The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance 49µH and a capacitance of 2.5nF. It is modulated by an audio signal of 12kHz. The frequency range occupied by the side bands is:

ω = 1/√LC = 1/√(49 × 10⁻⁶ × 2.5 × 10⁻⁹) = 1/(7 × 5 × 10⁻⁷) = 1/(35 × 10⁻⁷) = 10⁷/35 = ω = 285714.28 rad/s
ω = 2πf
285714.28 = 2 × 22/7 × f
285714.28 = 44/7 × f
285714.28 × 7/44 = f
f = 45454.54 Hz ≈ 454.54 kHz
For frequency range 454.54 ± 12 kHz
442 kHz to 466.54 kHz