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List of all download google placement papers in ms word and pdf format for job interview. Click Here View Job List. This page will help you to get all details about download google placement papers in ms word and pdf format for job interview. Download google placement papers in PDF and Ms word format. Latest and google last 5 years placement papers with solutions pdf download for campus job.

Google Placement Paper : Google Placement Paper Latest 2013

An interview is a final step for selection to any job. Eligibility for giving interview means that the candidate have right aptitude and knowledge for the job, he has required knowledge about the subject. A one-one communication in the form of interview makes the decision final that whether the candidate should be selected for the job or not.

Different types of interview sessions

1) Questions asked on the basis of your CV and past academics background.

2) Interview by a number of people where the candidate is pressurized by asking number of question during the same time.

3) Interview on doing and explaining some task on some traits like leadership, management etc.

General Tips before interview

Try to appear your best at the Interview. Your appearance should convey that you have taken the interview seriously. Do not try to turn up in the interview in a manner that does not suit you. Some basics in grooming will help.

a. Well Groomed Hair

b. Well Pressed Shirt

c. Polished Shoes

2. Know about the company. You should learn as much as you can about the company. A good place to start is the company,s website. If you have been referred through a friend also have a frank discussion with him or her. Also, do a google search on the company to understand what others are saying about the company.

3. Answer clearly and directly. Spell out your ideas as clearly as you can. Also try to substantiate your ideas with examples. Don,t be overly wordy and try to keep your answers to the point. Do not try to deviate too much from the question.

4. Do not be argumentative. Present your viewpoint and be professional. If you do not agree with something the Interviewer has said do not spurn it as invalid. Learn to understand their point of view even if it clashed with your own. This does not mean that you need to accept their point of view.

5. Be prepared with questions for the Interviewer. Most interviewers will give you a chance to ask questions. Use this opportunity to show your knowledge and interest in the company. Also this is a good opportunity to clear any doubts that you have.

6. Address the Interviewer politely. It is always polite to refer to the Interviewer as SIR or Maam. You can also address them their Surname (Mr. XXX or Mrs. XXX). Do not use terms such as Honey, Girl, Dude, Yaar etc.

7. Be Confident. Be confident, you have prepared well and this should show in your confidence level in the interview.

Preparation tips for interview round

1) Read your resume completely.

2) Prepare question which can be asked by the interview panel. Questions related to your academic records and your hobbies are generally asked by the interview panel.

3) Read about the organisation for which you are interviewed, go through the official website of the organisation once completely and have a look on the products and services offered by the company.

4) Rehearse your interview round, gave interview in front of your teacher or an interview expert few times before the actual interview.

"Be punctual - Arrive on time better half an hour earlier. Have a positive body language, good eye contact, wear neat and clean clothes"

Common Interview Questions

Tell Me a Little About Yourself?

Ans - This is the most general and probably the most difficult question, as one has to cover up the entire life story within a couple of minutes.

What,s Your Biggest Weakness?

Ans - This is one of the most common questions that every job applicant face and by this, the Interviewer wants to check your challenging ability to face different situation.

What experience do you have in this field?

Ans - Mention specific information related to the position you are attaining the interview otherwise tell him that you are a fresher and have just completed your academics.

Are you a team player?

Ans - Working together as a team is the key point in achieving greater goal than anyone could have achieved individually.

Different types of interview sessions

1) Questions asked on the basis of your CV and past academics background.

2) Interview by a number of people where the candidate is pressurized by asking number of question during the same time.

3) Interview on doing and explaining some task on some traits like leadership, management etc.

General Tips before interview

Try to appear your best at the Interview. Your appearance should convey that you have taken the interview seriously. Do not try to turn up in the interview in a manner that does not suit you. Some basics in grooming will help.

a. Well Groomed Hair

b. Well Pressed Shirt

c. Polished Shoes

2. Know about the company. You should learn as much as you can about the company. A good place to start is the company,s website. If you have been referred through a friend also have a frank discussion with him or her. Also, do a google search on the company to understand what others are saying about the company.

3. Answer clearly and directly. Spell out your ideas as clearly as you can. Also try to substantiate your ideas with examples. Don,t be overly wordy and try to keep your answers to the point. Do not try to deviate too much from the question.

4. Do not be argumentative. Present your viewpoint and be professional. If you do not agree with something the Interviewer has said do not spurn it as invalid. Learn to understand their point of view even if it clashed with your own. This does not mean that you need to accept their point of view.

5. Be prepared with questions for the Interviewer. Most interviewers will give you a chance to ask questions. Use this opportunity to show your knowledge and interest in the company. Also this is a good opportunity to clear any doubts that you have.

6. Address the Interviewer politely. It is always polite to refer to the Interviewer as SIR or Maam. You can also address them their Surname (Mr. XXX or Mrs. XXX). Do not use terms such as Honey, Girl, Dude, Yaar etc.

7. Be Confident. Be confident, you have prepared well and this should show in your confidence level in the interview.

Preparation tips for interview round

1) Read your resume completely.

2) Prepare question which can be asked by the interview panel. Questions related to your academic records and your hobbies are generally asked by the interview panel.

3) Read about the organisation for which you are interviewed, go through the official website of the organisation once completely and have a look on the products and services offered by the company.

4) Rehearse your interview round, gave interview in front of your teacher or an interview expert few times before the actual interview.

"Be punctual - Arrive on time better half an hour earlier. Have a positive body language, good eye contact, wear neat and clean clothes"

Common Interview Questions

Tell Me a Little About Yourself?

Ans - This is the most general and probably the most difficult question, as one has to cover up the entire life story within a couple of minutes.

What,s Your Biggest Weakness?

Ans - This is one of the most common questions that every job applicant face and by this, the Interviewer wants to check your challenging ability to face different situation.

What experience do you have in this field?

Ans - Mention specific information related to the position you are attaining the interview otherwise tell him that you are a fresher and have just completed your academics.

Are you a team player?

Ans - Working together as a team is the key point in achieving greater goal than anyone could have achieved individually.

Google Placement Paper : Google Placement Paper Telephonic Interview 2012

Google Interview Questions: Product Marketing Manager

1) Why do you want to join Google?

2) What do you know about Google’s product and technology?

3) If you are Product Manager for Google’s Adwords, how do you plan to market this?

4) What would you say during an AdWords or AdSense product seminar?

5) Who are Google competitors, and how does Google compete with them?

6) Have you ever used Google’s products? Gmail?

7) What’s a creative way of marketing Google’s brand name and product?

8) If you are the product marketing manager for Google’s Gmail product, how do you plan to market it so as to achieve 100 million customers in 6 months?

Google Interview Questions: Product Manager

1) How would you boost the GMail subscription base?

2) What is the most efficient way to sort a million integers?

3) How would you re-position Google’s offerings to counteract competitive threats from Microsoft?

4) How many golf balls can fit in a school bus?

5) You are shrunk to the height of a nickel and your mass is proportionally reduced so as to maintain your original density. You are then thrown into an empty glass blender. The blades will start moving in 60 seconds. What do you do?

6) How much should you charge to wash all the windows in Seattle?

7) How would you find out if a machine’s stack grows up or down in memory?

8) Explain a database in three sentences to your eight-year-old nephew.

9) How many times a day does a clock’s hands overlap?

10) You have to get from point A to point B. You don’t know if you can get there. What would you do?

11) Imagine you have a closet full of shirts. It’s very hard to find a shirt. So what can you do to organize your shirts for easy retrieval?

12) Every man in a village of 100 married couples has cheated on his wife. Every wife in the village instantly knows when a man other than her husband has cheated, but does not know when her own husband has. The village has a law that does not allow for adultery. Any wife who can prove that her husband is unfaithful must kill him that very day. The women of the village would never disobey this law. One day, the queen of the village visits and announces that at least one husband has been unfaithful. What happens?

13) In a country in which people only want boys, every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is the proportion of boys to girls in the country?

14) If the probability of observing a car in 30 minutes on a highway is 0.95, what is the probability of observing a car in 10 minutes (assuming constant default probability)?

If you look at a clock and the time is 3:15, what is the angle between the hour and the minute hands? (The answer to this is not zero!)

15) Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it’s only strong enough to support two people at any given time. Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?

16) You are at a party with a friend and 10 people are present including you and the friend. your friend makes you a wager that for every person you find that has the same birthday as you, you get $1; for every person he finds that does not have the same birthday as you, he gets $2. would you accept the wager?

17) How many piano tuners are there in the entire world?

18) You have eight balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you find the ball that is heavier by using a balance and only two weighing?

19) You have five pirates, ranked from 5 to 1 in descending order. The top pirate has the right to propose how 100 gold coins should be divided among them. But the others get to vote on his plan, and if fewer than half agree with him, he gets killed. How should he allocate the gold in order to maximize his share but live to enjoy it? (Hint: One pirate ends up with 98 percent of the gold.)

20) You are given 2 eggs. You have access to a 100-story building. Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100th floor. Both eggs are identical. You need to figure out the highest floor of a 100-story building an egg can be dropped without breaking. The question is how many drops you need to make. You are allowed to break 2 eggs in the process.

Describe a technical problem you had and how you solved it.

21) How would you design a simple search engine?

22) Design an evacuation plan for San Francisco.

23) There’s a latency problem in South Africa. Diagnose it.

24) What are three long term challenges facing google?

Google Interview Questions: Software Engineer

1. Why are manhole covers round?

2. What is the difference between a mutex and a semaphore? Which one would you use to protect access to an increment operation?

