Google Rude

Today I was trying a website which generated rude comments everytime it was refreshed. Some of the rude comments were:
"Ya silly ninny!"
"Ya mouth breather!"
"Ya COBOL expert!"

Looking closely, I realized that the website chose a random comment whenever it was refreshed. It chose the comment randomly from a set of 100 rude comments.

After a while, I started seeing comments I had seen before, and the website became boring for me.
Can you tell me the probability that I have already seen the comment that I see on my 10th refresh?

2-SAT & Who will read my blog

How many positive integral solutions can you find to this system of equations?

x1+x2=8
x2-x3=-3
x3+x4=14
x4-x5=-5
x5+x6=18
x6-x7=4
x7-x8=-3

Note:
1)xi>=1.
2)Neither I nor Shivanker could find a simple enough solution for this problem. Can you come up with the awesome and simple solution?

The JEE - A Final Word

To all JEE-2012 aspirants,

All the very best for tomorrow. :)

I hope you are content with your preparation. Because that feeling is what's the
most important. Even if you're not, tell your heart that you are. Ah, yes, aal iz well. :)
Believe me, it helps.

Now this is yet another simple exam. You can't change anything
at this point even if you treat it like something special. Its just another Test Series Examination!
(No I seriously don't mean the all-devastating AITS! Just another 6 hour exam.)

You can do it. But still, keep overconfidence at bay. Yes, you can do it.
Just be open. Open your eyes, mind, and conscience. Open to all the good things around you. :)

All the best once again.
(Nah.. I don't say best of luck.. Why luck? Believe in yourself.)

Cheers!
Anuj, Shivanker and Sambhav

Some Thermochemistry

Find ΔS and ΔG for the conversion of 10.0g of supercooled water at -10° C and 1 atm to ice at -10° C and 1 atm. Average c_p values for ice and supercooled water in the range 0° C and -10° C are 0.50 and 1.01 cal/(°C g) respectively. Given that the latent heat of fusion of ice is 79.7 cal/g at the normal boiling point.

GCD-LCM problems are always fun. The solution is simple, yet it takes a long time to get there.

Here is one for you. Do not Google it because you'll obviously find the solution there.

How many unordered pairs of numbers (a,b) are there such that their GCD is 100 and their LCM is 137062800?

Noobs may try this also:
How many unordered pairs of numbers (a,b) are there such that their LCM is 137062800?

Quiz:

Here are some moderately difficult problems for your revision:

1)
Consider dD(t)/dt=k1*L(t)-k2*D(t). Also, L(t)=Lo*e^(-k1*t). Find an expression for the critical time Tc: the time when D(t) is maximum. Take D(0)=Do. Note that k1,k2, Lo and Do are constants and k2>k1.
--3 marks
What is this time (Tc) when k1*Lo is less than Do*(k2-k1)?
--3 marks

2)What is the magnetic moment of a disc sector (angle=pi/3) of radius R and charge Q (uniformly spread) rotated with angular velocity w about its natural axis??
--2 marks

3)A point charge is kept at the center of a cylinder of length L and radius R. What is the ratio of electric flux thru the curved surface to the flux thru the end caps?
--2 marks

4)The volume charge density varies with the distance from origin 'r' as rho=a*r+b*r*r.
What is the variation of electric field with r?
--2 marks

5)A 3:1 (by moles) mixture of oxygen and nitrogen effuses through a tiny orifice. What is the molecular mass of the mixture effusing out? (Do NOT consult your class notes!).
--1 mark

Note: Part 2 of Q1 is my favorite. Please try it! It looks (and is) difficult but it is solvable by you!

Note: You're through with JEE if you can solve 4 problems!

Expectations

 

A random variable is a variable whose value results from a measurement on some type of random process. Expectation E(X) of a random variable X is given by :



Suppose that n balls are tossed into n bins. Each toss is independent and each ball is equally likely to end up in any bin.
Using (or maybe not) the fact that E(X+Y) = E(X) + E(Y) even if X&Y are dependent variables, give the expected value of:

• Number of balls in a bin?
• Number of tosses till a given bin contains a ball?
• Number of tosses till every bin has a ball?
• Number of tosses till a given bin contains two balls?
• Number of tosses till at least a bin contains two balls?
• Number of empty bins?
• Number of bins with exactly one ball?

P.S.: Take n to be very very large.

PlayLists

I have 10 songs with me. On my way home, I want to listen to 30 songs (some songs will be repeated). However, I don't want to listen the same song again too soon. Precisely, there should be at-least an interval of 5 songs before I hear the same song again.

Example: Say, I have songs A, B, C, D, E,..
Then, the playlist A,B,C,D,E,F,A,B,C,D,E,F...is valid but the playlist A,B,C,A,... is not valid because there are only 2 songs between 2 occurrences of song A.

How many playlists can I have?

Sneak Peek

I was going to throw in these problems in the next One Round Match, but it turns out 6th semester at IIT is pretty heavy and I don't get enough time to set up the contest website. So, here is a simple question for you. Choose ONE word/phrase which best explains the phenomenon:

Q1)Washing machine detergents are different from hand-wash detergents.
Q2)Life is all about replication (and duplication). So, life is carbon based and not silicon based.
Q3)Life is also about making and breaking bonds with oxygen. So, life is carbon based and not silicon based.

Note: 'Life' here refers to biological life (cells, DNA etc). And finally we have a chemistry question on the blog!

Match 1 results

Name                                 Section1      Section2      Section3      Score
Simarjit                             24.5          5             50.85         250
lalitkundu1995                       24.5          1500          47.122        250
deboshish                            24.5          6             18.84         250
rishabh                              24.5          900000        24.60504      250
Pulkit                               24.500        5.000         143.325       250
himanshu                             24.5          0             0.206         250
shivam                               24.500        750.000       0.457         250
luv.this.world@gmail.com             24.500        5.000         143.325       250
rohin                                24.500        31363636.363  18.840        250
prateekchaudhry                      24.500        450000.000    18.840        250
rockon                               28.000        0             0             0
rahuljain2410                        0             0             0             0
addas1395                            29.500        0             0             0
happy                                14.500        0             0.206         0
abhishek                             14.500        0             0.206         0
hbk                                  0             0             0             0
abcd                                 0             0             0             0
lakshaybansal                        21.500        450000.000    26.92714      0
sandeep                              0             0             0             0
rajatjain                            0             0             0             0
admin                                12            3123          312           0
Mayank                               0             0             0             0
akhilkumar                           29.952        4500.000      47.100        0
sumantra                             0             0             0             0
vipulverma                           0             0             0             0
shubhamsinghspecial                  0             0             0             0
vinayak                              0             0             0             0
vipulverma10                         0             0             0             0
MayankJain                           0             0             0             0
NEXUS                                0             0             0             0