Question

A 120 resistor must carry a maximum current of 25 ma. its rating should be at least

Answer 1

I will assume that this is not in a very hot ambient temperature nor is it sandwiched between other hot components.

In that case, good engineering practice is to use a resistor rated for at least 2x the required power dissipation.

One formula for power is I squared times R.
P = 0.025A^2 x 120 ohms = 0.075W or 75mW

So a resistor rated at least double that. 150mW, or in this case the next highest standard size is 250mW aka 1/4 W.

Resistors are rated based on ambient temperature of around 20 to 25C, no nearby hot components, and no components right next to it, with nothing blocking natural air flow. Any other conditions and they must be derated. Derating means to use them as if they were rated for a lower power dissipation.

Since resistors usually end up in the middle of a circuit board surrounded by other components which also produce some heat, and inside a box with poor or no airflow, and temperatures may rise well above 25C, this is why we use 2x as a rule of thumb. An individual situation may require the use of a much larger resistor.

I used to live in Phoenix, Arizona, USA. I designed alarm systems for apartments and cars, and car stereo amplifiers that had to sit in -very- hot environments. So I had to be very aggressive about derating parts.