3. A man pushed his car to a hotel and lost his fortune. What happened?

4. Explain the significance of “dead beef”.

5. Write a C program which measures the the speed of a context switch on a UNIX/Linux system.

6. Given a function which produces a random integer in the range 1 to 5, write a function which produces a random integer in the range 1 to 7.

7. Describe the algorithm for a depth-first graph traversal.

8. Design a class library for writing card games.

You need to check that your friend, Bob, has your correct phone number, but you cannot ask him directly. You must write a the question on a card which and give it to Eve who will take the card to Bob and return the answer to you. What must you write on the card, besides the question, to ensure Bob can encode the message so that Eve cannot read your phone number?

9. How are cookies passed in the HTTP protocol?

10. Design the SQL database tables for a car rental database.

11. Write a regular expression which matches a email address.

12. Write a function f(a, b) which takes two character string arguments and returns a string containing only the characters found in both strings in the order of a. Write a version which is order N-squared and one which is order N.

13. You are given a the source to a application which is crashing when run. After running it 10 times in a debugger, you find it never crashes in the same place. The application is single threaded, and uses only the C standard library. What programming errors could be causing this crash?

14. How would you test each one?

15. Explain how congestion control works in the TCP protocol.

16. In Java, what is the difference between final, finally, and finalize?

17. What is multithreaded programming? What is a deadlock?Write a function (with helper functions if needed) called to Excel that takes an excel column value (A,B,C,D…AA,AB,AC,… AAA..) and returns a corresponding integer value (A=1,B=2,… AA=26..).

18. You have a stream of infinite queries (ie: real time Google search queries that people are entering). Describe how you would go about finding a good estimate of 1000 samples from this never ending set of data and then write code for it.

19. Tree search algorithms. Write BFS and DFS code, explain run time and space requirements. Modify the code to handle trees with weighted edges and loops with BFS and DFS, make the code print out path to goal state.

20. You are given a list of numbers. When you reach the end of the list you will come back to the beginning of the list (a circular list). Write the most efficient algorithm to find the minimum # in this list. Find any given # in the list. The numbers in the list are always increasing but you don’t know where the circular list begins, ie: 38, 40, 55, 89, 6, 13, 20, 23, 36.

21. Describe the data structure that is used to manage memory. (stack)

22. What’s the difference between local and global variables?

23. If you have 1 million integers, how would you sort them efficiently? (modify a specific sorting algorithm to solve this)

24. In Java, what is the difference between static, final, and const. (if you don’t know Java they will ask something similar for C or C++).

25. Talk about your class projects or work projects (pick something easy)… then describe how you could make them more efficient (in terms of algorithms).

26. Suppose you have an NxN matrix of positive and negative integers. Write some code that finds the sub-matrix with the maximum sum of its elements.

27. Write some code to reverse a string.

Implement division (without using the divide operator, obviously).

28. Write some code to find all permutations of the letters in a particular string.

29. What method would you use to look up a word in a dictionary?

Imagine you have a closet full of shirts. It’s very hard to find a shirt. So what can you do to organize your shirts for easy retrieval?

30. You have eight balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you fine the ball that is heavier by using a balance and only two weighings?

31. What is the C-language command for opening a connection with a foreign host over the internet?

32. Design and describe a system/application that will most efficiently produce a report of the top 1 million Google search requests. These are the particulars: 1) You are given 12 servers to work with. They are all dual-processor machines with 4Gb of RAM, 4x400GB hard drives and networked together.(Basically, nothing more than high-end PC’s) 2) The log data has already been cleaned for you. It consists of 100 Billion log lines, broken down into 12 320 GB files of 40-byte search terms per line. 3) You can use only custom written applications or available free open-source software.

33. There is an array A[N] of N numbers. You have to compose an array Output[N] such that Output[i] will be equal to multiplication of all the elements of A[N] except A[i]. For example Output[0] will be multiplication of A[1] to A[N-1] and Output[1] will be multiplication of A[0] and from A[2] to A[N-1]. Solve it without division operator and in O(n).

34. There is a linked list of numbers of length N. N is very large and you don’t know N. You have to write a function that will return k random numbers from the list. Numbers should be completely random. Hint: 1. Use random function rand() (returns a number between 0 and 1) and irand() (return either 0 or 1) 2. It should be done in O(n).

35. Find or determine non existence of a number in a sorted list of N numbers where the numbers range over M, M>> N and N large enough to span multiple disks. Algorithm to beat O(log n) bonus points for constant time algorithm.

36. You are given a game of Tic Tac Toe. You have to write a function in which you pass the whole game and name of a player. The function will return whether the player has won the game or not. First you to decide which data structure you will use for the game. You need to tell the algorithm first and then need to write the code. Note: Some position may be blank in the game। So your data structure should consider this condition also.

37. You are given an array [a1 To an] and we have to construct another array [b1 To bn] where bi = a1*a2*…*an/ai. you are allowed to use only constant space and the time complexity is O(n). No divisions are allowed.

38. How do you put a Binary Search Tree in an array in a efficient manner. Hint :: If the node is stored at the ith position and its children are at 2i and 2i+1(I mean level order wise)Its not the most efficient way.

39. How do you find out the fifth maximum element in an Binary Search Tree in efficient manner. Note: You should not use use any extra space. i.e sorting Binary Search Tree and storing the results in an array and listing out the fifth element.

40. Given a Data Structure having first n integers and next n chars. A = i1 i2 i3 … iN c1 c2 c3 … cN.Write an in-place algorithm to rearrange the elements of the array ass A = i1 c1 i2 c2 … in cn

41. Given two sequences of items, find the items whose absolute number increases or decreases the most when comparing one sequence with the other by reading the sequence only once.

42. Given That One of the strings is very very long , and the other one could be of various sizes. Windowing will result in O(N+M) solution but could it be better? May be NlogM or even better?

43. How many lines can be drawn in a 2D plane such that they are equidistant from 3 non-collinear points?

Let’s say you have to construct Google maps from scratch and guide a person standing on

44. Gateway of India (Mumbai) to India Gate(Delhi). How do you do the same?

45. Given that you have one string of length N and M small strings of length L. How do you efficiently find the occurrence of each small string in the larger one?

46.

47. Given a binary tree, programmatically you need to prove it is a binary search tree.

You are given a small sorted list of numbers, and a very very long sorted list of numbers – so long that it had to be put on a disk in different blocks. How would you find those short list numbers in the bigger one?

48. Suppose you have given N companies, and we want to eventually merge them into one big company. How many ways are theres to merge?

49. Given a file of 4 billion 32-bit integers, how to find one that appears at least twice?

50. Write a program for displaying the ten most frequent words in a file such that your program should be efficient in all complexity measures.

51. Design a stack. We want to push, pop, and also, retrieve the minimum element in constant time.

52. Given a set of coin denominators, find the minimum number of coins to give a certain amount of change.

53. Given an array, i) find the longest continuous increasing subsequence. ii) find the longest increasing subsequence.

54. Suppose we have N companies, and we want to eventually merge them into one big company.

55. How many ways are there to merge?

56. Write a function to find the middle node of a single link list.

57. Given two binary trees, write a compare function to check if they are equal or not. Being equal means that they have the same value and same structure.

Implement put/get methods of a fixed size cache with LRU replacement algorithm.

58. You are given with three sorted arrays ( in ascending order), you are required to find a triplet ( one element from each array) such that distance is minimum.

59. Distance is defined like this : If a[i], b[j] and c[k] are three elements then distance=max(abs(a[i]-b[j]),abs(a[i]-c[k]),abs(b[j]-c[k]))” Please give a solution in O(n) time complexity

60. How does C++ deal with constructors and deconstructors of a class and its child class?

61. Write a function that flips the bits inside a byte (either in C++ or Java). Write an algorithm that take a list of n words, and an integer m, and retrieves the mth most frequent word in that list.

62. What’s 2 to the power of 64?

63. Given that you have one string of length N and M small strings of length L. How do you efficiently find the occurrence of each small string in the larger one?

64. How do you find out the fifth maximum element in an Binary Search Tree in efficient manner.

65. Suppose we have N companies, and we want to eventually merge them into one big company.

66. How many ways are there to merge?

There is linked list of millions of node and you do not know the length of it. Write a function which will return a random number from the list.

67. You need to check that your friend, Bob, has your correct phone number, but you cannot ask him directly. You must write a the question on a card which and give it to Eve who will take the card to Bob and return the answer to you. What must you write on the card, besides the question, to ensure Bob can encode the message so that Eve cannot read your phone number?

68. How long it would take to sort 1 trillion numbers? Come up with a good estimate.

Order the functions in order of their asymptotic performance: 1) 2^n 2) n^100 3) n! 4) n^n

There are some data represented by(x,y,z). Now we want to find the Kth least data. We say (x1, y1, z1) > (x2, y2, z2) when value(x1, y1, z1) > value(x2, y2, z2) where value(x,y,z) = (2^x)*(3^y)*(5^z). Now we can not get it by calculating value(x,y,z) or through other indirect calculations as lg(value(x,y,z)). How to solve it?

69. How many degrees are there in the angle between the hour and minute hands of a clock when the time is a quarter past three?

70. Given an array whose elements are sorted, return the index of a the first occurrence of a specific integer. Do this in sub-linear time. I.e. do not just go through each element searching for that element.

71. Given two linked lists, return the intersection of the two lists: i.e. return a list containing only the elements that occur in both of the input lists.

