I want to use a 12v rechargeable battery for powering up arduino uno interfacing with GSM module 900a and ultrasonic sensor. So i want to make sure that the board and circuit should not be burn or short circuited. So how much resistor, capacitor could I use ??? And Can u please suggest me the best way for this circuit ???
Get yourself a buck converter.
I would replace the 12V battery with a single LiPo one. No regulator or so needed.
Get a 3.3V version of the HC-SR04, and make sure your Arduino runs at no more than 12 MHz.
In short, you do not use a UNO for this sort of thing (they are really primarily for experimental or demonstration use). They are really suitable only for mains powered 5 V arrangements.
As has been pointed out, the UNO does not operate at 12 V, so to provide the necessary 5 V, you would require a "buck" converter, and presuming the GSM module requires 3.3 to 3.7 V, a second regulator to power that.
Using 3.3/ 3.7 V components, such as a 3.3 V Pro Mini would make far more sense.