If the maximum frequency of the baseband signal in an AM system is fm , how much bandwidth is needed overall to send the modulated signal?

Correct option is B

​$$\text{In a conventional \textbf{Amplitude Modulation (AM)} system:} \\[6pt]\bullet \ \text{Let the maximum frequency of the baseband (modulating) signal be } f_m . \\[4pt]\bullet \ \text{AM produces two sidebands:} \\[2pt]\quad \bullet \ \text{Upper sideband (USB): } f_c + f_m \\[2pt]\quad \bullet \ \text{Lower sideband (LSB): } f_c - f_m \\[8pt]\text{The total transmission bandwidth is the difference between the highest and lowest frequency components:} \\[6pt]\text{Bandwidth} = (f_c + f_m) - (f_c - f_m) = 2f_m \\[8pt]\text{This bandwidth requirement is independent of the modulation index } \beta .$$​​