72. What’s the difference between a hashtable and a hashmap?

73. If a person dials a sequence of numbers on the telephone, what possible words/strings can be formed from the letters associated with those numbers?

74. How would you reverse the image on an n by n matrix where each pixel is represented by a bit?

75. Create a fast cached storage mechanism that, given a limitation on the amount of cache memory, will ensure that only the least recently used items are discarded when the cache memory is reached when inserting a new item. It supports 2 functions: String get(T t) and void put(String k, T t).

76. Create a cost model that allows Google to make purchasing decisions on to compare the cost of purchasing more RAM memory for their servers vs. buying more disk space.

77. Design an algorithm to play a game of Frogger and then code the solution. The object of the game is to direct a frog to avoid cars while crossing a busy road. You may represent a road lane via an array. Generalize the solution for an N-lane road.

78. What sort would you use if you had a large data set on disk and a small amount of ram to work with?

79. What sort would you use if you required tight max time bounds and wanted highly regular performance.

80. How would you store 1 million phone numbers?

81. Design a 2D dungeon crawling game. It must allow for various items in the maze – walls, objects, and computer-controlled characters. (The focus was on the class structures, and how to optimize the experience for the user as s/he travels through the dungeon.)

82. What is the size of the C structure below on a 32-bit system? On a 64-bit?

struct foo {

char a; char* b; };

Google Interview: Software Engineer in Test

1. Efficiently implement 3 stacks in a single array.

2. Given an array of integers which is circularly sorted, how do you find a given integer.

3. Write a program to find depth of binary search tree without using recursion.

4. Find the maximum rectangle (in terms of area) under a histogram in linear time.

5. Most phones now have full keyboards. Before there there three letters mapped to a number button. Describe how you would go about implementing spelling and word suggestions as people type.

6. Describe recursive mergesort and its runtime. Write an iterative version in C++/Java/Python.

7. How would you determine if someone has won a game of tic-tac-toe on a board of any size?

8. Given an array of numbers, replace each number with the product of all the numbers in the array except the number itself *without* using division.

9. Create a cache with fast look up that only stores the N most recently accessed items.

10. How to design a search engine? If each document contains a set of keywords, and is associated with a numeric attribute, how to build indices?

11. Given two files that has list of words (one per line), write a program to show the intersection.

Google Interview: Quantitative Compensation Analyst

How many resumes does Google receive each year for software engineering?

Anywhere in the world, where would you open up a new Google office and how would you figure out compensation for all the employees at this new office?

What is the probability of breaking a stick into 3 pieces and forming a triangle

Google Interview: Engineering Manager

You’re the captain of a pirate ship, and your crew gets to vote on how the gold is divided up. If fewer than half of the pirates agree with you, you die. How do you recommend apportioning the gold in such a way that you get a good share of the booty, but still survive?

1) Why do you want to join Google?

2) What do you know about Google’s product and technology?

3) If you are Product Manager for Google’s Adwords, how do you plan to market this?

4) What would you say during an AdWords or AdSense product seminar?

5) Who are Google competitors, and how does Google compete with them?

6) Have you ever used Google’s products? Gmail?

7) What’s a creative way of marketing Google’s brand name and product?

8) If you are the product marketing manager for Google’s Gmail product, how do you plan to market it so as to achieve 100 million customers in 6 months?

Google Interview Questions: Product Manager

1) How would you boost the GMail subscription base?

2) What is the most efficient way to sort a million integers?

3) How would you re-position Google’s offerings to counteract competitive threats from Microsoft?

4) How many golf balls can fit in a school bus?

5) You are shrunk to the height of a nickel and your mass is proportionally reduced so as to maintain your original density. You are then thrown into an empty glass blender. The blades will start moving in 60 seconds. What do you do?

6) How much should you charge to wash all the windows in Seattle?

7) How would you find out if a machine’s stack grows up or down in memory?

8) Explain a database in three sentences to your eight-year-old nephew.

9) How many times a day does a clock’s hands overlap?

10) You have to get from point A to point B. You don’t know if you can get there. What would you do?

11) Imagine you have a closet full of shirts. It’s very hard to find a shirt. So what can you do to organize your shirts for easy retrieval?

12) Every man in a village of 100 married couples has cheated on his wife. Every wife in the village instantly knows when a man other than her husband has cheated, but does not know when her own husband has. The village has a law that does not allow for adultery. Any wife who can prove that her husband is unfaithful must kill him that very day. The women of the village would never disobey this law. One day, the queen of the village visits and announces that at least one husband has been unfaithful. What happens?

13) In a country in which people only want boys, every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is the proportion of boys to girls in the country?

14) If the probability of observing a car in 30 minutes on a highway is 0.95, what is the probability of observing a car in 10 minutes (assuming constant default probability)?

If you look at a clock and the time is 3:15, what is the angle between the hour and the minute hands? (The answer to this is not zero!)

15) Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it’s only strong enough to support two people at any given time. Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?

16) You are at a party with a friend and 10 people are present including you and the friend. your friend makes you a wager that for every person you find that has the same birthday as you, you get $1; for every person he finds that does not have the same birthday as you, he gets $2. would you accept the wager?

17) How many piano tuners are there in the entire world?

18) You have eight balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you find the ball that is heavier by using a balance and only two weighing?

19) You have five pirates, ranked from 5 to 1 in descending order. The top pirate has the right to propose how 100 gold coins should be divided among them. But the others get to vote on his plan, and if fewer than half agree with him, he gets killed. How should he allocate the gold in order to maximize his share but live to enjoy it? (Hint: One pirate ends up with 98 percent of the gold.)

20) You are given 2 eggs. You have access to a 100-story building. Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100th floor. Both eggs are identical. You need to figure out the highest floor of a 100-story building an egg can be dropped without breaking. The question is how many drops you need to make. You are allowed to break 2 eggs in the process.

Describe a technical problem you had and how you solved it.

21) How would you design a simple search engine?

22) Design an evacuation plan for San Francisco.

23) There’s a latency problem in South Africa. Diagnose it.

24) What are three long term challenges facing google?

Google Interview Questions: Software Engineer

1. Why are manhole covers round?

2. What is the difference between a mutex and a semaphore? Which one would you use to protect access to an increment operation?

3. A man pushed his car to a hotel and lost his fortune. What happened?

4. Explain the significance of “dead beef”.

5. Write a C program which measures the the speed of a context switch on a UNIX/Linux system.

6. Given a function which produces a random integer in the range 1 to 5, write a function which produces a random integer in the range 1 to 7.

7. Describe the algorithm for a depth-first graph traversal.

8. Design a class library for writing card games.

You need to check that your friend, Bob, has your correct phone number, but you cannot ask him directly. You must write a the question on a card which and give it to Eve who will take the card to Bob and return the answer to you. What must you write on the card, besides the question, to ensure Bob can encode the message so that Eve cannot read your phone number?

9. How are cookies passed in the HTTP protocol?

10. Design the SQL database tables for a car rental database.

11. Write a regular expression which matches a email address.

12. Write a function f(a, b) which takes two character string arguments and returns a string containing only the characters found in both strings in the order of a. Write a version which is order N-squared and one which is order N.

13. You are given a the source to a application which is crashing when run. After running it 10 times in a debugger, you find it never crashes in the same place. The application is single threaded, and uses only the C standard library. What programming errors could be causing this crash?

14. How would you test each one?

15. Explain how congestion control works in the TCP protocol.

16. In Java, what is the difference between final, finally, and finalize?

17. What is multithreaded programming? What is a deadlock?Write a function (with helper functions if needed) called to Excel that takes an excel column value (A,B,C,D…AA,AB,AC,… AAA..) and returns a corresponding integer value (A=1,B=2,… AA=26..).

18. You have a stream of infinite queries (ie: real time Google search queries that people are entering). Describe how you would go about finding a good estimate of 1000 samples from this never ending set of data and then write code for it.

19. Tree search algorithms. Write BFS and DFS code, explain run time and space requirements. Modify the code to handle trees with weighted edges and loops with BFS and DFS, make the code print out path to goal state.

20. You are given a list of numbers. When you reach the end of the list you will come back to the beginning of the list (a circular list). Write the most efficient algorithm to find the minimum # in this list. Find any given # in the list. The numbers in the list are always increasing but you don’t know where the circular list begins, ie: 38, 40, 55, 89, 6, 13, 20, 23, 36.

21. Describe the data structure that is used to manage memory. (stack)

22. What’s the difference between local and global variables?

23. If you have 1 million integers, how would you sort them efficiently? (modify a specific sorting algorithm to solve this)

24. In Java, what is the difference between static, final, and const. (if you don’t know Java they will ask something similar for C or C++).

25. Talk about your class projects or work projects (pick something easy)… then describe how you could make them more efficient (in terms of algorithms).

26. Suppose you have an NxN matrix of positive and negative integers. Write some code that finds the sub-matrix with the maximum sum of its elements.

27. Write some code to reverse a string.

Implement division (without using the divide operator, obviously).

28. Write some code to find all permutations of the letters in a particular string.

29. What method would you use to look up a word in a dictionary?

Imagine you have a closet full of shirts. It’s very hard to find a shirt. So what can you do to organize your shirts for easy retrieval?

30. You have eight balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you fine the ball that is heavier by using a balance and only two weighings?

