A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is

Assuming zero initial condition, the response y (t) of the system given below to a unit step input u(t) is

Let g(t) = $${e^{ - \pi {t^2}}}$$, and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t), then the Fourier transform of the output is

For a periodic signal v(t) = 30 sin 100t + 10cos 300t + 6sin $${\rm{(500t + }}\,\pi /4)$$, the fundamental frequency in rad/s is