TCS questions post 1
November 11, 2010 by admin
Filed under TCS Mock Test Papers
21 Comments
# 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
0.5
0.25
Answere::
Let the outer circle be the required dashboard of radius 1 foot. So let us assume a circle with
exactly half of the radius of the outer circle. So if the dart falls in the inner circle it will be
near to center other wise it will be near to periphery or the circumference . so the required
probability is
Probability= (area of inner circle)/(area of outer circle)
i.e (r/2)^2/r^2 =1/4=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?
24
12
8
16
Ans:: simple substitution problem
# 3 ) 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
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?
4/9
2/3
1/9
5/9
Paul will choose the team with the same probability as the team will win
So the final probability is (2/3)*(2/3)+(1/3)*(1/3)=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?
18
72
12
apply (n1)*(t1)/(w1)= (n2)*(t2)/(w2) where
n1,n2 are number of people
t1,t2 are time
w1,w2 are work
# 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?
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
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).
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?
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?
12/212
11/12
1/12
ans :: – - – - -
First 3 places can be filled in 125 ways (5*5*5)
Lsat 2 places can be fill in 5 ways (12.24.32.44.52)
So ans is 125*5=625
# 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 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
Ans::: 3 lines are given so ans is 4 one incenter and 3 excenters. If it is 3 line segments
then ans would be 1