31. What is the C-language command for opening a connection with a foreign host over the internet?

32. Design and describe a system/application that will most efficiently produce a report of the top 1 million Google search requests. These are the particulars: 1) You are given 12 servers to work with. They are all dual-processor machines with 4Gb of RAM, 4x400GB hard drives and networked together.(Basically, nothing more than high-end PC’s) 2) The log data has already been cleaned for you. It consists of 100 Billion log lines, broken down into 12 320 GB files of 40-byte search terms per line. 3) You can use only custom written applications or available free open-source software.

33. There is an array A[N] of N numbers. You have to compose an array Output[N] such that Output[i] will be equal to multiplication of all the elements of A[N] except A[i]. For example Output[0] will be multiplication of A[1] to A[N-1] and Output[1] will be multiplication of A[0] and from A[2] to A[N-1]. Solve it without division operator and in O(n).

34. There is a linked list of numbers of length N. N is very large and you don’t know N. You have to write a function that will return k random numbers from the list. Numbers should be completely random. Hint: 1. Use random function rand() (returns a number between 0 and 1) and irand() (return either 0 or 1) 2. It should be done in O(n).

35. Find or determine non existence of a number in a sorted list of N numbers where the numbers range over M, M>> N and N large enough to span multiple disks. Algorithm to beat O(log n) bonus points for constant time algorithm.

36. You are given a game of Tic Tac Toe. You have to write a function in which you pass the whole game and name of a player. The function will return whether the player has won the game or not. First you to decide which data structure you will use for the game. You need to tell the algorithm first and then need to write the code. Note: Some position may be blank in the game। So your data structure should consider this condition also.

37. You are given an array [a1 To an] and we have to construct another array [b1 To bn] where bi = a1*a2*…*an/ai. you are allowed to use only constant space and the time complexity is O(n). No divisions are allowed.

38. How do you put a Binary Search Tree in an array in a efficient manner. Hint :: If the node is stored at the ith position and its children are at 2i and 2i+1(I mean level order wise)Its not the most efficient way.

39. How do you find out the fifth maximum element in an Binary Search Tree in efficient manner. Note: You should not use use any extra space. i.e sorting Binary Search Tree and storing the results in an array and listing out the fifth element.

40. Given a Data Structure having first n integers and next n chars. A = i1 i2 i3 … iN c1 c2 c3 … cN.Write an in-place algorithm to rearrange the elements of the array ass A = i1 c1 i2 c2 … in cn

41. Given two sequences of items, find the items whose absolute number increases or decreases the most when comparing one sequence with the other by reading the sequence only once.

42. Given That One of the strings is very very long , and the other one could be of various sizes. Windowing will result in O(N+M) solution but could it be better? May be NlogM or even better?

43. How many lines can be drawn in a 2D plane such that they are equidistant from 3 non-collinear points?

Let’s say you have to construct Google maps from scratch and guide a person standing on

44. Gateway of India (Mumbai) to India Gate(Delhi). How do you do the same?

45. Given that you have one string of length N and M small strings of length L. How do you efficiently find the occurrence of each small string in the larger one?

46.

47. Given a binary tree, programmatically you need to prove it is a binary search tree.

You are given a small sorted list of numbers, and a very very long sorted list of numbers – so long that it had to be put on a disk in different blocks. How would you find those short list numbers in the bigger one?

48. Suppose you have given N companies, and we want to eventually merge them into one big company. How many ways are theres to merge?

49. Given a file of 4 billion 32-bit integers, how to find one that appears at least twice?

50. Write a program for displaying the ten most frequent words in a file such that your program should be efficient in all complexity measures.

51. Design a stack. We want to push, pop, and also, retrieve the minimum element in constant time.

52. Given a set of coin denominators, find the minimum number of coins to give a certain amount of change.

53. Given an array, i) find the longest continuous increasing subsequence. ii) find the longest increasing subsequence.

54. Suppose we have N companies, and we want to eventually merge them into one big company.

55. How many ways are there to merge?

56. Write a function to find the middle node of a single link list.

57. Given two binary trees, write a compare function to check if they are equal or not. Being equal means that they have the same value and same structure.

Implement put/get methods of a fixed size cache with LRU replacement algorithm.

58. You are given with three sorted arrays ( in ascending order), you are required to find a triplet ( one element from each array) such that distance is minimum.

59. Distance is defined like this : If a[i], b[j] and c[k] are three elements then distance=max(abs(a[i]-b[j]),abs(a[i]-c[k]),abs(b[j]-c[k]))” Please give a solution in O(n) time complexity

60. How does C++ deal with constructors and deconstructors of a class and its child class?

61. Write a function that flips the bits inside a byte (either in C++ or Java). Write an algorithm that take a list of n words, and an integer m, and retrieves the mth most frequent word in that list.

62. What’s 2 to the power of 64?

63. Given that you have one string of length N and M small strings of length L. How do you efficiently find the occurrence of each small string in the larger one?

64. How do you find out the fifth maximum element in an Binary Search Tree in efficient manner.

65. Suppose we have N companies, and we want to eventually merge them into one big company.

66. How many ways are there to merge?

There is linked list of millions of node and you do not know the length of it. Write a function which will return a random number from the list.

67. You need to check that your friend, Bob, has your correct phone number, but you cannot ask him directly. You must write a the question on a card which and give it to Eve who will take the card to Bob and return the answer to you. What must you write on the card, besides the question, to ensure Bob can encode the message so that Eve cannot read your phone number?

68. How long it would take to sort 1 trillion numbers? Come up with a good estimate.

Order the functions in order of their asymptotic performance: 1) 2^n 2) n^100 3) n! 4) n^n

There are some data represented by(x,y,z). Now we want to find the Kth least data. We say (x1, y1, z1) > (x2, y2, z2) when value(x1, y1, z1) > value(x2, y2, z2) where value(x,y,z) = (2^x)*(3^y)*(5^z). Now we can not get it by calculating value(x,y,z) or through other indirect calculations as lg(value(x,y,z)). How to solve it?

69. How many degrees are there in the angle between the hour and minute hands of a clock when the time is a quarter past three?

70. Given an array whose elements are sorted, return the index of a the first occurrence of a specific integer. Do this in sub-linear time. I.e. do not just go through each element searching for that element.

71. Given two linked lists, return the intersection of the two lists: i.e. return a list containing only the elements that occur in both of the input lists.

72. What’s the difference between a hashtable and a hashmap?

73. If a person dials a sequence of numbers on the telephone, what possible words/strings can be formed from the letters associated with those numbers?

74. How would you reverse the image on an n by n matrix where each pixel is represented by a bit?

75. Create a fast cached storage mechanism that, given a limitation on the amount of cache memory, will ensure that only the least recently used items are discarded when the cache memory is reached when inserting a new item. It supports 2 functions: String get(T t) and void put(String k, T t).

76. Create a cost model that allows Google to make purchasing decisions on to compare the cost of purchasing more RAM memory for their servers vs. buying more disk space.

77. Design an algorithm to play a game of Frogger and then code the solution. The object of the game is to direct a frog to avoid cars while crossing a busy road. You may represent a road lane via an array. Generalize the solution for an N-lane road.

78. What sort would you use if you had a large data set on disk and a small amount of ram to work with?

79. What sort would you use if you required tight max time bounds and wanted highly regular performance.

80. How would you store 1 million phone numbers?

81. Design a 2D dungeon crawling game. It must allow for various items in the maze – walls, objects, and computer-controlled characters. (The focus was on the class structures, and how to optimize the experience for the user as s/he travels through the dungeon.)

82. What is the size of the C structure below on a 32-bit system? On a 64-bit?

struct foo {

char a; char* b; };

Google Interview: Software Engineer in Test

1. Efficiently implement 3 stacks in a single array.

2. Given an array of integers which is circularly sorted, how do you find a given integer.

3. Write a program to find depth of binary search tree without using recursion.

4. Find the maximum rectangle (in terms of area) under a histogram in linear time.

5. Most phones now have full keyboards. Before there there three letters mapped to a number button. Describe how you would go about implementing spelling and word suggestions as people type.

6. Describe recursive mergesort and its runtime. Write an iterative version in C++/Java/Python.

7. How would you determine if someone has won a game of tic-tac-toe on a board of any size?

8. Given an array of numbers, replace each number with the product of all the numbers in the array except the number itself *without* using division.

9. Create a cache with fast look up that only stores the N most recently accessed items.

10. How to design a search engine? If each document contains a set of keywords, and is associated with a numeric attribute, how to build indices?

11. Given two files that has list of words (one per line), write a program to show the intersection.

Google Interview: Quantitative Compensation Analyst

How many resumes does Google receive each year for software engineering?

Anywhere in the world, where would you open up a new Google office and how would you figure out compensation for all the employees at this new office?

What is the probability of breaking a stick into 3 pieces and forming a triangle

Google Interview: Engineering Manager

You’re the captain of a pirate ship, and your crew gets to vote on how the gold is divided up. If fewer than half of the pirates agree with you, you die. How do you recommend apportioning the gold in such a way that you get a good share of the booty, but still survive?

Google Placement Paper : Google Placement Paper Hyderabad 24 November 2012

The online test consists of 4 modules.

For each module a timer is set (at the right hand side bottom of the screen).Total time given is 40 minutes.

Module 1:English (duration 5 min).

It consists of a single passage followed by 5 questions.

Module 2:General aptitude(duration 10 min)

It consists of 6 questions based on simple logics. For eg:1),Z, was invited by his brother ,A, to attend his daughter ,B,s birthday party who was busy dancing with her brother ,C,.

What is ,Z, to ,C,?

a)Uncle

b)Nephew

c)Cousin

d)No relation at all

ANS:- a, Uncle.

In a similar way questions based on relations,cost etc etc were asked.

