sample questions given by tcs

Note: These are not sample questions, but questions that explore some of the concepts that
may be used. The intention is that you should get prepared with the concepts rather than just
focusing on a set of questions.
-----------------------------------------------------------------------------------
1. What are the total number of divisors of 600(including 1 and 600)?
a. 24
b. 40
c. 16
d. 20
2. What is the sum of the squares of the first 20 natural numbers (1 to 20)?
a. 2870
b. 2000
c. 5650
d. 44100
3. What is∑


(
 ), where
 is the number of ways of choosing k items from 28
items?
a. 406 *

b. 306 *

c. 28 *

d. 56 *

4. What is ∑


(
 ) where
 is the number of ways of choosing k items from 28
items?
a.

b.

c.

d.

5. A call center agent has a list of 305 phone numbers of people in alphabetic order of names
(but she does not have any of the names). She needs to quickly contact Deepak Sharma to
convey a message to him. If each call takes 2 minutes to complete, and every call is
answered, what is the minimum amount of time in which she can guarantee to deliver the
message to Mr Sharma.
a. 18 minutes
b. 610 minutes
c. 206 minutes
d. 34 minutes6. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively.
What is the average time per call?
a. 4 minutes
b. 7 minutes
c. 1 minutes
d. 5 minutes
7. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively.
What is the median time per call?
a. 5 minutes
b. 7 minutes
c. 1 minutes
d. 4 minutes
8. Eric throws two dice, and his score is the sum of the values shown. Sandra throws one die,
and her score is the square of the value shown. What is the probability that Sandra’s score
will be strictly higher than Eric’s score?
a. 137/216
b. 17/36
c. 173/216
d. 5/6
9. What is the largest integer that divides all three numbers 23400,272304,205248 without
leaving a remainder?
a. 48
b. 24
c. 96
d. 72
10. Of the 38 people in my office, 10 like to drink chocolate, 15 are cricket fans, and 20
neither like chocolate nor like cricket. How many people like both cricket and chocolate?
a. 7
b. 10
c. 15
d. 18
11. If f(x) = 2x+2 what is f(f(3))?
a. 18
b. 8
c. 64
d. 1612. If f(x) = 7 x +12, what is f-1(x) (the inverse function)?
a. (x-12)/7
b. 7x+12
c. 1/(7x+12)
d. No inverse exists
13. A permutation is often represented by the cycles it has. For example, if we permute the
numbers in the natural order to 2 3 1 5 4, this is represented as (1 3 2) (5 4). In this the
(132) says that the first number has gone to the position 3, the third number has gone to
the position 2, and the second number has gone to position 1, and (5 4) means that the
fifth number has gone to position 4 and the fourth number has gone to position 5. The
numbers with brackets are to be read cyclically.
If a number has not changed position, it is kept as a single cycle. Thus 5 2 1 3 4 is
represented as (1345)(2).
We may apply permutations on itself If we apply the permutation (132)(54) once, we get
2 3 1 5 4. If we apply it again, we get 3 1 2 4 5 , or (1 2 3)(4) (5)
If we consider the permutation of 7 numbers (1457)(263), what is its order (how many
times must it be applied before the numbers appear in their original order)?
a. 12
b. 7
c. 7! (factorial of 7)
d. 14
14. What is the maximum value of x3y3 + 3 x*y when x+y = 8?
a. 4144
b. 256
c. 8192
d. 102
15. Two circles of radii 5 cm and 3 cm touch each other at A and also touch a line at B and C.
The distance BC in cms is?
a. 60
b. 62
c. 68
d. 64
16. In Goa beach, there are three small picnic tables. Tables 1 and 2 each seat three people.
Table 3 seats only one person, since two of its seats are broken. Akash, Babu, Chitra,
David, Eesha, Farooq, and Govind all sit at seats at these picnic tables. Who sits with
whom and at which table are determined by the following constraints:
a. Chitra does not sit at the same table as Govind.
b. Eesha does not sit at the same table as David.
c. Farooq does not sit at the same table as Chitra.d. Akash does not sit at the same table as Babu.
e. Govind does not sit at the same table as Farooq.
Which of the following is a list of people who could sit together at table 2?
a. Govind, Eesha, Akash
b. Babu, Farooq, Chitra
c. Chitra, Govind, David.
d. Farooq, David, Eesha.
17. There are a number of chocolates in a bag. If they were to be equally divided among 14
children, there are 10 chocolates left. If they were to be equally divided among 15
children, there are 8 chocolates left. Obviously, this can be satisfied if any multiple of 210
chocolates are added to the bag. What is the remainder when the minimum feasible
number of chocolates in the bag is divided by 9?
a. 2
b. 5
c. 4
d. 6
18. Let f(m,n) =45*m + 36*n, where m and n are integers (positive or negative) What is the
minimum positive value for f(m,n) for all values of m,n (this may be achieved for various
values of m and n)?
a. 9
b. 6
c. 5
d. 18
19. What is the largest number that will divide 90207, 232585 and 127986 without leaving a
remainder?
a. 257
b. 905
c. 351
d. 498
20. We have an equal arms two pan balance and need to weigh objects with integral weights
in the range 1 to 40 kilo grams. We have a set of standard weights and can place the
weights in any pan. . (i.e) some weights can be in a pan with objects and some weights
can be in the other pan. The minimum number of standard weights required is:
a. 4
b. 10
c. 5
d. 621. A white cube(with six faces) is painted red on two different faces. How many different
ways can this be done (two paintings are considered same if on a suitable rotation of the
cube one painting can be carried to the other)?
a. 2
b. 15
c. 4
d. 30
22. How many divisors (including 1, but excluding 1000) are there for the number 1000?
a. 15
b. 16
c. 31
d. 10
23. In the polynomial f(x) =2*x^4 - 49*x^2 +54, what is the product of the roots, and what is
the sum of the roots (Note that x^n denotes the x raised to the power n, or x multiplied
by itself n times)?
a. 27,0
b. 54,2
c. 49/2,54
d. 49,27
24. In the polynomial f(x) = x^5 + a*x^3 + b*x^4 +c*x + d, all coefficients a, b, c, d are integers.
If 3 + sqrt(7) is a root, which of the following must be also a root?(Note that x^n denotes
the x raised to the power n, or x multiplied by itself n times. Also sqrt(u) denotes the
square root of u, or the number which when multiplied by itself, gives the number u)?
a. 3-sqrt(7)
b. 3+sqrt(21)
c. 5
d. sqrt(7) + sqrt(3)

