TCS Qustions Post 1
# 1 ) 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
0.5
0.25
# 2) 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 * v (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?
d = 4 * v (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?
24
12
8
16
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
27
18
20
0.0
# 5 )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?
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?
4/9
2/3
1/9
5/9
# 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 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
# 7) 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 3s are used in numbering these buildings?
buildings numbered 1 to
1000. How many 3s are used in numbering these buildings?
256
54
192
64
# 8 ) 36 people {a1, a2, …, a36}
meet and shake hands in a circular fashion. In other words, there are totally
36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {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
12
13
18
11
# 9 )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 coinis the third coin from the top. Then
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
In order to win, Alice’s
first move should be a 0-move.
In order to win, Alice’s
first move should be a 1-move.
Alice has no winning
strategy.
In order to win, Alice’s
first move can be a 0-move or a 1-move.
# 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?
The even numbered statements
are true and the odd numbered statements are false.
The 39th statement is true
and the rest are false.
The odd numbered statements
are true and the even numbered statements are false.
All the statements are
false.
# 11) 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).
7
6
9
8
# 12) 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?
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
625
500
3125
# 13) 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
# 14) 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. All suspects are lying or the leftmost suspect is innocent.
B. All suspects are lying and the leftmost suspect is innocent .
A only
Neither A nor B
Both A and B
B only
# 15Given 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
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