Hi Rakesh!
About the Dirac delta pulse. Yes, the value at t=0 is inifinity or not defined. But the integral is! That is the Dirac delta pulse, see also
http://en.wikipedia.org/wiki/Dirac_delta_functionThis is more or less exactly what happens when you using r=>0. If you try to solve the electronic problem with two caps you will not be able to get expressions how the current and voltage looks like during the recharging, whithout putting in a resistor. (If you are a skilled math pro, I'm not, you maybe can use the Dirac delta function) This is like saying that the problem without a resistor is non-physical and the basic relationship of a capacitor, i=C*dv/dt, can not be solved for this problem.