About TCS

About TCS
Tata Consultancy Services (TCS) is a software services consulting company headquartered in Mumbai, India. TCS is the largest provider of information and business process outsourcing services in Asia. TCS has offices in 42 countries with more than 142 branches across the globe. The company is listed on the National Stock Exchange and Bombay Stock Exchange of India.

Tata Consultancy Services (TCS) is a software services consulting company headquartered in Mumbai, India. TCS is the largest provider of information and business process outsourcing services in Asia. TCS has offices in 42 countries with more than 142 branches across the globe. The company is listed on the National Stock Exchange and Bombay Stock Exchange of India.

TCS is a flagship subsidiary of one of India's largest and oldest conglomerate company, the Tata Group, which has interests in areas such as energy, telecommunications, financial services, manufacturing, chemicals, engineering, materials, government and healthcare.

Founded: 1968

Headquarters: Mumbai, Maharashtra, India

Key people: Ratan Tata (Chairman)

S Ramadorai (Vice Chairman)

N Chandrasekaran (CEO & MD

Employees: 160,429 (As on 31 March 2010)

Website: www.tcs.com

TCS - India Locations:

Bangalore, Chennai, Ahmedabad, Baroda, Bhubaneswar, Coimbatore, Delhi, Gandhinagar, Goa, Gurgaon, Hyderabad , Cochin , Kolkata, Mumbai, Jamshedpur, Pune, Thiruvananthapuram.

Working at TCS - Why Should i Join TCS?

The work environment at TCS is built around the belief of growth beyond boundaries. Some of the critical elements that define our work culture are global exposure, cross-domain experience, and work-life balance. Each of these elements goes much deeper than what it ostensibly conveys.

The TCS employer brand positioning builds on our strengths and communicates TCS as an organization that offers its employees a complete Global IT Career by highlighting the three main value propositions:Global exposure, Freedom to work across domains, Work life balance.

Jobs at TCS:

Diploma Holders:

BPO, Voice/non-voice, Data-Entry, Testing.

Bsc Graduates(Any specialization):

TCS’ Ignite focuses on creating strong fundamentals in software programming skills among trainees, but it also teaches soft skills, customer orientation and project management skills.TCS provides Ignite programme for all BSc graduates and provides them software jobs

Engineers:

TCS recruits Engineers from all streams across India and trains them according to industrial needs. TCS is mainly into Consulting and Services. Engineers are trained in the following streams.1.soft engg 2. data structure 3. OS 4.Dbms 5. boot programming 6. Unix at their Thiruvanthapuram training centre.

Company Culture:

TCS culture

At TCS we have an energetic and open workplace environment, and a collaborative culture that's based on teamwork. Pulling together is a central tenet of our work ethic.

Energetic and full of enthusiasm, we enjoy our day (and night) at work. Life at TCS is a stimulating and exciting experience. Not only do our offices have the best infrastructure and technology, our colleagues have a knack of working hard — and partying harder.

If you'd like to spend your career in an extremely vibrant, stimulating and fun place, TCS is where you have to be.

We take pride in adhering to the Tata 'code of conduct', which is in place across the entire Tata Group. The code is a means of upholding and strengthening the trust reposed on us by our various stakeholders, be it our customers or the wider society.

Diversity at work:

TCS is an equal-opportunity employer and TCSers come from many nationalities and speak many languages. And, since we believe in celebrating everything under the sun, you will find us singing carols at Christmas and doing the dandiya dance at Navrathri with equal enthusiasm.

We are also habituated to do the regular outing, be it with our project teams, with Maitree or with just a bunch of other like-minded TCSers. We are off to treks, nature camps, picnics or just bus rides whenever we get the chance.

Awards and Recognition:

TCS has won 2010 SAP pinnacle award.

TCS has also won 2009-Utility Industry Achievement Awards.

Higher studies at TCS:

TCS offers IGNITE programme for science graduates, which transforms them to world-class Software Professionals.

After the training programme, these science graduates would be placed in areas like IT, business process outsourcing, consulting and infrastructure management.

Tata Consultancy Services (TCS) signed an MoU with SASTRA University, Thanjavur to facilitate higher education opportunities to all the TCS Ignite trainees.

TCS offers SAP certification for all its Employees.

More About TCS:

TCS has 142 offices in more than 42 Countries across the globe.

TCS Placement Paper 2012
1. Which Is The Smallest No Divides 2880 And Gives A Perfect Square?

