TCS MOCK
TEST 2
1.1/3 of a number is 6
more than 1/6 of that number then what is the number?
(a) 12
(b) 36
(c) 24
(d) 48
(a) 12
(b) 36
(c) 24
(d) 48
2.The pace length P is
the distance between the rear of two consecutive footprints. For men, the
formula n/P = 180 gives an approximate relationship between n and P where, n =
number of steps per minute and P = pace length in meters. Bernard knows his
pace length is 120 cm. The formula applies to Bernard’s walking. Calculate
Bernard’s walking speed in kmph.
(a) 236.16
(b) 8.78
(c) 15.56
(d) 23.62
(a) 236.16
(b) 8.78
(c) 15.56
(d) 23.62
3.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 24 such programmers take 24 minutes to write 24 lines of code in total,
how long will it take 72 programmers to write 72 lines of code in total?
(a) 12
(b) 24
(c) 6
(d) 72
(a) 12
(b) 24
(c) 6
(d) 72
4.A sheet of paper has
statements numbered from 1 to 40. For each value of n from 1 to 40, statement n
says “Exactly 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) Second last
statement is true and the remaining statements are false. (d) The even numbered
statements are true and the odd numbered are false.
5.Alok and Bhanu play the
following min-max game. Given the expression N = 25 + 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) 43
(b) 16
(c) 36
(d) 34
(a) 43
(b) 16
(c) 36
(d) 34
6.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)First half of the statements are
true and the rest are false. (b) The odd numbered statements are true the even
numbered are false. (c) First half of the statements are false and the rest are
true. (d) The even numbered statements are true and the odd numbered are false.
7.10 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) B and C
(a) A only
(b) A and B
(c) B only
(d) B and C
8.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 6) buildings numbered 1 to
1000. How many 3s are used in numbering these buildings?
(a) 108
(b) 192
(c) 54
(d) 102
(a) 108
(b) 192
(c) 54
(d) 102
9.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 hour has 90 minutes while each minute has
60 seconds. As on earth, hour hand covers the dial twice every day. Find the
approximate angle between the hands of clock on Oz when the time is 14.40 a.m.
(a) 83
(b) 74
(c) 129
(d) 65
(a) 83
(b) 74
(c) 129
(d) 65
10.On planet zorba, a
solar blast has melted the ice caps on its equator. 8 years after the ice
melts, tiny planetoids 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 = 2 * √ (t - 8) for t ≥
8 where d represents the diameter in mm and t the number of years since the
solar blast. Jegan recorded the radius of some echina at a particular spot as 4
mm. How many years back did the solar blast occur?
(a) 18
(b) 12
(c) 16
(d) 24
(a) 18
(b) 12
(c) 16
(d) 24
11.It is dark in my
bedroom and I want to get two socks of the same colour from my drawer, which
contains 26 red and 24 blue, 34 brown socks. How many socks do I have to take
from the drawer to get at least two socks of the each colour?
(a) 6
(b) 74
(c) 61
(d) 62
(a) 6
(b) 74
(c) 61
(d) 62
12.For the FIFA world
cup, Paul the octopus has been predicting the winner of each match with amazing
success. It is rumoured 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 rumours
to be true and that in a match between Ghana and Bolivia, Ghana the stronger
team has a probability of 5/6 of winning. What is the probability that Paul
will correctly pick the winner of the Ghana-Bolivia game?
(a) 0.72
(b) 0.50
(c) 0.64
(d) 0.83
(a) 0.72
(b) 0.50
(c) 0.64
(d) 0.83
13.Given 3 lines in the
plane such that the points of intersection form a triangle with sides of length
19, 19 and 19, 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
14.66 people {a1, a2,...,
a66} meet and shake hands in a circular fashion. In other words, there are
totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a65, a66},
{a66, a1}. The size of the smallest set of people such that the rest have
shaken hands with at least one person in the set is
(a) 22
(b) 33
(c) 65
(d) 11
(a) 22
(b) 33
(c) 65
(d) 11
15.The IT giant Tirnop
has recently crossed a head count of 150000 and earning 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 16 such programmers take 16 minutes to write 16 lines of code in
total, how many lines of code can be written by 96 programmers in 96 minutes?
(a) 16
(c) 432
(d) 96
(b) 576
(a) 16
(c) 432
(d) 96
(b) 576
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 3 times as fast
as Mohit’s old Mercedes. If the speed of Mohit’s Mercedes is 33 km/hr and the
distance travelled by the Ferrari is 909 km, find the total time taken in hours
for Rohit to drive that distance.
(a) 9.18
(b) 10.18
(c) 9
(d) 99
(a) 9.18
(b) 10.18
(c) 9
(d) 99
17.Anoop managed to draw
6 circles of equal radii with their centers 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 side of the
square to the radius of the circles. Assume Ö2 is
1.4.
(a) 9 : 1
(b) 6.2 : 1
(c) 10.4 : 1
(d) 7.6 : 1
(a) 9 : 1
(b) 6.2 : 1
(c) 10.4 : 1
(d) 7.6 : 1
18.A hare and a tortoise
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 of
its distance and that too leisurely. The hare and tortoise meet when the hare
has covered only 1/4 of the distance. By what factor should the hare increase
its speed so as to tie the race?
