The ac voltage v(t) =10sin(100pt) is applied separately across (i) and (ii) below:
(i) a 1H inductor.
(ii) a 1mF capacitor

What are the frequency and rms values of the currents that flow in each instance?

 

If you have a capacitor connected with the inductor, the frequency can be determined by:

1 / (2 * pi * sqr(L * C))

sqr = square root of.

L = inductor value in Henries
C = capacitor value in farads
result = frequency in Hertz
pi = the Pi button on your calculator.

this might not help much, but it determines a frequency based on a capacitor and inductor connected to each other.

 

The ac voltage v(t) =10sin(100pt) is applied separately across (i) and (ii) below:
(i) a 1H inductor.
(ii) a 1mF capacitor

What are the frequency and rms values of the currents that flow in each instance?

If I write v(t) =10sin(100pt) is equivalent to v(t) =Asin(2πft), can you draw an equivalence for the frequency? (I'm not sure what "p" is from your equation for the voltage).

As for current you need to consider the current equations for:

An Inductor: v(t) = L(di(t)/dt)

A Capacitor: i(t) = C(dV/dt)

A bit of differentiation and the fact that the RMS current can be calculated by: I(rms) = I(peak)/√2 and you are there.

Dave