A.1 B.2 C.5 D.6

Ans: C

2. Two Bowls Are Taken, One Contains Water And Another Contains Tea  Equal Amount . One Spoon Of Water From 1st Is Added To Second Bowl And Mixed Well, And A Spoon Of Mixture Is Taken From Second Bowl And Added To The 1st Bowl. Which Statement Will Hold Good For The Above?
{
Thought Process :
Water Bowl Tea Bowl
100 100
90w (+10w= Spoon Volume) 100tea+10water
90w+ (10*10/11)Tea+ 10/11 W 100t- (10*10/11) T
+ 10w- 10/11w
(1st Bowl’s Water Volume Is Equal To 2nd Bowls Tea Volume)

3. Form 8 Digit Numbers From By Using 1, 2,3,4,5 With Repetition Is Allowed And Must Be Divisible By 4?

A.31250 B.97656 C.78125 D.97657

Ans: C

4. Rearrange And Categorize The Word ‘Rapeteka’?

Ans: Bird

5. One Problem On (785^3-235^3)/(785^2+785*235+235^2)

Ans: You Are Free To Carry A Calculator With You But You Should Not Use It To Solve This Kind Of Problem. Because It Is Simple:

A3-b3 / A2+ab+b2

Ans Is : A-b Here 785-235= 550 That's It.

6. In School There Are Some Bicycles And 4 Wheeler Wagons. One Tuesday There Are 190 Wheels In The Campus. How Many Bicycles Are There?

Ans: 15

Thought Process : B*2+w*4=190 I.E. , B+2w=95 Now See U Can Not Solve 2 Unknowns From 1 Equation, So Just Plot Options Here To Get The Right Answer And Verify If You Are Getting Integers As Values Of B And W.

7. There Are Two Persons Paul And Jay .Paul Lies On Monday, Tuesday, Wednesday And The Remaining Days He Speaks Truth. Jay Lies On Thursday, Friday, Saturday And The Remaining Days He Speaks Truth. Once They Meet Each Other, In Their Conversation Paul Says That Yesterday Is The Day One Among Those I Lie. Jay Also Says That Yesterday I Also Lie. What Is That Day?

A) Sunday. B) Tuesday. C) Thursday. D) Wednesday

[Thought Process: Now This Day Cannot Be Sunday Because In Monday Paul Speaks Truth And Sunday Everyone Tells Truth. So It Must Be Weekdays. Again, Tuesday Can Not Possible Because Monday And Tuesday Paul Speaks Truth. In Case Of Thrust Day, Paul Speaks Lie And Wednesday He Speaks True. And Joy Speaks Truth In Thursday And He Speak Lies In Wednesday. So, Thursday Is The Answer.

8. A Father Has 7 Penny’s With Him And 1 Water Melon Is For 1p, 2chickoos For 1p, 3 Grapes Foe 1p. He Has Three Sons. How Can He Share The Fruits Equally?

Ans: 1 Watermelon, 2chickoos, 1grape

9. (1/2) Of A Number Is 3 Times More Than The (1/6) Of The Same Number?

Ans: 9

10. There Are Two Pipes A And B. If A Filled 10 Liters In Hour B Can Fills 20 Liters In Same Time. Likewise B Can Fill 10, 20, 40, 80,160…. If B Filled In (1/16) Th Of A Tank In 3 Hours, How Much Time Will It Take To Fill Completely?

Ans: 7 Hours

11.A certain pump can drain a full 375-gallon tank in 15 minutes. At this rate, how many more minutes would it take to drain a full 600-gallon tank?

(A) 9 (B) 15 (C) 18 (D) 24 (E) 25

12. If n is an even integer, which of the following must be an odd integer?

(A) 3n-2 (B) 3(n+1) (C)n-2 (D)n/3 (E)n^2

13. Cindy has a collection of 80 records. If 40 percent of her records are jazz records, and the rest are blues records, how many blues records does she have?

(A) 32
(B) 40
(C) 42
(D) 48
(E) 50

14. Express 2,750,389 in scientific notation.

(A) 27.50389 x 105
(B) 275.0389 x 103
(C) 27.50389 x 106
(D) 0.2750389 x 107
(E) 2.750389 x 106

15. A rectangle and a triangle have equal areas. The length of the rectangle is 12 inches, and its width is 8 inches. If the base of the triangle is 32 inches, what is the length, in inches, of the altitude drawn to the base?

(A) 6
(B) 8
(C) 9
(D) 12
(E) 16

16. If the area of a triangle is 24 and its base is 6, what is the length of the altitude to that base?

(A)3 (B)6 (C)8 (D)10 (E)unknown

17.Lenny's average score after 3 tests is 88. What score on the 4th test would bring Lenny's average up to exactly 90?

(A)92 (B)93 (C)94 (D)95 (E)96

18. If an integer is divisible by 6 and by 9, then the integer must be divisible by which of the following?

A. 12
B. 18
C. 24
D. 36
E. 54

19.If Jeff and Jimmy have less than 22 dollars between them, and Jeff has 8 dollars, which of the following could be the number of dollars that Jimmy has?
I.12 II. 14 III. 16

A. I only
B. III only
C. I & III.
D. I & II
E. Neither I, II, nor III are correct

20.Stephanie drove at an average rate of 50 miles per hour for two hours and then increased her average rate by 50% for the next 3 hours. Her average rate of speed for the 5 hours was t miles per hour. What is the value of t?

A. 55 mph
B. 60 mph
C. 65 mph
D. 70 mph
E. 75 mph

21. How many complete tanks of water, each with a capacity of 3 cubic meters, are needed to fill an empty cylindrical tank whose height is 3 meters and whose base has a radius of 2 meters?

A) 12 B) 13 C) 14 D) 15 E) 16

22. Any serious policy discussion about acceptable levels of risk in connection with explosions is not well served if the participants fail to use the word “explosion” and use the phrase “energetic disassembly” instead. In fact, the word “explosion” elicits desirable reactions, such as a heightened level of attention, whereas the substitute phrase does not. Therefore, of the two terms, “explosion” is the one that should be used throughout discussions of this sort.