Module 3:-Technical questions(duration 15 min)

It consists of 15 questions where some are web based, html, protocals etc etc.

For this section going through COMPUTER NETWORKS subject will be helpful to a great extent.

Module 4:-Test on Analysis(duration 10 min)

This section is the most time consuming one.Here we are asked to Rate certain sites along with an explanation. The images of these sites are also provided to us for a clear view and better understanding.

The completion of this section(on time)is entirely based on your typing speed and at the same time you have to be good at assesing.

For each module a timer is set (at the right hand side bottom of the screen).Total time given is 40 minutes.

Module 1:English (duration 5 min).

It consists of a single passage followed by 5 questions.

Module 2:General aptitude(duration 10 min)

It consists of 6 questions based on simple logics. For eg:1),Z, was invited by his brother ,A, to attend his daughter ,B,s birthday party who was busy dancing with her brother ,C,.

What is ,Z, to ,C,?

a)Uncle

b)Nephew

c)Cousin

d)No relation at all

ANS:- a, Uncle.

In a similar way questions based on relations,cost etc etc were asked.

Module 3:-Technical questions(duration 15 min)

It consists of 15 questions where some are web based, html, protocals etc etc.

For this section going through COMPUTER NETWORKS subject will be helpful to a great extent.

Module 4:-Test on Analysis(duration 10 min)

This section is the most time consuming one.Here we are asked to Rate certain sites along with an explanation. The images of these sites are also provided to us for a clear view and better understanding.

The completion of this section(on time)is entirely based on your typing speed and at the same time you have to be good at assesing.

Google Placement Paper : Google Placement Paper 24 November 2012

Friends’ some memory based questions in Google Recruitment

Google Placement Paper with answers

1. 5,5,,13,13,21,21 Ans: 29

2. 0,7,26,63,124, Ans: 215 i.e.n**3-1 rule following

3. 1,3,5,7, Ans: 9 ,1, is not a prime number

4. If a person walks at 4/5th of his usual spee he reaches 40min late. If he walks athis usual speed how much time does he travels. Ans:160min or 2hr 40min

5. Two trains A&B start at opposite points 120km at 60kmph. A fly starting along with train A at 120kmph reaches B then returns back to touch and continue. By the time two trains meet howmuch distance the fly would have travelled?Ans : By 1hour both trains meet, so the distance travel by fly in 1hr is 120km.

6. In a class 80% have passed english,70% passed Hindi 10% didnot passed either. If 144 students passed both. What is the total strength of the class. Ans: 240

7. Find the least number when divided by 7 gives the reminder 6, when divided by 6 gives reminder 5, when divided by 5 gives reminder 4 and so on.... Ans: 419

8. If a man stands in front of sun what is the first letter of the direction which is left to him:

Ans: North(N)

9. A square is to circle what is cube to Ans: sphere

10. Synonyms

i) Joy = gay

ii) Inert = Inactive

11. One wordswill begiven find oddman out: Ans:sickle like that

a) sow b) cut c) d) sickel

Google Aptitude Questions

12. If I bought a cycle before 2days of my birthday and I broke it after 3 days of my birthday the day I broke is Mar2, 1956? Answer following logical questions? i) When is his birthday?

Ans: April,28 (due to leap year i.e.1956) but do not keep answer blindly we just think before choosing answer Iam just giving idea of question

14. What is my father,s sons son to my son? Ans: cousin brother

15. On cutting which solid parabola would be generated Ans: cone

16. Eulers formula: Ans: F+V-E=2;

F= faces; V= vertices; E = number of edges

17. Newton Rapson method is to find Ans:to find the root of f(x) = 0;

18. How many tangents can be dran within three circles if they donot lie within each other

Ans : 12 But this answer is not there I kept 8 as answer

19. In language the fortran which is true. A) fortran uses call by value

20. When a program is compiled what it produces

Ans:source code to object code

21. In the following venn diagram shaded region is represented by some question like that I can,t draw figure here thats why Iam sendinganswer only

Ans: (B-A), i.e. (B-A) whole dash

22. xy-x+2y = 6 equation is shifted to form equation xy=c what is c? Ans : 4

23.When x is real what is the least value of (x**2-6*x+5)/(x**2+2*x+1) Ans:-1/3

Google Technical questions

24. What is the mistake in the following program segment ?

f()

{

int a;

void c;

f2(&c,&a);}

25.

a=0;

b=(a=0)?2:3;

a) What will be the value of b and why ?

b) If in first statement a=0 is replaced by a = -1, b= ?

c) If in second statement a=0 is replaced by a = -1, b=?

26.

char *a[2];

int const *p;

int *const p;

struct new { int a;int b; *var[5] (struct new)}

Describe the statements in the above given construct ?

27.

f()

{

int a=2;

f1(a++);

}

f1(int c)

{

printf("%d", c);

}

What is the value of c ?

28.

f1()

{

f(3);

}

f(int t)

{

switch(t);

{

case 2: c=3;

case 3: c=4;

case 4: c=5;

case 5: c=6;

default: c=0;

}

What is the value of c?

29 Write a haiku describing possible methods for predicting search traffic seasonality.

MathWorld,s search engine seemed slowed this May. Undergrads prepping for finals.

Q 30.

1

1 1

2 1

1 2 1 1

1 1 1 2 2 1

What,s the next line?

31 2211. This is the "look and say" sequence in which each term after the first describes the previous term: one 1 (11); two 1s (21); one 2 and one 1 (1211); one 1, one 2, and two 1,s (111221); and so on. See the look and say sequence entry on MathWorld for a complete write-up and the algebraic form of a fascinating related quantity known as Conway,s constant.

31. You are in a maze of twisty little passages, all alike. There is a dusty laptop here with a weak wireless connection. There are dull, lifeless gnomes strolling around. What dost thou do?

A) Wander aimlessly, bumping into obstacles until you are eaten by a grue.

B) Use the laptop as a digging device to tunnel to the next level.

C) Play MPoRPG until the battery dies along with your hopes.

D) Use the computer to map the nodes of the maze and discover an exit path.

E) Email your resume to Google, tell the lead gnome you quit and find yourself in whole different world [sic].

In general, make a state diagram . However, this method would not work in certain pathological cases such as, say, a fractal maze. For an example of this and commentary, see Ed Pegg,s column about state diagrams and mazes .

32. What,s broken with Unix? Their reproductive capabilities.How would you fix it?

33 On your first day at Google, you discover that your cubicle mate wrote the textbook you used as a primary resource in your first year of graduate school. Do you:

A) Fawn obsequiously and ask if you can have an autograph.

B) Sit perfectly still and use only soft keystrokes to avoid disturbing her concentration

C) Leave her daily offerings of granola and English toffee from the food bins.

D) Quote your favorite formula from the textbook and explain how it,s now your mantra.

E) Show her how example 17b could have been solved with 34 fewer lines of code.

34. Which of the following expresses Google,s over-arching philosophy?

A) "I,m feeling lucky"

B) "Don,t be evil"

C) "Oh, I already fixed that"

D) "You should never be more than 50 feet from food"

E) All of the above

35. How many different ways can you color an icosahedron with one of three colors on each face?

For an asymmetric 20-sided solid, there are possible 3-colorings . For a symmetric 20-sided object, the Polya enumeration theorem can be used to obtain the number of distinct colorings. Here is a concise Mathematica implementation:

What colors would you choose?

36. This space left intentionally blank. Please fill it with something that improves upon emptiness.

For nearly 10,000 images of mathematical functions, see The Wolfram Functions Site visualization gallery .

37. On an infinite, two-dimensional, rectangular lattice of 1-ohm resistors, what is the resistance between two nodes that are a knight,s move away?

This problem is discussed in J. Cserti,s 1999 arXiv preprint . It is also discussed in The Mathematica GuideBook for Symbolics, the forthcoming fourth volume in Michael Trott,s GuideBook series, the first two of which were published just last week by Springer-Verlag. The contents for all four GuideBooks, including the two not yet published, are available on the DVD distributed with the first two GuideBooks.

38. It,s 2PM on a sunny Sunday afternoon in the Bay Area. You,re minutes from the Pacific Ocean, redwood forest hiking trails and world class cultural attractions. What do you do?

39. In your opinion, what is the most beautiful math equation ever derived?

There are obviously many candidates. The following list gives ten of the authors, favorites:

1. Archimedes, recurrence formula : , , ,

2. Euler formula :

3. Euler-Mascheroni constant :

4. Riemann hypothesis: and implies

5. Gaussian integral :

6. Ramanujan,s prime product formula:

7. Zeta-regularized product :

8. Mandelbrot set recursion:

9. BBP formula :

10. Cauchy integral formula:

40. Which of the following is NOT an actual interest group formed by Google employees?

A. Women,s basketball B. Buffy fans C. Cricketeers D. Nobel winners E. Wine club

41. What will be the next great improvement in search technology?

42. What is the optimal size of a project team, above which additional members do not contribute productivity equivalent to the percentage increase in the staff size?

A) 1 B) 3 C) 5 D) 11 E) 24

43. Given a triangle ABC, how would you use only a compass and straight edge to find a point P such that triangles ABP, ACP and BCP have equal perimeters? (Assume that ABC is constructed so that a solution does exist.)

This is the isoperimetric point , which is at the center of the larger Soddy circle. It is related to Apollonius, problem . The three tangent circles are easy to construct: The circle around has diameter , which gives the other two circles. A summary of compass and straightedge constructions for the outer Soddy circle can be found in " Apollonius, Problem: A Study of Solutions and Their Connections" by David Gisch and Jason M. Ribando.

