Is it true that fix cost remains same when output increases?

The real answer is it depends, ultimately all costs are variable even those costs that would initially appear fixed. Take for example business rates, these are set for the year and will remain the same regardless of the change in volume of the output, however should the output need to rise above the capacity of the existing business premises additional premises or even new premises would need to be acquired and with it a new level of fixed cost. This is sometimes described as step fixed cost, i.e. the cost remains at the same level until a step change is required and then the costs are again fixed at this new level until another step change is required