Which of the following is an assumption on which the argument above depends?

(A) In the kind of discussion at issue, the advantages of desirable reactions to the term “explosion” outweigh the drawbacks, if any, arising from undesirable reactions to that term.
(B) The phrase “energetic disassembly” has not so far been used as a substitute for the word “explosion” in the kind of discussion at issue.
(C) In any serious policy discussion, what is said by the participants is more important than how it is put into words.
(D) The only reason that people would have for using “energetic disassembly” in place of “explosion” is to render impossible any serious policy discussion concerning explosions.
(E) The phrase “energetic disassembly” is not necessarily out of place in describing a controlled rather than an accidental explosion

23. A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?

(A) 2 (B) 2 ½ (C) 3 (D) 3 ½ (E) 4

24. To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from.
(A) 96 (B)98 (C)98.5 (D) 94 (E)100

25. A student can select one of 6 different mathematics books, one of 3 different chemistry books and one of 4 different science books. In how many different ways can a student select a book of mathematics, a book of chemistry and a book of science?

A) 14 (B)12 (C)72 (D) 74 (E)76

2011 TCS Technical Interview Questions:-

• What does static variable mean?
• What is a pointer?
• What is a structure?
• What are the differences between structures and arrays?
• In header files whether functions are declared or defined?
• What are the differences between malloc() and calloc()?
• What are macros? what are its advantages and disadvantages?
• Difference between pass by reference and pass by value?
• What is static identifier?
• Where are the auto variables stored?
• Where does global, static, local, register variables, free memory and C Program instructions get stored?
• Difference between arrays and linked list?
• What are enumerations?
• What is a class?
• What is an object?
• What is the difference between an object and a class?
• What is the difference between class and structure?
• What is public, protected, private?
• What are virtual functions?
• What is friend function?
• What is a scope resolution operator?
• What do you mean by inheritance?
• What is abstraction?
• What is a data structure?
• What does abstract data type means?
• Evaluate the following prefix expression " ++ 26 + - 1324" (Similar types can be asked)
• Convert the following infix expression to post fix notation ((a+2)*(b+4)) -1 (Similar types can be asked)
• How is it possible to insert different type of elements in stack?
• Stack can be described as a pointer. Explain.
• Write a Binary Search program
• What is the difference between an Abstract class and Interface?
• What is user defined exception?
• What do you know about the garbage collector?
• What is the difference between java and c++?
• In an HTML form I have a button which makes us to open another page in 15 seconds. How will you do that?
• What is the difference between process and threads?
• What is update method called?
• Have you ever used HashTable and Directory?
• What are statements in Java?
• What is RMI?
• Explain about RMI Architecture?
• What are Servelets?
• What is the use of servlets?
• Explain RMI Architecture?
• How will you pass values from HTML page to the servlet?
• How do you load an image in a Servelet?
• What is purpose of applet programming?
• How will you communicate between two applets?
• What are the basic functions of an operating system?
• Explain briefly about, processor, assembler, compiler, loader, linker and the functions executed by them.
• What are the difference phases of software development? Explain briefly?
• Differentiate between RAM and ROM?
• What is DRAM? In which form does it store data?
• What is cache memory?
• What is hard disk and what is its purpose?
• Differentiate between Complier and Interpreter?
• What are the different tasks of Lexical analysis?
• What are the different functions of Syntax phase, Sheduler?

TCS Placement Paper January 2011:-
Writen Test:-

1. (1/2) of a number is 3 more than the (1/6) of the same number?

a) 6
b) 7
c) 8
d) 9

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. (At the end of first hour, B has 10 liters, second hour it has 20 liters and so on). If tank B is 1/32 filled of the 21 hours, what is total duration of hours required to fill it completely?

a) 26
B) 25
c) 5
d) 27

3. Smita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number of cubes needed to make a hollow cube looking of the same shape?

a) 98
b)104
c)100
d) 61

4. A lady has fine gloves and hats in her closet- 25blue, 7 red, and 9 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?

5. A game is played between 2 players and one player is declared as winner. All the winners from first round are played in second round. All the winners from second round are played in third round and so on. If 8 rounds are played to declare only one player as winner, how many players are played in first round?

a) 256
b) 512
c) 64
d) 128

6. 1. There is 7 friends (A1, A2, A3....A7).If A1 have to have shake with all without repeat. How many handshakes possible?
a) 6
b) 21
c) 28
d) 7

7. 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

8. 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

9. 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.

10. 3 persons a, b ,c were there A always says truth lies on Monday, Tuesday,& Wednesday. but C lies on thrusday, Friday & Saturday .one day A said" that B & C said to A that” B said “yesterday way one of the days when I lies”, C said that” yesterday way one of the days when I lies too". then which day was that?
a) Sunday
b) Thursday
c) Saturday
d) Tuesday

11. By using 1,2,3,4,5,how many 5 digit no. can be formed which is divisible by 4,repetation of no. is allowed??

12. 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 coins 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 can be a 0-move or a 1-move.
C) In order to win, Alice's first move should be a 1-move.
D) Alice has no winning strategy.

13. 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) 4/9
B) 1/9
C) 2/3
D) 5/3

14. 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

15. 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) B only
B) Neither A nor B
C) A only
D) Both A and B

16. 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?

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 ball is maximized. This maximum probability is

18. One grandfather has three grandchildren, two of their age difference is 3, eldest child age is 3 times youngest child’s age and eldest child’s age is two times of sum of other two children. What is the age of eldest child?

