Modulation of real-valued signal I have one doubt according to modulation of a real signal.

there are so many examples where the real signal was modulated with frequency bigger then 0.

Why the signal could not be putted in f=0?

is there connection with a sending power?
( Antenna send bandpass signal $\rightarrow$ signal is matched $\rightarrow$antenna send low P $\rightarrow$power will be reflected, Tx get P again)
It all depends on the transmission medium (the so-called communication channel). Some media do not tolerate components at DC (i.e., zero frequency) or near DC. A typical channel where a carrier frequency greater than zero is required is the radio channel.