Refractive Index!!!(A Physics Related Question In Mathematics)

Let there be 2011 crystal bars of different materials with a same thickness of 10 units and of same size. The bars are placed from bottom to top one after another having refractive indices 1, 1.001, 1.002, 1.003,.....(bottom to top) respectively. Now what is apparent depth when looking from top to bottom?

[Note: A refractive index of a crystal material(b) or a medium(b) with respect to 1st material(a) or 1st medium(a) is defined by aμb=sin(i)/sin(r) where i=incident angle of 1st medium and r=refractive angle of 2nd medium]

How many terms are there?

If it is a Determinant of 2010th order of which constituents (elements) are distinct, then how many polynomials (terms) are there when it is expanded?

Which Locker???

Let there be 2500 lockers. You have to unlock lockers. You should proceed in such a way that you have unlocked the 1st one, then the 2nd one, then the 3rd one and so on. When you finish a trial, you will do in the same way. Thus you'll have a locker that has never been unlocked.

What is the place of that locker in 2500 lockers???

A Paradox

We all know about complex numbers dealing with imaginary numbers. If we try to solve
then we get where x is positive.

is symbolized by , that is, .

Now try to solve the paradox stated below, i.e. to find out the inconsistency of the paradox.

We know but here is . How is it possible???

Is the switch On or Off ?

Let there be n numbered switches. Suppose scientist Dalton operated 1st switch for 1 time, 2nd for 2 times, 3rd for 3 times.........................thus he operated n th switch for n times. If a switch gets Off from On, then the next switch is operated automatically.

If all the switches were Off at first,
Then how many switches were On at last?

What is the 2010th term?

Today's math problem is only for fun and intellect. Here is the problem stated below.

If a number goes forward by natural numbers such like 123456789101112131415.............................9999, then what is the 2010th term(digit) of this number?

Please find the digit with proof.

(The answer will be published soon).

Try First

Hello, Everyone!

Welcome to my own math-world.

Please try to prove that 1=2 as many as you can.