19.  In a school, for a student out of 100 he got 74 of average for 7 subjects and he got 79 marks in the 8th subject. what is the average of all the subject?

a)76.251 b)80.25 c)74.265 d)74.625

20.  3 persons a,b,c were there A always says truth,B lies on Monday,tusday,& Wednesday.but C lies on thrusday,Friday & saturday .one day A said”that B & C said to A that” B said “yesterday way one of the days when I lies”,C said that”yesterday way one of the days when I lies too”.then which day was that?
a)Sunday b)Thursday c)Saturday d)Tuesday

21. Which is the smallest no which divides 2880 and gives a perfect square?

a)4 b)9 c)3 d)5

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)57 b)56 c)59 d)58

23.  how many 13 digit numbers are possible by using the digits 1,2,3,4,5 which are divisible by 4 if repetition of digits is allowed?

24.  By using 1,2,3,4,5,how many 5 digit no. can be formed which is divisible by 4,repetation of no. is allowed??

25.  Form 8 digit numbers from by using 1, 2,3,4,5 with repetition is allowed and must be divisible by4?

26.  How many of 14 digit numbers we can make with 1,2,3,4,5 that are divisible by 4. Repetitions allowed.

27. Six friends decide to share a big cake. Since all of them like the cake, they begin quarreling who gets to first cut and have a piece of the cake. One friend suggests that they have a blindfold friend choose from well shuffled set of cards numbered one to six. You check and find that this method works as it should simulating a fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfold and throwing a die. You note that the number shown by the method of picking up a card and throwing a real world die, sums to a number between 2 and 12. Which total would be likely to appear more often – 8,9 or 10?

a) 8 b)All are equally likely c)9 d)10

28. 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

29. 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

30. 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

31. 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.

32. 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

33. 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

34. 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.

35. 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

36. 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


37.12 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)

38. 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

39. 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)**

40. Amal bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what Amal had paid. What % of the total amount paid by Amal was paid for pens?

a) 37.5% 
b) 62.5%
c) 50%
d) None of these

TCS Placement Paper December 2010:-
Writen Test:-

Q 1: 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

Ans: 22+log 2 base 8=22+4=26

Note: The question arise more than 1 time.

Ques 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

Note: For this type of Questions, follow this:
--At least- I'st half are true, Last half are false
--Exactly- Last second one is true or (N-1)th Statement is true
--Almost- All are true.

Ques 3: 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 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 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 those the answer you got.

Ques4: 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?

For this type question you should follow d step of basic math that will helpful you get enough time from  that.
12 prog 12 line 12 min
1 prog 12 line 12*12
1 1 12*12/12
72 1 12*12/(12*72)
72 72 12*12*72/(12*72)

Ans:12

Note: This question appears 3 times in our question but app is different please follow basic rule think it it is very very easy.

Ques 5: 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)

Ques 6: 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

Note: Remember it I don't know the logic

Ques 7: 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

Ques 8: 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

Ques 9 )The age of the two friends were in the ration of 6:5.If the sum of their ages is 66.Then after how many years their ratio will become 7:6?

a)11 b)6 c)10 d)12

Ques 10) The age of the two friends were in the ration of 2:3.If the sum of their ages is 55.Then after how many years their ratio will become 4:5?

a)11 b)33 c)22 d)44

Ques 11)A volume of 10936 l water is in a container of sphere.How many semisphere of volume 4l each will be required to tranfer all the water into the small semispheres?

a)2812 b)8231 c)2734 d)4222

Ques 12)A person ismanufacturing a house.He bought 20 ropes of wire which has a density of 300 Kg/m3.The height of the building to be constructed is 40 m.If the capacity of the current passed in the wire is 20 A and the voltage capacity is 80 Volts.Then what will be the opposing force to the current if the wire is used ?

a)2 b)4 c)8 d)1600

Ques 13)A horse chases a pony 2 hours after the pony runs.Horse takes 3 hours to reach the pony.If the average speed of the horse is 81Kmph.Then what is the average speed of the pony?

a)46.4 b)51 c)53.4 d)48.6

Ques 14)The difference between two no is 9 and the product of the two is 14.What is the square of their sum?

a)120 b)130 c)137 d)145

Ques 15) 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

Ques 16)A man goes 50Km north , then turned left walked 40Km, then turned right ? In which direction he is?

a)North b)South c)East d)West

Ques 16)In T.Nagar the building were numbered from 1 to 100.Then how many 4’s will be present in the numbers?

a)18 b)19 c)20 d)21

Ques 17)In T.Nagar the building were numbered from 1 to 100.Then how many 6’s will be present in the numbers?

a)18 b)19 c)20 d)21

Ques 18)In T.Nagar the building were numbered from 1 to 100.Then how many 1’s will be present in the numbers?

a)18 b)19 c)20 d)21

Ques 19)In T.Nagar the building were numbered from 1 to 100.Then how many 0’s will be present in the numbers?

a)18 b)19 c)20 d)11

Ques 20) 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.

20.72 b) 5.18 c) 238.25 d) 6.18

Ques 21) 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.

Ques 22) A man goes north 37km.turns left goes 2km.turns right goes 17km.turns right goes 2km. find distance b/w starting ending point.

a) 54 b) 27 c) 81 d) 67

Ques 23) If there are 30 cans out of them one is poisoned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mices are required to find the poisoned can?

a) 3 b) 2 c) 6 d) 1

Ques 24) If a and b are mixed in 3:5 ration and b and c are mixed in 8:5 ration if the final mixture is 35 liters, find the amount of b?

A) 13.34 b) 15.73 c) 16.73 d) 9.45

Ques 25) If we subtract a number with y, we get 4 increase of number, once it got divided by y itself... Find that number??

