Assuming other parameters unchanged if the modulating frequency

Assuming other parameters unchanged if the modulating frequency is halved in a modulating systems, the modulation index is doubled. The modulation system is—

Since modulation index is given by

β =	K_fA_m
	ω_m

given,

ω'_m =	ω_m
	2

Now,

β' =	K_fA_m	= 2β
	ω_m/2

Hence alternative (B) is the correct choice.
Since here,

β ∝	1
	ω_m