44.

{

long l=1024;

int i=1;

while(l>=1)

{ l=l/2;

i=i+1;}

}

a)8 b)11 c)10 d)100 ans:b

45 This question is based on the complexity ...

Q3) s->AB

A->a

B->bbA

Which one is false for above grammar.

46 Some Tree were given & the question is to fine preorder traversal.

47. One c++ program,to find output of the program..

48. If the mean failure hour is 10,000 and 20 is the mean repair hour. If the printer is used by 100 customer, then find the availability. 1)80% 2)90% 3)98% 4)99.8% 5)100%

Google Placement Paper with answers

1. 5,5,,13,13,21,21 Ans: 29

2. 0,7,26,63,124, Ans: 215 i.e.n**3-1 rule following

3. 1,3,5,7, Ans: 9 ,1, is not a prime number

4. If a person walks at 4/5th of his usual spee he reaches 40min late. If he walks athis usual speed how much time does he travels. Ans:160min or 2hr 40min

5. Two trains A&B start at opposite points 120km at 60kmph. A fly starting along with train A at 120kmph reaches B then returns back to touch and continue. By the time two trains meet howmuch distance the fly would have travelled?Ans : By 1hour both trains meet, so the distance travel by fly in 1hr is 120km.

6. In a class 80% have passed english,70% passed Hindi 10% didnot passed either. If 144 students passed both. What is the total strength of the class. Ans: 240

7. Find the least number when divided by 7 gives the reminder 6, when divided by 6 gives reminder 5, when divided by 5 gives reminder 4 and so on.... Ans: 419

8. If a man stands in front of sun what is the first letter of the direction which is left to him:

Ans: North(N)

9. A square is to circle what is cube to Ans: sphere

10. Synonyms

i) Joy = gay

ii) Inert = Inactive

11. One wordswill begiven find oddman out: Ans:sickle like that

a) sow b) cut c) d) sickel

Google Aptitude Questions

12. If I bought a cycle before 2days of my birthday and I broke it after 3 days of my birthday the day I broke is Mar2, 1956? Answer following logical questions? i) When is his birthday?

Ans: April,28 (due to leap year i.e.1956) but do not keep answer blindly we just think before choosing answer Iam just giving idea of question

14. What is my father,s sons son to my son? Ans: cousin brother

15. On cutting which solid parabola would be generated Ans: cone

16. Eulers formula: Ans: F+V-E=2;

F= faces; V= vertices; E = number of edges

17. Newton Rapson method is to find Ans:to find the root of f(x) = 0;

18. How many tangents can be dran within three circles if they donot lie within each other

Ans : 12 But this answer is not there I kept 8 as answer

19. In language the fortran which is true. A) fortran uses call by value

20. When a program is compiled what it produces

Ans:source code to object code

21. In the following venn diagram shaded region is represented by some question like that I can,t draw figure here thats why Iam sendinganswer only

Ans: (B-A), i.e. (B-A) whole dash

22. xy-x+2y = 6 equation is shifted to form equation xy=c what is c? Ans : 4

23.When x is real what is the least value of (x**2-6*x+5)/(x**2+2*x+1) Ans:-1/3

Google Technical questions

24. What is the mistake in the following program segment ?

f()

{

int a;

void c;

f2(&c,&a);}

25.

a=0;

b=(a=0)?2:3;

a) What will be the value of b and why ?

b) If in first statement a=0 is replaced by a = -1, b= ?

c) If in second statement a=0 is replaced by a = -1, b=?

26.

char *a[2];

int const *p;

int *const p;

struct new { int a;int b; *var[5] (struct new)}

Describe the statements in the above given construct ?

27.

f()

{

int a=2;

f1(a++);

}

f1(int c)

{

printf("%d", c);

}

What is the value of c ?

28.

f1()

{

f(3);

}

f(int t)

{

switch(t);

{

case 2: c=3;

case 3: c=4;

case 4: c=5;

case 5: c=6;

default: c=0;

}

What is the value of c?

29 Write a haiku describing possible methods for predicting search traffic seasonality.

MathWorld,s search engine seemed slowed this May. Undergrads prepping for finals.

Q 30.

1

1 1

2 1

1 2 1 1

1 1 1 2 2 1

What,s the next line?

31 2211. This is the "look and say" sequence in which each term after the first describes the previous term: one 1 (11); two 1s (21); one 2 and one 1 (1211); one 1, one 2, and two 1,s (111221); and so on. See the look and say sequence entry on MathWorld for a complete write-up and the algebraic form of a fascinating related quantity known as Conway,s constant.

31. You are in a maze of twisty little passages, all alike. There is a dusty laptop here with a weak wireless connection. There are dull, lifeless gnomes strolling around. What dost thou do?

A) Wander aimlessly, bumping into obstacles until you are eaten by a grue.

B) Use the laptop as a digging device to tunnel to the next level.

C) Play MPoRPG until the battery dies along with your hopes.

D) Use the computer to map the nodes of the maze and discover an exit path.

E) Email your resume to Google, tell the lead gnome you quit and find yourself in whole different world [sic].

In general, make a state diagram . However, this method would not work in certain pathological cases such as, say, a fractal maze. For an example of this and commentary, see Ed Pegg,s column about state diagrams and mazes .

32. What,s broken with Unix? Their reproductive capabilities.How would you fix it?

33 On your first day at Google, you discover that your cubicle mate wrote the textbook you used as a primary resource in your first year of graduate school. Do you:

A) Fawn obsequiously and ask if you can have an autograph.

B) Sit perfectly still and use only soft keystrokes to avoid disturbing her concentration

C) Leave her daily offerings of granola and English toffee from the food bins.

D) Quote your favorite formula from the textbook and explain how it,s now your mantra.

E) Show her how example 17b could have been solved with 34 fewer lines of code.

34. Which of the following expresses Google,s over-arching philosophy?

A) "I,m feeling lucky"

B) "Don,t be evil"

C) "Oh, I already fixed that"

D) "You should never be more than 50 feet from food"

E) All of the above

35. How many different ways can you color an icosahedron with one of three colors on each face?

For an asymmetric 20-sided solid, there are possible 3-colorings . For a symmetric 20-sided object, the Polya enumeration theorem can be used to obtain the number of distinct colorings. Here is a concise Mathematica implementation:

What colors would you choose?

36. This space left intentionally blank. Please fill it with something that improves upon emptiness.

For nearly 10,000 images of mathematical functions, see The Wolfram Functions Site visualization gallery .

37. On an infinite, two-dimensional, rectangular lattice of 1-ohm resistors, what is the resistance between two nodes that are a knight,s move away?

This problem is discussed in J. Cserti,s 1999 arXiv preprint . It is also discussed in The Mathematica GuideBook for Symbolics, the forthcoming fourth volume in Michael Trott,s GuideBook series, the first two of which were published just last week by Springer-Verlag. The contents for all four GuideBooks, including the two not yet published, are available on the DVD distributed with the first two GuideBooks.

38. It,s 2PM on a sunny Sunday afternoon in the Bay Area. You,re minutes from the Pacific Ocean, redwood forest hiking trails and world class cultural attractions. What do you do?

39. In your opinion, what is the most beautiful math equation ever derived?

There are obviously many candidates. The following list gives ten of the authors, favorites:

1. Archimedes, recurrence formula : , , ,

2. Euler formula :

3. Euler-Mascheroni constant :

4. Riemann hypothesis: and implies

5. Gaussian integral :

6. Ramanujan,s prime product formula:

7. Zeta-regularized product :

8. Mandelbrot set recursion:

9. BBP formula :

10. Cauchy integral formula:

40. Which of the following is NOT an actual interest group formed by Google employees?

A. Women,s basketball B. Buffy fans C. Cricketeers D. Nobel winners E. Wine club

41. What will be the next great improvement in search technology?

42. What is the optimal size of a project team, above which additional members do not contribute productivity equivalent to the percentage increase in the staff size?

A) 1 B) 3 C) 5 D) 11 E) 24

43. Given a triangle ABC, how would you use only a compass and straight edge to find a point P such that triangles ABP, ACP and BCP have equal perimeters? (Assume that ABC is constructed so that a solution does exist.)

This is the isoperimetric point , which is at the center of the larger Soddy circle. It is related to Apollonius, problem . The three tangent circles are easy to construct: The circle around has diameter , which gives the other two circles. A summary of compass and straightedge constructions for the outer Soddy circle can be found in " Apollonius, Problem: A Study of Solutions and Their Connections" by David Gisch and Jason M. Ribando.

44.

{

long l=1024;

int i=1;

while(l>=1)

{ l=l/2;

i=i+1;}

}

a)8 b)11 c)10 d)100 ans:b

45 This question is based on the complexity ...

Q3) s->AB

A->a

B->bbA

Which one is false for above grammar.

46 Some Tree were given & the question is to fine preorder traversal.

47. One c++ program,to find output of the program..

48. If the mean failure hour is 10,000 and 20 is the mean repair hour. If the printer is used by 100 customer, then find the availability. 1)80% 2)90% 3)98% 4)99.8% 5)100%

Google Placement Paper : Google Placement Paper IIT Guwahati 9 November 2010

Package: 16 Lakh

Paper Type: CSE B Tech/M Tech /PHD

Experience: Question is base on C/C++/Algo ,OS(little), Puzzles mixed Aptitude.

Questions: 30 questions and 2 programs time 1 hour.