A) 13 b) 12 c) 14 d) 11

Ques 26) It is the class with the seating arrangement in 4 rows and 8 columns. When the teacher says 'start' the girl who is sitting in first row and first column will say 1, then the next girl sitting behind her will say 4, the next girl sitting behind that girl will say 7, in a particular order each girl is telling a number, the following girls told 10, 13 next turn is yours what u will say?

a) 15 b) 17 c) 14 d) 16

Ques 27) It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same color?

A) 2 b) 3 c) 48 d) 25

Ques 28) If the Valentine’s Day in 2005 falls on Monday, then on which day will the Valentine’s Day fall on 2010?

A) Saturday b) Thursday c) Wednesday d) Sunday

Ques 29). A person run from A to B.He took ¼ of the time less to reach B when compare to run at normal Speed.Then how many percentage he has increased his speed?

a)40 b)44.4 c)33.3 d)22.2

Ques 30). An athlete decides to run the same distance in 1/4th less time that she usually took. By how much percent will she have to increase her average speed?

a)40 b)44.4 c)33.3 d)22.2

Ques 31). In a building there are 5 rooms.Each having a equal area .The length of the room is 4m and breadht is 5 m.The height of the rooms are 2m.If 17 bricks are needed to make a square meter then how many bricks are needed to make the floor of a particular room?

a)320 b)380 c)340 d)300

Ques 32). One man want to build a wall .The length and breadth of the wall are 20 and 30 respectively. He need 35 bricks for one square centimeter then how many bricks he need?

a)21,500 b)30,000 c)21,000 d)20,000

Ques 33). In a hotel we can order two types of varities,but we can make 6 more variteis in home.One can choose the four varities with two from hotel as must.Find how many ways one can order.

a)14 b)15 c)56 d)28

Ques 34). If a pipe can fill the tank within 6hrs.But due to leak it takes 30 min more.Now the tank is full then how much time will it take to empty the tank throught the leak.?

a)78 b)56 c)66 d)59

Ques 35).The bacteria has the probability of split into 3 and probability to die is 1/3rd of the total bacteria.Let the probability is P.Some of them survived with probability 1/5.Then which among the following relation is true?
a)P=1/3+1/5*3 b)P=1/5*(1/8-3)

Ques 36). There is a bacteria which has the probability of die 1/3 of its total number or it may tripled. Find out the probability

A. P=1/3+(2/3*p^3) B. P=2/3+(2/3*p^3) C. P=2/3+(1/3*p^3) D P=2/3+(2/3*p^3)

Ques 37) In T.Nagar the building were numbered from 1 to 100.Then how many 4’s will be present in the numbers?

a)18 b)19 c)20 d)21

Ques 38)Amrith told to Anand in front of a Photo that “He is the son of my father’s son”.Find who is in the picture if amrith have no brothers and sisters.

a)Amrith himself b)Amrith’s Uncle c)Amrith’s Father d)Amrith’s son

Ques 39) One person has no siblings and says,” the guy in the photo is the only son of my father ‘s son”. What is the relation of the guy to the person?

Ques 40) One grand father has 3 grand children two of the age difference is 3.Eldest child age is 3 times the youngest childs age and the eldest child age is two year more than the sum of other two children. Find what is the age of the elders child?

a)18 b)22 c)30 d)10.
 

TCS HR Interview Questions:-

 Introduce Yourself ?
Introduction is easy for every one . The main aim of that question is, the interviewer wants to know how much you really know about yourself . In job interview you must sell what the buyer is buying. This is the single most important strategy in job hunting.

How to make an effective introduction? Recommended Answer 
Why should I take you in TCS?

Who inspired you to become an Engineer?

There's a bond of 2 years ....... u' re ok with it?

You'll be sent to any part of the country for work...... will you be ok with that?

Have you discussed about your job with your family?

Why you want to join TCS?
Example : I heard from my friends that TCS has a very good work environment where.................
 What do you know about TCS as a company?
Best sources for researching your target company: annual reports, the corporate newsletter, contacts you know at the company or its suppliers, advertisements, articles about the company in the trade press.
 Why do you want to join TCS and not any other company?

Do you have any questions for me?

TCS MODEL TEST

TCS New Pattern Placement paper 2013

As you already aware of the fact that TCS has changed the database of questions for its aptitude test.  The questions below give you an overview of the models to be prepared.  But don't depend on these models only.  We solved these questions only as an indicative purpose.  You are requested to go through all the arithmetic topics given in this site so that you become confident of sitting for TCS or any other written test.  All the best... The question below have been taken from https://campus.tcs.com/OpenSeesame/

1.  If 3y + x > 2 and x + 2y≤3, What can be said about the value of y?
A. y = -1          B. y >-1           C. y <-1           D. y = 1
Answer: B

Multiply the second equation with -1 then it will become - x - 2y≥ - 3.  Add the equations.  You will get y > -1.

2. If the price of an item is decreased by 10% and then increased by 10%, the net effect on the price of the item is
A. A decrease of 99%
B. No change
C. A decrease of 1%
D. An increase of 1%
Answer: C

If a certain number is increased by x% then decreased by x% or vice versa, the net change is always decrease.  This change is given by a simple formula −(x10)2= −(1010)2= −1%.  Negitive sign indicates decrease.

3. If m is an odd integer and n an even integer, which of the following is definitely odd?
A. (2m+n)(m-n)
B. (m+n2)+(m−n2)
C. m2+mn+n2
D. m +n
Answer: C and D (Original Answer given as D)

You just remember the following odd ± odd = even; even ± even = even; even ± odd = odd
Also odd x odd = odd; even x even = even; even x odd = even.

