
- 23.
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?
- A.
7 hours
- B.
10 hours
- C.
9 hours
- D.
8 hours
Correct Answer
D. 8 hoursExplanation
B’s volume after 4 hours 1/16 B’s volume after 5 hours 1/8 B’s volume after 6 hours ¼ B’s volume after 7 hours ½ So, tank will be filled in 8 hourRate this question:
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- 24.
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.
6
- B.
7
- C.
8
- D.
9
Correct Answer
D. 9Explanation
The maximum possible non cyclic handshakes are (a1,a2),(a2,a3),(a3,a4),(a4,a5),(a5,a6),(a6,a7),(a7,a8),(a8,a10),(a10,a9) i.e 9Rate this question:
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- 25.
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 other 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 following statements 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?
- A.
Thursday
- B.
Tuesday
- C.
Sunday
- D.
Monday
Correct Answer
A. Thursday -
- 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
- A.
1
- B.
4
- C.
3
- D.
0
Correct Answer
A. 1 -
- 27.
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?
- A.
48
- B.
32
- C.
64
- D.
96
Correct Answer
C. 64 -
- 28.
(#)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 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.
- A.
15.88
- B.
476
- C.
14.88
- D.
29.75
Correct Answer
C. 14.88Explanation
Time = (Distance/Speed) = (952/32) Therefore the total time = time = (952/32)/2 = 14.88Rate this question:
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- 29.
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 second bowl and added to the first bowl. Which statement will hold good for the above?
- A.
Second liquid in first bowl is less than the first mixture in second bowl
- B.
Second liquid in first bowl is more than the first mixture in second bowl
- C.
Second liquid in first bowl is equal to the first mixture in second bowl
- D.
None of the above
Correct Answer
C. Second liquid in first bowl is equal to the first mixture in second bowl -
- 30.
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.
- A.
1/4
- B.
1/2
- C.
2/4
- D.
2/3
Correct Answer
A. 1/4Explanation
The sample space S of the experiment described in question 5 is as follows S = { (1,H),(2,H),(3,H),(4,H),(5,H),(6,H) (1,T),(2,T),(3,T),(4,T),(5,T),(6,T)} Let E be the event "the die shows an odd number and the coin shows a head". Event E may be described as follows E={(1,H),(3,H),(5,H)} The probability P(E) is given by P(E) = n(E) / n(S) = 3 / 12 = 1 / 4Rate this question:
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