Google Placement Papers & Campus Selection Process

2011 google placement paper:

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

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

2.

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.

3. 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 .

4. What's broken with Unix?

Their reproductive capabilities.

How would you fix it?

5. 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.

6. 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

7. 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?

8. 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 .

9. 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.

10. 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?

11. 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:

12. 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

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

14. 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


15. 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.


16.

{

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


17. This question is based on the complexity ...


Q3) s->AB
A->a
B->bbA

Which one is false for above grammar.

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


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


20. 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%

21. 5,5,,13,13,21,21

Ans: 29

22. 0,7,26,63,124,

Ans: 215 i.e.n**3-1 rule following

23. 1,3,5,7,

Ans: 9 '1' is not a prime number

24. 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

25. 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.

26. 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

27. 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

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

Ans: North(N)

29. A square is to circle what is cube to

Ans: sphere

30. Synonyms
i) Joy = gay
ii) Inert = Inactive

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

a) sow b) cut c) d) sickel

32. 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 ideaof question

33. What is my father's sons son to my son?

Ans: cousin brother

34. On cutting which solid parabola would be generated

Ans: cone

35. Eulers formula:

Ans: F+V-E=2;
F= faces; V= vertices; E = number of edges

36. Newton Rapson method is to find

Ans:to find the root of f(x) = 0;

37. 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

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

39. When a program is compiled what it produces

Ans:source code to object code

40. 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

41. xy-x+2y = 6 equation is shifted to form equation xy=c what is c?

Ans : 4

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

Ans:-1/3

43. What is the mistake in the following program segment ?
f()
{
int a;
void c;
f2(&c,&a);}

44.
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=?

45.
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 ?

46.
f()
{
int a=2;
f1(a++);
}
f1(int c)
{
printf("%d", c);
}
What is the value of c ?

47.
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?

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