4.  What is the sum of all even integers between 99 and 301?
A. 40000
B. 20000
C. 40400
D. 20200
Answer: D

The first even number after 99 is 100 and last even number below 301 is 300.  We have to find the sum of even numbers from 100 to 300.  i.e., 100 + 102 + 104 + ............... 300.
Take 2 Common.  2 x ( 50 + 51 + ...........150)
There are total 101 terms in this series.  So formula for the sum of n terms when first term and last term is known is n2(a+l)
So 50 + 51 + ...........150 = 1012(50+150)
So 2 x 1012(50+150) = 20200

5. There are 20 balls which are red, blue or green.  If 7 balls are green and the sum of red balls and green balls is less than 13, at most how many red balls are there?
A. 4
B. 5
C. 6
D. 7
Answer: B

Given R + B + G = 17; G = 7; and R + G < 13.  Substituting G = 7 in the last equation, We get R < 6.  So maximum value of R = 6

6.  If n is the sum of two consecutive odd integers and less than 100, what is greatest possibility of n?
A. 98
B. 94
C. 96
D. 99
Answer : C

We take two odd numbers as (2n + 1) and (2n - 1).
Their sum should be less than 100. So (2n + 1) + (2n - 1) < 100 ⇒ 4n < 100.
The largest 4 multiple which is less than 100 is 96

7. x2 < 1/100, and x < 0 what is the highest range in which x can lie?
A. -1/10 < x < 0
B. -1 < x < 0
C. -1/10 < x < 1/10
D. -1/10 < x
Answer: A

Remember:
(x - a)(x - b) < 0 then value of x lies in between a and b.
(x - a)(x - b) > 0 then value of x does not lie inbetween a and b. or ( −∞, a) and (b, −∞) if a < b
x2 < 1/100 ⇒
(x2−1/100)<0⇒(x2−(1/10)2)<0⇒(x−1/10)(x+1/10)<0
So x should lie inbetween - 1/10 and 1/10.  But it was given that x is -ve. So x lies in -1/10 to 0

8.  There are 4 boxes colored red, yellow, green and blue.  If 2 boxes are selected, how many combinations are there for at least one green box or one red box to be selected?
A. 1
B . 6
C. 9
D. 5
Answer: 5

Total ways of selecting two boxes out of 4 is 4C2 = 6.  Now, the number of ways of selecting two boxes where none of the green or red box included is only 1 way.  (we select yellow and blue in only one way).  If we substract this number from total ways we get 5 ways.

9. All faces of a cube with an eight - meter edge are painted red.  If the cube is cut into smaller cubes with a two - meter edge, how many of the two meter cubes have paint on exactly one face?
A. 24
B. 36
C. 60
D. 48
Answer : A

If there are n cubes lie on an edge, then total number of cubes with one side painting is given by 6×(n−2)2.  Here side of the bigger cube is 8, and small cube is 2.  So there are 4 cubes lie on an edge. Hence answer = 24

10. Two cyclists begin training on an oval racecourse at the same time.  The professional cyclist completes each lap in 4 minutes; the novice takes 6 minutes to complete each lap.  How many minutes after the start will both cyclists pass at exactly the same spot where they began to cycle?
A. 10
B. 8
C. 14
D. 12
Answer: D

The faster cyclyst comes to the starting point for every 4 min so his times are 4, 8, 12, .........  The slower cyclist comes to the starting point for every 6 min so his times are 6, 12, 18, .........  So both comes at the end of the 12th min.

11. M, N, O and P are all different individuals; M is the daughter of N; N is the son of O; O is the father of P; Among the following statements, which one is true?
A. M is the daughter of P
B. If B is the daughter of N, then M and B are sisters
C. If C is the granddaughter of O, then C and M are sisters
D. P and N are bothers. 
Answer: B

From the diagram it is clear that If B is the daughter of N, then M and B are sisters.  Rectangle indicates Male, and Oval indicates Female.



12. In the adjoining diagram, ABCD and EFGH are squres of side 1 unit such that they intersect in a square of diagonal length (CE) = 1/2.  The total area covered by the squares is

A. Cannot be found from the information
B. 1 1/2
C. 1 7/8
D. None of these
Answer:  C

Let CG = x then using pythogerous theorem CG2+GE2=CE2
⇒  x2+x2=(1/2)2⇒2x2=1/4⇒x2=1/8
Total area covered by two bigger squares = ABCD + EFGE - Area of small square = 2 - 1/8 = 15/8


13. There are 10 stepping stones numbered 1 to 10 as shown at the side.  A fly jumps from the first stone as follows; Every minute it jumps to the 4th stone from where it started - that is from 1st it would go to 5th and from 5th it would go to 9th and from 9th it would go to 3rd etc.  Where would the fly be at the 60th minute if it starts at 1?
A. 1
B. 5
C. 4
D. 9
Answer : A

Assume these steps are in circular fashion.
Then the fly jumps are denoted in the diagram.  It is clear that fly came to the 1st position after 5th minute.  So again it will be at 1st position after 10th 15th .....60th. min.

So the fly will be at 1st stone after 60th min.

 

14. What is the remainder when 617+1176  is divided by 7?
A. 1
B. 6
C. 0
D. 3
Answer: C

617 = (7−1)17 =
17C0.717−17C1.716.11.....+17C16.71.116−17C17.117

If we divide this expansion except the last term each term gives a remainder 0.  Last term gives a remainder of - 1.

