The Maths and Science Thread - Collection of Problems and Facts

[Varun]

Hey Friends I have started this thread to collect cool and interesting Maths and Science questions.
Post any science and Maths questions and facts so that we have a great collection.
Also, you can post your queries here so that our well reputed members solve them.

Limit - Anything that makes sense.
Note: Please don't post silly text book stuff here.Put questions that require reasoning and thinking.

Science

1.) TumTum's questions on free fall - Questions
2.) Blake's confusion about metal extraction - Question - Answer
3.) My curiousity for a capacitor - Question - Answer - Answer2
4.) Newton Law Interconnection - Question - Simple Answer - Complex Answer
5.) Amino Acid .. or base ? - Question - Answer
6.) Reflection or Refraction, Uggghhhh!!! - Question - Answer
7.) The sound of my echo has speed? - Question - Answer1 - Answer2
8.) Car rolls off a cliff, you can surely get a question out of that - Question(s) - Solution1 - Solution2
9.) Dig through the earth!! - Question - Answer
10.) The speed of light, another hypothetical argument - Question - Answer
11.) The blood group question - Question - Answer1 - Answer2
12.) Change in blood group in a child - Question - Answer


Maths

1.) 1000 students and 1000 lockers - Question - Solution
2.) A surprise from Dutchad - Question - Solution
3.) Three Childrens! - Question - Solution
4.) Cancel the Minus - Question - Solution
5.) Bill confusion - Question - Answer
6.) Derivation - Question - Answer
7.) Derivation of a derivation - Question - Answer
8.) Hell of a question - Question
9.) How long is the cube? - Question - Answer

Logical Reasoning

1.) North, East and South - The same place? - Question - Solution
2.) Sqeezies - Do you want any ? - Question - Answer - Explanation
3.) Akshay's plate of questions - Question(s) - Answer1 - Answer2 - Answer3

Facts

1.) Did you know that if you chewed constantly for an hour you'd burn a whooping 6 calories?
2.) Did you know that by remembering just 3 courses - Bsc MA PhD, you can learn the names of the major coastal cities of Australia clockwise.
It expands to Brisbane, Sydney, Canberra, Melbourne, Adelaide, Perth, Hobart and Darwin.

 

[mattfb]

This thread = my two most hated subjects. When I saw "The Maths and Science thread", I thought it would be all about complaining about there suckiness and ripping on them. Obviously not.

I'll be leaving now...

 

[Varun]

You are free to follow what you like.

Some people here are diehard fans of Science.
You can also discuss LOGICAL REASONING questions here.

 

[Pranav]

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

Is the answer 400?

 

[Varun]

Is the answer 400?

Nope. It is 31. How that I will post here later on.

 

[deathrevenge9]

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

My question:
At a download speed of 50KB/s,how much time wil it take to download a file of 4.45GB

 

[Sureshot]

Assuming one maintains that speed, 24 and 3/4 hours.

Useless Science fact.

Did you know that if you chewed constantly for an hour you'd burn a whooping 6 calories?

 

[drainpipe32]

*shudders* Ew, Science and Maths in one thread!

 

[TumTum]

"It's a warm summer evening in ancient greece"

1. What is the acceleration of a free falling object near the surface of the earth?

2. If the free falling object (of 64kg) is falling at a constant speed, what is the force applied by the wind resistance?

3. If the wind resistance coefficient is 4kg/m, what speed is the object falling at?

4. Create a differential equation of motion of the object as it starts falling from rest.

5. Assuming 95% is close enough to 100%, how long will it take for the object to achieve full speed?

Answer those questions correctly, and I will call you a legend in my sig

 

[Pranav]

1. What is the acceleration of a free falling object near the surface of the earth?

-9.8 m/s2

I can answer the rest as well because that's what we study in Physics (grade 11th and 12th) here in India, but I can't be bothered.

 

[Kshitiz_Indian]

Yeah all those are pretty darn easy questions. If only something like that came in the IIT's...

 

[Varun]

Nope. It is 31. How that I will post here later on.

The only lockers that remain open are perfect squares (1, 4, 9, 16, etc) because they are the only numbers divisible by an odd number of whole numbers; every factor other than the number's square root is paired up with another. Thus, these lockers will be "changed" an odd number of times, which means they will be left open. All the other numbers are divisible by an even number of factors and will consequently end up closed.

So the number of open lockers is the number of perfect squares less than or equal to one thousand. These numbers are one squared, two squared, three squared, four squared, and so on, up to thirty one squared. (Thirty two squared is greater than one thousand, and therefore out of range.) So the answer is thirty one.

P.S.- I have not just copied that but first understood it and then copied.

 

[TumTum]

Answer 4 and 5 then, bet you haven't learn that in your Physics classes

 

[Dutch]

Okay two maths problems here:

1. Half of twelve is seven: how can I be right?

2. 62 - 63 = 1

Rearrange one digit one place to make this equation correct. You may not change the mathematical sign or move it. You may not swap two numbers.


Good luck, if you can be bothered that is!

 

[Varun]

For indexing purpose.....


A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?