(a) 8
(b) 37
(c) 45
(d) 6.6
(a) 8
(b) 37
(c) 45
(d) 6.6
19.There are two boxes,
one containing 21 red balls and the other containing 25 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) 0.5
(b) 0.63
(c) 0.72
(d) 0.48
(a) 0.5
(b) 0.63
(c) 0.72
(d) 0.48
20.Alok and Bhanu play
the following min-max game. Given the expression N = 32 + 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) 113
(b) 32
(c) -49
(d) 50
(a) 113
(b) 32
(c) -49
(d) 50
21.A sheet of paper has
statements numbered from 1 to 40. For each value of n from 1 to 40, statement n
says "At most n of the statements on this sheet are true." Which
statements are true and which are false? (a) All statements are true (b) The
odd numbered statements are true the even numbered are false (c) The first half
of the statements are true and the remaining statements are false (d) The even
numbered statements are true and the odd numbered are false
22.After a 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) 23/25
(b) 0
(c) 2/25
(d) 1
(a) 23/25
(b) 0
(c) 2/25
(d) 1
23.There are two water
tanks A and B, where 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, liters….., 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 1/64 filled after 17 hours, what is the total duration
required to fill it completely?
(a) 6 hours
(b) 24 hours
(c) 22 hours
(d) 23 hours
(a) 6 hours
(b) 24 hours
(c) 22 hours
(d) 23 hours
24.You have a jar
containing water absorbing marbles which will take 21 hours to set completely
when fixed with white cement. There are 50 red marbles, 52 blue marbles and 63
black marbles. The jar is kept inside a dark room. What is the minimum number
of marbles that you need to pick to make sure that you have a pair of marbles
in each color?
(a) 117
(b) 98
(c) 120
(d) 114
(a) 117
(b) 98
(c) 120
(d) 114
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?
(a) 0.25
(b) 0.50
(c) 0.75
(d) 0.3333
(a) 0.25
(b) 0.50
(c) 0.75
(d) 0.3333
26.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 only 2 faces of the outer surface of the cube are painted, totally how
many faces of the smaller cubes remain unpainted?
(a) 210
(b) 465
(c) 450
(d) 538
(a) 210
(b) 465
(c) 450
(d) 538
27.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.
- The diameter of the coins should be at least 256 mm and not exceed 4096 mm.
- Given a coin, the diameter of the next larger coin is at least 50% greater.
- The diameter of a 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) 7
(b) 8
(c) 9
(d) 6
- The diameter of the coins should be at least 256 mm and not exceed 4096 mm.
- Given a coin, the diameter of the next larger coin is at least 50% greater.
- The diameter of a 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) 7
(b) 8
(c) 9
(d) 6
28.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 7 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) 5000
(b) 15625
(c) 2500
(d) 3179
(a) 5000
(b) 15625
(c) 2500
(d) 3179
29.Alice and Bob play the
following coins-on-a-stack game. 20 coins are stacked one above the other. One
of them is a special (gold) coin and the rest are ordinary coins. 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 coin is 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
30.There are 5 pentagonal
pyramid shaped bottles whose volumes are in geometric progression and there are
5 materials to make a perfume inside the bottle viz., Lilac, Balsamic, Lemon,
Woody and Mimosaic. Also, all the faces of the pyramids are painted in
different colours. To make a perfume that is in demand, the following
conditions are to be followed: Lilac and Balsamic go together. Woody and
Mimosaic go together. Woody and Balsamic never go together. Lemon can be added
with any material. All of the following combinations are possible to make a
perfume EXCEPT (a) Balsamic and Lilac (b) Woody and Lemon (c) Mimosaic and
Woody (d) Mimosaic and Lilac
31.20 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) 19
(b) 18
(c) 20
(d) 21
(a) 19
(b) 18
(c) 20
(d) 21
32.There are 45 cans out
of which one is poisoned. If a person tastes very little of this, he will die
within 14 hours; so they decided to test it with mice. Given that a mouse dies
in 24 hours and you have 24 hours in all to find out the poisoned can, how many
mice are required to find the poisoned can?
(a) 44
(b) 29
(c) 6
(d) 5
(a) 44
(b) 29
(c) 6
(d) 5
33.Middle-earth is a
fictional land inhabited by hobbits, elves, dwarves and men. The hobbits and
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 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 9 rounds played in a knockout tournament, how many matches were
played?
(a) 511
(b) 512
(c) 256
(d) 255
(a) 511
(b) 512
(c) 256
(d) 255
34.The IT giant Tirnop
has recently crossed a head count of 150000 and earning 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 will complete 96 lines in 96 minutes?
(a) 12
(b) 96
(c) 1152
(d) 32
(a) 12
(b) 96
(c) 1152
(d) 32
35.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
(a) 5
(b) 10
(c) 9
(d) 9
(a) 5
(b) 10
(c) 9
(d) 9
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