GATE Electronics and Communications (EC) 2017 Shift 2 Solved Paper

A modulating signal given by x(t) = 5 sin (4π 10³t - 10π cos 2π 10³t) V is fed to a phase modulator with phase deviation constant k_p = 5 rad/V. If the carrier frequency is 20 kHz, the instantaneous frequency (in kHz) at t = 0.5 ms is ___________.