At t = 0 , the plates of a capacitor of capacitance 10 ext ,...

The charge on a discharging capacitor at time $t$ is given by the equation:

$q(t) = q_0 e^{-t/\tau}$

where the time constant is $\tau = RC$.

Given values are:
Initial charge, $q_0 = 60 \mu\text{C}$
Resistance, $R = 10 \Omega$
Capacitance, $C = 10 \mu\text{F}$
Time, $t = 120 \mu\text{s}$

Calculating the time constant $\tau$:

$\tau = 10 \Omega \times 10 \mu\text{F} = 100 \mu\text{s}$

Substituting the values into the discharging equation:

$q(120 \mu\text{s}) = 60 e^{-120/100}$

$q = 60 e^{-1.2}$

Using the approximate value $e^{-1.2} \approx 0.301$:

$q \approx 60 \times 0.301 \approx 18.06 \mu\text{C}$

Rounding to the nearest integer, the charge on the capacitor is $18 \mu\text{C}$.