Now From Fermat little theorem, [ap−1p]Rem=1
So [1767]Rem=1

Adding these two remainders we get the final remainder = 0

15. In base 7, a number is written only using the digits 0, 1, 2, .....6.  The number 135 in base 7 is 1 x 72 + 3 x 7 + 5 = 75 in base 10.  What is the sum of the base 7 numbers 1234 and 6543 in base 7.
A. 11101
B. 11110
C. 10111
D. 11011
Answer: B

In base 7 there is no 7.  So to write 7 we use 10.  for 8 we use 11...... for 13 we use 16, for 14 we use 20 and so on.
So from the column d, 4 + 3 = 7 = 10, we write 0 and 1 carried over.  now 1 + 3 + 4 = 8 = 11, then we write 1 and 1 carried over.  again 1 + 2 + 5 = 8 = 11 and so on



16. The sequence {An} is defined by A1 = 2 and An+1=An+2n what is the value of A100
A. 9902
B. 9900
C. 10100
D. 9904
Answer: A
We know that A1 = 2 so A2=A1+1=A1+2(1)=4
A3=A2+1=A2+2(2)=8
A4=A3+1=A3+2(3)=14
So the first few terms are 2, 4, 8, 14, 22, ......
The differences of the above terms are 2, 4, 6, 8, 10...
and the differences of differences are 2, 2, 2, 2.  all are equal.  so this series represents a quadratic equation.
Assume  An = an2+bn+c
Now A1 = a + b + c = 2
A2 = 4a + 2b + c = 4
A3 = 9a + 3b + c = 8
Solving above equations we get a = 1, b = - 1 and C = 2
So substituting in An = n2+bn+c = n2−n+2
Substitute 100 in the above equation we get 9902.

17.Find the number of rectangles from the adjoining figure (A square is also considered a rectangle)

A. 864
B. 3276
C. 1638
D. None

Answer: C

To form a rectangle we need two horizontal lines and two vertical lines.  Here there are 13 vertical lines and 7 horizontal lines.  The number of ways of selecting 2 lines from 13 vertical lines is 13C2 and the number of ways of selecting 2 lines from 7 horizontals is 7C2. So total rectangles = 7C2x13C2

18. A, B, C and D go for a picnic.  When A stands on a weighing machine, B also climbs on, and the weight shown was 132 kg.  When B stands, C also climbs on, and the machine shows 130 kg.  Similarly the weight of C and D is found as 102 kg and that of B and D is 116 kg.  What is D's weight
A. 58kg
B. 78 kg
C. 44 kg
D. None
Answer : C

Given A + B = 132; B + C = 130; C + D = 102, B + D = 116
Eliminate B from 2nd and 4th equation and solving this equation and 3rd we get D value as 44.

19.  Roy is now 4 years older than Erik and half of that amount older than Iris.  If in 2 years, roy will be twice as old as Erik, then in 2 years what would be Roy's age multiplied by Iris's age?
A. 28
B. 48
C. 50
D. 52
Answer: 48

20. X, Y, X and W are integers.  The expression X - Y - Z is even and the expression Y - Z - W is odd.  If X is even what must be true?
A. W must be odd
B. Y - Z must be odd
C. W must be odd
D. Z must be odd
Answer: A or C (But go for C)

21.  Mr and Mrs Smith have invited 9 of their friends and their spouses for a party at the Waikiki Beach resort.  They stand for a group photograph.  If Mr Smith never stands next to Mrs Smith (as he says they are always together otherwise). How many ways the group can be arranged in a row for the photograph?
A. 20!
B. 19! + 18!
C. 18 x 19!
D. 2 x 19!
Answer: C

22.  In a rectanglular coordinate system, what is the area of a triangle whose vertices whose vertices have the coordinates (4,0), (6, 3) adn (6 , -3)
A. 6
B. 7
C. 7.5
D. 6.5
Answer: A

23. A drawer holds 4 red hats and 4 blue hats.  What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?
A. 1/2
B. 1/8
C. 1/4
D. 3/8
Answer: B

24. In how many ways can we distribute 10 identical looking pencils to 4 students so that each student gets at least one pencil?
A. 5040
B. 210
C. 84
D. None of these
Answer: C

25. The prime factorization of intezer N is A x A x B x C, where A, B and C are all distinct prine intezers.  How many factors does N have?
A. 12
B. 24
C. 4
D. 6
Answer: A

26. Tim and Elan are 90 km from each other.they start to move each other simultanously tim at speed 10 and elan 5 kmph. If every hour they double their speed what is the distance that Tim will pass until he meet Elan 
A. 45
B. 60
C. 20
D. 80
Answer: B

27. A father purchases dress for his three daughter. The dresses are of same color but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress.
A.  2/3
B.  1/3
C.  1/6
D.  1/9
Answer: B

28. N is an integer and N>2, at most how many integers among N + 2, N + 3, N + 4, N + 5, N + 6,  and N + 7 are prime integers?
A. 1
B. 3
C. 2
D. 4
Answer: C

29. A turtle is crossing a field.  What is the total distance (in meters) passed by turtle? Consider the following two statements
(X) The average speed of the turtle is 2 meters per minute
(Y) Had the turtle walked 1 meter per minute faster than his average speed it would have finished 40 minutes earlier
A. Statement X alone is enough to get the answer
B. Both statements X and Y are needed to get the answer
C. Statement Y alone is enough to get the answer
D. Data inadequate
Answer: B

30. Given the following information, who is youngest?
C is younger than A; A is talled than B
C is older than B; C is younger than D
B is taller than C; A is older than D
A. D
B. B
C. C
D. A
Answer: B

31. If P(x) = ax4+bx3+cx2+dx+e has roots at x = 1, 2, 3, 4 and P(0) = 48, what is P(5)
A. 48
B. 24
C. 0
D. 50
Answer: A