All Questions are multiple type. I just mention the questions options not remember

Section A:

1. Find the value of n the following code:

int F(int n)

if( n!=0& !(n&(n-1)))

printf("%d",n)

n is

i. Even no

ii. Odd nos

iii. Non zero numbers

iv. Number with power 2

Ans: iv.

Description: Take a number like 8.

so n= 8 and n-1= 7

So n =1000 and

n-1= 111

And n&n-1= 1000 & 111=1111( All bits one)

Now !(n & n-1) = 0000

So if(0) which satisfies the if condition. Means when and is a number of power 2, it will satisfy if condition.

More Doubt Comments me.

Paper Type: CSE B Tech/M Tech /PHD

Experience: Question is base on C/C++/Algo ,OS(little), Puzzles mixed Aptitude.

Questions: 30 questions and 2 programs time 1 hour.

All Questions are multiple type. I just mention the questions options not remember

Section A:

1. Find the value of n the following code:

int F(int n)

if( n!=0& !(n&(n-1)))

printf("%d",n)

n is

i. Even no

ii. Odd nos

iii. Non zero numbers

iv. Number with power 2

Ans: iv.

Description: Take a number like 8.

so n= 8 and n-1= 7

So n =1000 and

n-1= 111

And n&n-1= 1000 & 111=1111( All bits one)

Now !(n & n-1) = 0000

So if(0) which satisfies the if condition. Means when and is a number of power 2, it will satisfy if condition.

More Doubt Comments me.

Google Placement Paper : Google Placement Paper chennai 2 September 2010

Hello Everyone,

Google has conducted recruitment process in our collage.The criteria was first 30% topper

in the class.So around 40 student has attended the test & only 4 could clear the test.

Test consist of 15 question based on c,c++,and data structure.and two c programs.

So i am listing some of the question as i remembered.

Q1)

What is the value of i after execution of the following program.

void main()

{

long l=1024;

int i=1;

while(l>=1)

{ l=l/2;

i=i+1;

}

}

a)8 b)11 c)10 d)100 ans:b

Q2)

This question is based on the complexity ...

Q3)

s->AB

A->a

B->bbA

Which one is false for above grammer..

Q3)

Some Tree were given & the question is to fine preorder traversal.

Q4)

One c++ program,to find output of the program..

Q5)

If the mean faliure hour is 10,000 and 20 is the mean repair hour.If the printer is used by

100 customer,then find the availability.

1)80% 2)90% 3)98% 4)99.8% 5)100%

Q6)One question on probability...

Q7)In a singly linked list if there is a pointer S on the first element and pointer L is on the last element.Then which operation will take more time based on the lenght of the list.

1)Adding element at the first.

2)adding element at the end of the list.

3)To exchange the fisrt 2 element.

4)Deleting the element from the end of the list.

ans:2 check it!

3 more question to fine the output of the program.

and rest of the question was based on data structure,

some condition where given and we have to conlude either y or n

The second section was coding...

1)Write a fucntion to multiply 2 N*N matrix

Write test cases for ur code.

2)S contains the set of positive integer.Find the largest number c such that c=a+b where a,b,c are distict number of the set.

Google has conducted recruitment process in our collage.The criteria was first 30% topper

in the class.So around 40 student has attended the test & only 4 could clear the test.

Test consist of 15 question based on c,c++,and data structure.and two c programs.

So i am listing some of the question as i remembered.

Q1)

What is the value of i after execution of the following program.

void main()

{

long l=1024;

int i=1;

while(l>=1)

{ l=l/2;

i=i+1;

}

}

a)8 b)11 c)10 d)100 ans:b

Q2)

This question is based on the complexity ...

Q3)

s->AB

A->a

B->bbA

Which one is false for above grammer..

Q3)

Some Tree were given & the question is to fine preorder traversal.

Q4)

One c++ program,to find output of the program..

Q5)

If the mean faliure hour is 10,000 and 20 is the mean repair hour.If the printer is used by

100 customer,then find the availability.

1)80% 2)90% 3)98% 4)99.8% 5)100%

Q6)One question on probability...

Q7)In a singly linked list if there is a pointer S on the first element and pointer L is on the last element.Then which operation will take more time based on the lenght of the list.

1)Adding element at the first.

2)adding element at the end of the list.

3)To exchange the fisrt 2 element.

4)Deleting the element from the end of the list.

ans:2 check it!

3 more question to fine the output of the program.

and rest of the question was based on data structure,

some condition where given and we have to conlude either y or n

The second section was coding...

1)Write a fucntion to multiply 2 N*N matrix

Write test cases for ur code.

2)S contains the set of positive integer.Find the largest number c such that c=a+b where a,b,c are distict number of the set.

Google Placement Paper : Candidate Experience - Google Adwords Representative Placement Paper

Questions I was asked for Adwords Representative Interview

--------------------------------------------------------------------------------

--------------------------------------------------------------------------------

- Give me a runthrough of your resume?
- What do you know about Google?
- What do you know about Adwords?
- What do you understand about your job profile?
- How you fit into that role?
- Are you willing to give up the role of a team leader and creative writer

to be an Adword Representative? - How do you think this position can help your job profile?
- If Adwords was not associated with Google, would you have accepted the

position? - Yahoo and Microsoft has similar positions, why do you want to join Google

only? - You say you want a change in your career and use more of your skills, what

other job profiles do you think would have suited you? - What is your biggest failure in life?
- Have you been in a position when one of your colleagues did not do his

share of work? How did you handle the situation? - Suppose there is a project going on in full swing and two of your colleagues

just fall sick, how will you handle the position? - If you had to sell the job of Adwords Representative to a friend, what

would you say to them? - Tell me about a situation where just couldn,t get along with one of your

team members. What did you do? - Have you ever faced a situation you didn,t like at job? How did you face

it? - Do you have any questions to ask?
- Besides what HR sent you, what did you do to research about the position?

- What Google services you have used till date? Choose one of them and tell

what change would you like to make in it? - Your company generates revenue through Adsense. What kind of ads show up

on your webpage? Why do you think Indian ads do not show up on your website,s

page? - Do you know any of the Google terms and policies regarding Adwords?
- What did you liked about Google? Do you like the peole here?
- Which interviewer you liked the best? Why?
- Google has a flat system with not much vertical hierarchy system. It is

based on meritocracy. If a person joins 6 months after you and becomes your

mentor in a year, how would you handle the situation? - Are you comfortable not having a vertical ladder to move on?
- At Google, you may have to deal with people who are freshers and ones who

are much more qualified than you are. How will you balance out the situation

and maintain relationships with all of them? - You say you are flexible, adaptable and client-friendly. How? Give examples.

What do you mean by people skills?

Google Placement Paper : Google General - other1

GOOGLE PAPER ON 25th NOVEMBER AT HYDERABAD

The online test consists of 4 modules.

For each module a timer is set (at the right hand side bottom of the screen).Total time given is 40 minutes.

**Module 1:English (duration 5 min)**.

It consists of a single passage followed by 5 questions.

**Module 2:General aptitude(duration 10 min)**

It consists of 6 questions based on simple logics. For eg:1),Z, was invited by his brother ,A, to attend his daughter ,B,s birthday party who was busy dancing with her brother ,C,.

What is ,Z, to ,C,?

a)Uncle

b)Nephew

c)Cousin

d)No relation at all

ANS:- a, Uncle.

In a similar way questions based on relations,cost etc etc were asked.

**Module 3:-Technical questions(duration 15 min)**

It consists of 15 questions where some are web based, html, protocals etc etc.

For this section going through COMPUTER NETWORKS subject will be helpful to a great extent.

**Module 4:-Test on Analysis(duration 10 min)**

This section is the most time consuming one.Here we are asked to Rate certain sites along with an explanation. The images of these sites are also provided to us for a clear view and better understanding.

The completion of this section(on time)is entirely based on your typing speed and at the same time you have to be good at assesing.

The online test consists of 4 modules.

For each module a timer is set (at the right hand side bottom of the screen).Total time given is 40 minutes.

It consists of a single passage followed by 5 questions.

It consists of 6 questions based on simple logics. For eg:1),Z, was invited by his brother ,A, to attend his daughter ,B,s birthday party who was busy dancing with her brother ,C,.

What is ,Z, to ,C,?

a)Uncle

b)Nephew

c)Cousin

d)No relation at all

ANS:- a, Uncle.

In a similar way questions based on relations,cost etc etc were asked.

It consists of 15 questions where some are web based, html, protocals etc etc.

For this section going through COMPUTER NETWORKS subject will be helpful to a great extent.

This section is the most time consuming one.Here we are asked to Rate certain sites along with an explanation. The images of these sites are also provided to us for a clear view and better understanding.

The completion of this section(on time)is entirely based on your typing speed and at the same time you have to be good at assesing.

Google Placement Paper : Google General - other

Hello Everyone,

Google has conducted recruitment process in our collage.The criteria was first 30% topper

in the class.So around 40 student has attended the test & only 4 could clear the test.

Test consist of 15 question based on c,c++,and data structure.and two c programs.

So i am listing some of the question as i remembered.

Q1)

What is the value of i after execution of the following program.

void main()

{

long l=1024;

int i=1;

while(l>=1)

{ l=l/2;

i=i+1;

}

}

a)8 b)11 c)10 d)100 ans:b

Q2)

This question is based on the complexity ...

Q3)

s->AB

A->a

B->bbA

Which one is false for above grammer..

Q3)

Some Tree were given & the question is to fine preorder traversal.

