The bus is going towards right of the screen as the door of the bus is not facing us. (assuming It is a right hand drive.)

Double post

[x] is non differentiable only at Integer points. At all other points it's derivative is zero.

Its graph is like steps:

Note: I have assumed 22/7 to be pi

3) A Lieutenant Colonel leads a Battalion not a Captain.

8)

Only once. After that you will be subtracting 5 from 20.

I think a forum expert should answer this 

A comparatively more difficult problem, but easy on the whole.

Prove that a whole number is divisible by 11 if difference of sum of alternate digits is a multiple of 11.

You can try proving the rest of the divisibility tests. They r very easy to do.

Energy is lost as heat even in ideal conditions as electrons collide with the negative plate of capacitor and +ve plate of battery and lose their kinetic energy which is radiated as heat.

First of all you must know that battery doesn't provide charge.

It accepts charge at lower potential and places it at a higher potential.

Lets take a 10 volt battery connected across a 10uf capacitor. Charge on capacitor will be 100uc. energy provided by battery is 1000uJ energy stored in the capacitor is 500uj. Now we connect the charged capacitor in the opposite way to the battery. Now final potential Energyu is still 500uJ (change in potential energy of capacitor is zero), but energy supplied by battery is 1000uj