Q4)

One c++ program,to find output of the program..

Q5)

If the mean faliure hour is 10,000 and 20 is the mean repair hour.If the printer is used by

100 customer,then find the availability.

1)80% 2)90% 3)98% 4)99.8% 5)100%

Q6)One question on probability...

Q7)In a singly linked list if there is a pointer S on the first element and pointer L is on the last element.Then which operation will take more time based on the lenght of the list.

1)Adding element at the first.

2)adding element at the end of the list.

3)To exchange the fisrt 2 element.

4)Deleting the element from the end of the list.

ans:2 check it!

3 more question to fine the output of the program.

and rest of the question was based on data structure,

some condition where given and we have to conlude either y or n

The second section was coding...

1)Write a fucntion to multiply 2 N*N matrix

Write test cases for ur code.

2)S contains the set of positive integer.Find the largest number c such that c=a+b where a,b,c are distict number of the set.

Google Placement Paper : Google Aptitude - General

1. Solve this cryptic equation, realizing of course that values for M and E could be interchanged. No leading zeros are allowed.

WWWDOT - GOOGLE = DOTCOM

This can be solved through systematic application of logic. For example, cannot be equal to 0, since . That would make , but , which is not possible.

Here is a slow brute-force method of solution that takes a few minutes on a relatively fast machine:

This gives the two solutions

777589 - 188106 == 589483

777589 - 188103 == 589486

Here is another solution using Mathematica,s Reduce command:

A faster (but slightly more obscure) piece of code is the following:

Faster still using the same approach (and requiring ~300 MB of memory):

Even faster using the same approach (that does not exclude leading zeros in the solution, but that can easily be weeded out at the end):

Here is an independent solution method that uses branch-and-prune techniques:

And the winner for overall fastest:

2. Write a haiku describing possible methods for predicting search traffic seasonality.

MathWorld,s search engine

seemed slowed this May. Undergrads

prepping for finals.

3. 1

1 1

2 1

1 2 1 1

1 1 1 2 2 1

What,s the next line?

312211. This is the "look and say" sequence in which each term after the first describes the previous term: one 1 (11); two 1s (21); one 2 and one 1 (1211); one 1, one 2, and two 1,s (111221); and so on. See the look and say sequence entry on MathWorld for a complete write-up and the algebraic form of a fascinating related quantity known as Conway,s constant.

4. You are in a maze of twisty little passages, all alike. There is a dusty laptop here with a weak wireless connection. There are dull, lifeless gnomes strolling around. What dost thou do?

A) Wander aimlessly, bumping into obstacles until you are eaten by a grue.

B) Use the laptop as a digging device to tunnel to the next level.

C) Play MPoRPG until the battery dies along with your hopes.

D) Use the computer to map the nodes of the maze and discover an exit path.

E) Email your resume to Google, tell the lead gnome you quit and find yourself in whole different world [sic].

In general, make a state diagram . However, this method would not work in certain pathological cases such as, say, a fractal maze. For an example of this and commentary, see Ed Pegg,s column about state diagrams and mazes .

5. What,s broken with Unix?

Their reproductive capabilities.

How would you fix it?

[This exercise is left to the reader.]

6. On your first day at Google, you discover that your cubicle mate wrote the textbook you used as a primary resource in your first year of graduate school. Do you:

A) Fawn obsequiously and ask if you can have an autograph.

B) Sit perfectly still and use only soft keystrokes to avoid disturbing her concentration

C) Leave her daily offerings of granola and English toffee from the food bins.

D) Quote your favorite formula from the textbook and explain how it,s now your mantra.

E) Show her how example 17b could have been solved with 34 fewer lines of code.

[This exercise is left to the reader.]

7. Which of the following expresses Google,s over-arching philosophy?

A) "I,m feeling lucky"

B) "Don,t be evil"

C) "Oh, I already fixed that"

D) "You should never be more than 50 feet from food"

E) All of the above

[This exercise is left to the reader.]

8. How many different ways can you color an icosahedron with one of three colors on each face?

For an asymmetric 20-sided solid, there are possible 3-colorings . For a symmetric 20-sided object, the Polya enumeration theorem can be used to obtain the number of distinct colorings. Here is a concise Mathematica implementation:

What colors would you choose?

[This exercise is left to the reader.]

9. This space left intentionally blank. Please fill it with something that improves upon emptiness.

For nearly 10,000 images of mathematical functions, see The Wolfram Functions Site visualization gallery .

10. On an infinite, two-dimensional, rectangular lattice of 1-ohm resistors, what is the resistance between two nodes that are a knight,s move away?

This problem is discussed in J. Cserti,s 1999 arXiv preprint . It is also discussed in The Mathematica GuideBook for Symbolics, the forthcoming fourth volume in Michael Trott,s GuideBook series, the first two of which were published just last week by Springer-Verlag. The contents for all four GuideBooks, including the two not yet published, are available on the DVD distributed with the first two GuideBooks.

11. It,s 2PM on a sunny Sunday afternoon in the Bay Area. You,re minutes from the Pacific Ocean, redwood forest hiking trails and world class cultural attractions. What do you do?

[This exercise is left to the reader.]

12. In your opinion, what is the most beautiful math equation ever derived?

There are obviously many candidates. The following list gives ten of the authors, favorites:

1. Archimedes, recurrence formula : , , ,

2. Euler formula :

3. Euler-Mascheroni constant :

4. Riemann hypothesis: and implies

5. Gaussian integral :

6. Ramanujan,s prime product formula:

7. Zeta-regularized product :

8. Mandelbrot set recursion:

9. BBP formula :

10. Cauchy integral formula:

An excellent paper discussing the most beautiful equations in physics is Daniel Z. Freedman,s " Some beautiful equations of mathematical physics ." Note that the physics view on beauty in equations is less uniform than the mathematical one. To quote the not-necessarily-standard view of theoretical physicist P.A.M. Dirac, "It is more important to have beauty in one,s equations than to have them fit experiment."

13. Which of the following is NOT an actual interest group formed by Google employees?

A. Women,s basketball

B. Buffy fans

C. Cricketeers

D. Nobel winners

E. Wine club

[This exercise is left to the reader.]

14. What will be the next great improvement in search technology?

Semantic searching of mathematical formulas. See http://functions.wolfram.com/About/ourvision.html for work currently underway at Wolfram Research that will be made available in the near future.

15. What is the optimal size of a project team, above which additional members do not contribute productivity equivalent to the percentage increase in the staff size?

A) 1

B) 3

C) 5

D) 11

E) 24

[This exercise is left to the reader.]

16. Given a triangle ABC, how would you use only a compass and straight edge to find a point P such that triangles ABP, ACP and BCP have equal perimeters? (Assume that ABC is constructed so that a solution does exist.)

This is the isoperimetric point , which is at the center of the larger Soddy circle. It is related to Apollonius, problem . The three tangent circles are easy to construct: The circle around has diameter , which gives the other two circles. A summary of compass and straightedge constructions for the outer Soddy circle can be found in " Apollonius, Problem: A Study of Solutions and Their Connections" by David Gisch and Jason M. Ribando.

17. Consider a function which, for a given whole number n, returns the number of ones required when writing out all numbers between 0 and n. For example, f(13)=6. Notice that f(1)=1. What is the next largest n such that f(n)=n?

The following Mathematica code computes the difference between [the cumulative number of 1s in the positive integers up to n] and [the value of n itself] as n ranges from 1 to 500,000:

The solution to the problem is then the first position greater than the first at which data equals 0:

which are the first few terms of sequence A014778 in the On-Line Encyclopedia of Integer Sequences.

Checking by hand confirms that the numbers from 1 to 199981 contain a total of 199981 1s:

18. What is the coolest hack you,ve ever written?

While there is no "correct" answer, a nice hack for solving the first problem in the SIAM hundred-dollar, hundred-digit challenge can be achieved by converting the limit into the strongly divergent series:

and then using Mathematica,s numerical function SequenceLimit to trivially get the correct answer (to six digits),

You must tweak parameters a bit or write your own sequence limit to get all 10 digits.

[Other hacks are left to the reader.]

19. ,Tis known in refined company, that choosing K things out of N can be done in ways as many as choosing N minus K from N: I pick K, you the remaining.

This simply states the binomial coefficient identity .

Find though a cooler bijection, where you show a knack uncanny, of making your choices contain all K of mine. Oh, for pedantry: let K be no more than half N.

,Tis more problematic to disentangle semantic meaning precise from the this paragraph of verbiage peculiar.

20. What number comes next in the sequence: 10, 9, 60, 90, 70, 66, ?

A) 96

B) 1000000000000000000000000000000000\

0000000000000000000000000000000000\

000000000000000000000000000000000

C) Either of the above

D) None of the above

This can be looked up and found to be sequence A052196 in the On-Line Encyclopedia of Integer Sequences, which gives the largest positive integer whose English name has n letters. For example, the first few terms are ten, nine, sixty, ninety, seventy, sixty-six, ninety-six, …. A more correct sequence might be ten, nine, sixty, googol, seventy, sixty-six, ninety-six, googolplex. And also note, incidentally, that the correct spelling of the mathematical term " googol" differs from the name of the company that made up this aptitude test.

The first few can be computed using the NumberName function in Eric Weisstein,s MathWorld packages:

A mathematical solution could also be found by fitting a Lagrange interpolating polynomial to the six known terms and extrapolating:

21. In 29 words or fewer, describe what you would strive to accomplish if you worked at Google Labs.